From b515ce223cf68757ebaf1128d46cb849e75037a5 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Dennis=20M=C3=BCller?= <d.mueller@jacobs-university.de>
Date: Fri, 24 Mar 2017 14:13:47 +0100
Subject: [PATCH] structurized
---
.../MitM/Models/$Base.omdoc | 321 +-----------------
.../MitM/Models/$Physical$Constants.omdoc | 27 +-
.../VanRoosbroeck/$Van$Roosbroeck.omdoc | 2 +-
...inuity$Boundary$Conditions$Electrons.omdoc | 22 +-
...Continuity$Boundary$Conditions$Holes.omdoc | 22 +-
.../$Continuity$Equation$Electrons.omdoc | 103 +++---
.../$Continuity$Equation$Holes.omdoc | 94 +++--
.../continuity/$Current$Electrons.omdoc | 132 +++----
.../Models/continuity/$Current$Holes.omdoc | 132 +++----
.../MitM/Models/continuity/$Mobilities.omdoc | 30 +-
.../densities/$Bandstructure$Parameters.omdoc | 39 ++-
.../densities/$Electrostatic$Potential.omdoc | 13 +-
.../$Fermi$Potential$Electrons.omdoc | 23 +-
.../densities/$Fermi$Potential$Holes.omdoc | 23 +-
.../MitM/Models/device/$Device$Geometry.omdoc | 18 +-
.../device/$Device$Operation$State.omdoc | 39 +--
.../MitM/Models/device/$Device.omdoc | 2 +-
.../MitM/Models/device/$Doping$Profile.omdoc | 8 +-
.../$Poisson$Boundary$Conditions.omdoc | 33 +-
.../Models/poisson/$Poisson$Equation.omdoc | 38 +--
.../Models/poisson/$Poisson$Parameters.omdoc | 43 ++-
.../poisson/$Thermodynamic$Equilibrium.omdoc | 28 +-
.../Models/recombination/$Recombination.omdoc | 140 ++++++--
.../$Spontaneous$Recombination.omdoc | 50 ++-
.../http..mathhub.info/MitM/Models/$Base.rel | 44 +--
.../MitM/Models/$Physical$Constants.rel | 11 +-
.../$Continuity$Equation$Electrons.rel | 17 +-
.../continuity/$Continuity$Equation$Holes.rel | 12 +
.../Models/continuity/$Current$Electrons.rel | 16 +-
.../MitM/Models/continuity/$Current$Holes.rel | 15 +-
.../densities/$Bandstructure$Parameters.rel | 1 +
.../densities/$Fermi$Potential$Electrons.rel | 1 -
.../densities/$Fermi$Potential$Holes.rel | 1 -
.../Models/device/$Device$Operation$State.rel | 6 +-
.../MitM/Models/device/$Doping$Profile.rel | 1 +
.../poisson/$Poisson$Boundary$Conditions.rel | 10 +
.../MitM/Models/poisson/$Poisson$Equation.rel | 10 +
.../Models/poisson/$Poisson$Parameters.rel | 8 +-
.../poisson/$Thermodynamic$Equilibrium.rel | 10 +
.../Models/recombination/$Recombination.rel | 13 +-
.../$Spontaneous$Recombination.rel | 11 +-
source/mmt/Quantities.mmt | 58 +++-
source/mmt/band.mmt | 24 ++
source/mmt/continuity.mmt | 66 +---
source/mmt/densities.mmt | 83 +----
source/mmt/poisson.mmt | 10 +-
source/mmt/recombination.mmt | 24 +-
source/mmt/species.mmt | 21 ++
48 files changed, 857 insertions(+), 998 deletions(-)
create mode 100644 source/mmt/band.mmt
create mode 100644 source/mmt/species.mmt
diff --git a/content/http..mathhub.info/MitM/Models/$Base.omdoc b/content/http..mathhub.info/MitM/Models/$Base.omdoc
index 61a797d..14826b4 100644
--- a/content/http..mathhub.info/MitM/Models/$Base.omdoc
+++ b/content/http..mathhub.info/MitM/Models/$Base.omdoc
@@ -1,320 +1 @@
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- <om:OMA><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/constants.mmt#1014.28.43:1033.28.62"/></metadata>
- <om:OMS base="http://gl.mathhub.info/MMT/LFX/Subtyping" module="PredSubSymbols" name="predsubtp"></om:OMS>
- <om:OMS base="http://mathhub.info/MitM/Models" module="Base" name="Real_vec_space2"></om:OMS><om:OMBIND><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/constants.mmt#1021.28.50:1031.28.60"/></metadata>
- <om:OMS base="http://cds.omdoc.org/urtheories" module="LambdaPi" name="lambda"></om:OMS>
- <om:OMBVAR><om:OMV name="z"><metadata><tag property="http://cds.omdoc.org/mmt?mmt?inferred-type"/><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/constants.mmt#1023.28.52:1023.28.52"/></metadata><type><om:OMS base="http://mathhub.info/MitM/Models" module="Base" name="Real_vec_space2"></om:OMS></type></om:OMV></om:OMBVAR>
- <om:OMA><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/constants.mmt#1026.28.55:1030.28.59"/></metadata>
- <om:OMS base="http://cds.omdoc.org/urtheories" module="LambdaPi" name="apply"></om:OMS>
- <om:OMS base="http://mathhub.info/MitM/Foundation" module="Logic" name="ded"></om:OMS><om:OMA><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/constants.mmt#1028.28.57:1030.28.59"/></metadata>
- <om:OMS base="http://cds.omdoc.org/urtheories" module="LambdaPi" name="apply"></om:OMS>
- <om:OMV name="P"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/constants.mmt#1028.28.57:1028.28.57"/></metadata></om:OMV><om:OMV name="z"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/constants.mmt#1030.28.59:1030.28.59"/></metadata></om:OMV>
- </om:OMA>
- </om:OMA>
- </om:OMBIND>
- </om:OMA>
- </om:OMBIND></om:OMOBJ></definition>
- <notations><notation dimension="1" precedence="0" fixity="mixfix" arguments="pred2 1"> <scope languages="" priority="0"/> </notation></notations>
- </constant><constant name="pred_as_sub3">
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- <type><om:OMOBJ xmlns:om="http://www.openmath.org/OpenMath"><om:OMA><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/constants.mmt#1065.29.16:1082.29.33"/></metadata>
- <om:OMS base="http://cds.omdoc.org/urtheories" module="LambdaPi" name="arrow"></om:OMS>
- <om:OMA>
- <om:OMS base="http://cds.omdoc.org/urtheories" module="LambdaPi" name="arrow"></om:OMS>
- <om:OMS base="http://mathhub.info/MitM/Models" module="Base" name="Real_vec_space3"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/constants.mmt#1066.29.17:1067.29.18"/></metadata></om:OMS><om:OMS base="http://mathhub.info/MitM/Foundation" module="Logic" name="bool"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/constants.mmt#1071.29.22:1074.29.25"/></metadata></om:OMS>
- </om:OMA><om:OMS base="http://cds.omdoc.org/urtheories" module="Typed" name="type"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/constants.mmt#1079.29.30:1082.29.33"/></metadata></om:OMS>
- </om:OMA></om:OMOBJ></type>
- <definition><om:OMOBJ xmlns:om="http://www.openmath.org/OpenMath"><om:OMBIND><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/constants.mmt#1088.29.39:1111.29.62"/></metadata>
- <om:OMS base="http://cds.omdoc.org/urtheories" module="LambdaPi" name="lambda"></om:OMS>
- <om:OMBVAR><om:OMV name="P"><metadata><tag property="http://cds.omdoc.org/mmt?mmt?inferred-type"/><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/constants.mmt#1089.29.40:1089.29.40"/></metadata><type><om:OMA>
- <om:OMS base="http://cds.omdoc.org/urtheories" module="LambdaPi" name="arrow"></om:OMS>
- <om:OMS base="http://mathhub.info/MitM/Models" module="Base" name="Real_vec_space3"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/constants.mmt#1066.29.17:1067.29.18"/></metadata></om:OMS><om:OMS base="http://mathhub.info/MitM/Foundation" module="Logic" name="bool"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/constants.mmt#1071.29.22:1074.29.25"/></metadata></om:OMS>
- </om:OMA></type></om:OMV></om:OMBVAR>
- <om:OMA><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/constants.mmt#1092.29.43:1111.29.62"/></metadata>
- <om:OMS base="http://gl.mathhub.info/MMT/LFX/Subtyping" module="PredSubSymbols" name="predsubtp"></om:OMS>
- <om:OMS base="http://mathhub.info/MitM/Models" module="Base" name="Real_vec_space3"></om:OMS><om:OMBIND><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/constants.mmt#1099.29.50:1109.29.60"/></metadata>
- <om:OMS base="http://cds.omdoc.org/urtheories" module="LambdaPi" name="lambda"></om:OMS>
- <om:OMBVAR><om:OMV name="z"><metadata><tag property="http://cds.omdoc.org/mmt?mmt?inferred-type"/><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/constants.mmt#1101.29.52:1101.29.52"/></metadata><type><om:OMS base="http://mathhub.info/MitM/Models" module="Base" name="Real_vec_space3"></om:OMS></type></om:OMV></om:OMBVAR>
- <om:OMA><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/constants.mmt#1104.29.55:1108.29.59"/></metadata>
- <om:OMS base="http://cds.omdoc.org/urtheories" module="LambdaPi" name="apply"></om:OMS>
- <om:OMS base="http://mathhub.info/MitM/Foundation" module="Logic" name="ded"></om:OMS><om:OMA><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/constants.mmt#1106.29.57:1108.29.59"/></metadata>
- <om:OMS base="http://cds.omdoc.org/urtheories" module="LambdaPi" name="apply"></om:OMS>
- <om:OMV name="P"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/constants.mmt#1106.29.57:1106.29.57"/></metadata></om:OMV><om:OMV name="z"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/constants.mmt#1108.29.59:1108.29.59"/></metadata></om:OMV>
- </om:OMA>
- </om:OMA>
- </om:OMBIND>
- </om:OMA>
- </om:OMBIND></om:OMOBJ></definition>
- <notations><notation dimension="1" precedence="0" fixity="mixfix" arguments="pred3 1"> <scope languages="" priority="0"/> </notation></notations>
- </constant><constant name="lift_type_one_to_three">
- <metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/constants.mmt#1130.31.1:1252.32.70"/></metadata>
- <type><om:OMOBJ xmlns:om="http://www.openmath.org/OpenMath"><om:OMA><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/constants.mmt#1155.31.26:1178.31.49"/></metadata>
- <om:OMS base="http://cds.omdoc.org/urtheories" module="LambdaPi" name="arrow"></om:OMS>
- <om:OMA>
- <om:OMS base="http://cds.omdoc.org/urtheories" module="LambdaPi" name="arrow"></om:OMS>
- <om:OMS base="http://mathhub.info/MitM/numberfields" module="realnumbers" name="Realnumbers"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/constants.mmt#1156.31.27:1156.31.27"/></metadata></om:OMS><om:OMS base="http://mathhub.info/MitM/Foundation" module="Logic" name="bool"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/constants.mmt#1160.31.31:1163.31.34"/></metadata></om:OMS>
- </om:OMA><om:OMA><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/constants.mmt#1168.31.39:1178.31.49"/></metadata>
- <om:OMS base="http://cds.omdoc.org/urtheories" module="LambdaPi" name="arrow"></om:OMS>
- <om:OMS base="http://mathhub.info/MitM/Models" module="Base" name="Real_vec_space3"></om:OMS><om:OMS base="http://mathhub.info/MitM/Foundation" module="Logic" name="bool"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/constants.mmt#1174.31.45:1177.31.48"/></metadata></om:OMS>
- </om:OMA>
- </om:OMA></om:OMOBJ></type>
- <definition><om:OMOBJ xmlns:om="http://www.openmath.org/OpenMath"><om:OMBIND><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/constants.mmt#1186.32.4:1238.32.56"/></metadata>
- <om:OMS base="http://cds.omdoc.org/urtheories" module="LambdaPi" name="lambda"></om:OMS>
- <om:OMBVAR><om:OMV name="P"><metadata><tag property="http://cds.omdoc.org/mmt?mmt?inferred-type"/><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/constants.mmt#1187.32.5:1187.32.5"/></metadata><type><om:OMA>
- <om:OMS base="http://cds.omdoc.org/urtheories" module="LambdaPi" name="arrow"></om:OMS>
- <om:OMS base="http://mathhub.info/MitM/numberfields" module="realnumbers" name="Realnumbers"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/constants.mmt#1156.31.27:1156.31.27"/></metadata></om:OMS><om:OMS base="http://mathhub.info/MitM/Foundation" module="Logic" name="bool"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/constants.mmt#1160.31.31:1163.31.34"/></metadata></om:OMS>
- </om:OMA></type></om:OMV></om:OMBVAR>
- <om:OMBIND><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/constants.mmt#1190.32.8:1238.32.56"/></metadata>
- <om:OMS base="http://cds.omdoc.org/urtheories" module="LambdaPi" name="lambda"></om:OMS>
- <om:OMBVAR><om:OMV name="v"><metadata><tag property="http://cds.omdoc.org/mmt?mmt?inferred-type"/><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/constants.mmt#1191.32.9:1191.32.9"/></metadata><type><om:OMS base="http://mathhub.info/MitM/Models" module="Base" name="Real_vec_space3"></om:OMS></type></om:OMV></om:OMBVAR>
- <om:OMA><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/constants.mmt#1194.32.12:1238.32.56"/></metadata>
- <om:OMS base="http://cds.omdoc.org/urtheories" module="LambdaPi" name="apply"></om:OMS>
- <om:OMS base="http://mathhub.info/MitM/Foundation" module="Logic" name="and"></om:OMS><om:OMA><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/constants.mmt#1194.32.12:1222.32.40"/></metadata>
- <om:OMS base="http://cds.omdoc.org/urtheories" module="LambdaPi" name="apply"></om:OMS>
- <om:OMS base="http://mathhub.info/MitM/Foundation" module="Logic" name="and"></om:OMS><om:OMA><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/constants.mmt#1194.32.12:1206.32.24"/></metadata>
- <om:OMS base="http://cds.omdoc.org/urtheories" module="LambdaPi" name="apply"></om:OMS>
- <om:OMV name="P"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/constants.mmt#1195.32.13:1195.32.13"/></metadata></om:OMV><om:OMA><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/constants.mmt#1197.32.15:1205.32.23"/></metadata>
- <om:OMS base="http://cds.omdoc.org/urtheories" module="LambdaPi" name="apply"></om:OMS>
- <om:OMS base="http://mathhub.info/MitM/Models" module="Base" name="comp1"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/constants.mmt#1198.32.16:1202.32.20"/></metadata></om:OMS><om:OMV name="v"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/constants.mmt#1204.32.22:1204.32.22"/></metadata></om:OMV>
- </om:OMA>
- </om:OMA><om:OMA><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/constants.mmt#1210.32.28:1222.32.40"/></metadata>
- <om:OMS base="http://cds.omdoc.org/urtheories" module="LambdaPi" name="apply"></om:OMS>
- <om:OMS base="http://mathhub.info/MitM/Foundation" module="Logic" name="eq"></om:OMS><om:OMS base="http://mathhub.info/MitM/numberfields" module="realnumbers" name="Realnumbers"></om:OMS><om:OMA><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/constants.mmt#1211.32.29:1217.32.35"/></metadata>
- <om:OMS base="http://cds.omdoc.org/urtheories" module="LambdaPi" name="apply"></om:OMS>
- <om:OMS base="http://mathhub.info/MitM/Models" module="Base" name="comp2"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/constants.mmt#1211.32.29:1215.32.33"/></metadata></om:OMS><om:OMV name="v"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/constants.mmt#1217.32.35:1217.32.35"/></metadata></om:OMV>
- </om:OMA><om:OMLIT type="http://mathhub.info/MitM/Foundation?Literals?nat_lit" value="0"/>
- </om:OMA>
- </om:OMA><om:OMA><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/constants.mmt#1226.32.44:1238.32.56"/></metadata>
- <om:OMS base="http://cds.omdoc.org/urtheories" module="LambdaPi" name="apply"></om:OMS>
- <om:OMS base="http://mathhub.info/MitM/Foundation" module="Logic" name="eq"></om:OMS><om:OMS base="http://mathhub.info/MitM/numberfields" module="realnumbers" name="Realnumbers"></om:OMS><om:OMA><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/constants.mmt#1227.32.45:1233.32.51"/></metadata>
- <om:OMS base="http://cds.omdoc.org/urtheories" module="LambdaPi" name="apply"></om:OMS>
- <om:OMS base="http://mathhub.info/MitM/Models" module="Base" name="comp3"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/constants.mmt#1227.32.45:1231.32.49"/></metadata></om:OMS><om:OMV name="v"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/constants.mmt#1233.32.51:1233.32.51"/></metadata></om:OMV>
- </om:OMA><om:OMLIT type="http://mathhub.info/MitM/Foundation?Literals?nat_lit" value="0"/>
- </om:OMA>
- </om:OMA>
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- <om:OMS base="http://cds.omdoc.org/urtheories" module="LambdaPi" name="arrow"></om:OMS>
- <om:OMA>
- <om:OMS base="http://cds.omdoc.org/urtheories" module="LambdaPi" name="arrow"></om:OMS>
- <om:OMS base="http://mathhub.info/MitM/Models" module="Base" name="Real_vec_space2"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/constants.mmt#1280.33.27:1281.33.28"/></metadata></om:OMS><om:OMS base="http://mathhub.info/MitM/Foundation" module="Logic" name="bool"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/constants.mmt#1285.33.32:1288.33.35"/></metadata></om:OMS>
- </om:OMA><om:OMA><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/constants.mmt#1293.33.40:1303.33.50"/></metadata>
- <om:OMS base="http://cds.omdoc.org/urtheories" module="LambdaPi" name="arrow"></om:OMS>
- <om:OMS base="http://mathhub.info/MitM/Models" module="Base" name="Real_vec_space3"></om:OMS><om:OMS base="http://mathhub.info/MitM/Foundation" module="Logic" name="bool"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/constants.mmt#1299.33.46:1302.33.49"/></metadata></om:OMS>
- </om:OMA>
- </om:OMA></om:OMOBJ></type>
- <definition><om:OMOBJ xmlns:om="http://www.openmath.org/OpenMath"><om:OMBIND><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/constants.mmt#1311.34.4:1358.34.51"/></metadata>
- <om:OMS base="http://cds.omdoc.org/urtheories" module="LambdaPi" name="lambda"></om:OMS>
- <om:OMBVAR><om:OMV name="P"><metadata><tag property="http://cds.omdoc.org/mmt?mmt?inferred-type"/><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/constants.mmt#1312.34.5:1312.34.5"/></metadata><type><om:OMA>
- <om:OMS base="http://cds.omdoc.org/urtheories" module="LambdaPi" name="arrow"></om:OMS>
- <om:OMS base="http://mathhub.info/MitM/Models" module="Base" name="Real_vec_space2"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/constants.mmt#1280.33.27:1281.33.28"/></metadata></om:OMS><om:OMS base="http://mathhub.info/MitM/Foundation" module="Logic" name="bool"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/constants.mmt#1285.33.32:1288.33.35"/></metadata></om:OMS>
- </om:OMA></type></om:OMV></om:OMBVAR>
- <om:OMBIND><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/constants.mmt#1315.34.8:1358.34.51"/></metadata>
- <om:OMS base="http://cds.omdoc.org/urtheories" module="LambdaPi" name="lambda"></om:OMS>
- <om:OMBVAR><om:OMV name="v"><metadata><tag property="http://cds.omdoc.org/mmt?mmt?inferred-type"/><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/constants.mmt#1316.34.9:1316.34.9"/></metadata><type><om:OMS base="http://mathhub.info/MitM/Models" module="Base" name="Real_vec_space3"></om:OMS></type></om:OMV></om:OMBVAR>
- <om:OMA><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/constants.mmt#1319.34.12:1358.34.51"/></metadata>
- <om:OMS base="http://cds.omdoc.org/urtheories" module="LambdaPi" name="apply"></om:OMS>
- <om:OMS base="http://mathhub.info/MitM/Foundation" module="Logic" name="and"></om:OMS><om:OMA><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/constants.mmt#1319.34.12:1342.34.35"/></metadata>
- <om:OMS base="http://cds.omdoc.org/urtheories" module="LambdaPi" name="apply"></om:OMS>
- <om:OMV name="P"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/constants.mmt#1320.34.13:1320.34.13"/></metadata></om:OMV><om:OMA><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/constants.mmt#1322.34.15:1341.34.34"/></metadata>
- <om:OMS base="http://gl.mathhub.info/MMT/LFX/Sigma" module="Symbols" name="Tuple"></om:OMS>
- <om:OMA><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/constants.mmt#1324.34.17:1330.34.23"/></metadata>
- <om:OMS base="http://cds.omdoc.org/urtheories" module="LambdaPi" name="apply"></om:OMS>
- <om:OMS base="http://mathhub.info/MitM/Models" module="Base" name="comp1"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/constants.mmt#1324.34.17:1328.34.21"/></metadata></om:OMS><om:OMV name="v"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/constants.mmt#1330.34.23:1330.34.23"/></metadata></om:OMV>
- </om:OMA><om:OMA><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/constants.mmt#1333.34.26:1339.34.32"/></metadata>
- <om:OMS base="http://cds.omdoc.org/urtheories" module="LambdaPi" name="apply"></om:OMS>
- <om:OMS base="http://mathhub.info/MitM/Models" module="Base" name="comp2"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/constants.mmt#1333.34.26:1337.34.30"/></metadata></om:OMS><om:OMV name="v"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/constants.mmt#1339.34.32:1339.34.32"/></metadata></om:OMV>
- </om:OMA>
- </om:OMA>
- </om:OMA><om:OMA><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/constants.mmt#1346.34.39:1358.34.51"/></metadata>
- <om:OMS base="http://cds.omdoc.org/urtheories" module="LambdaPi" name="apply"></om:OMS>
- <om:OMS base="http://mathhub.info/MitM/Foundation" module="Logic" name="eq"></om:OMS><om:OMS base="http://mathhub.info/MitM/numberfields" module="realnumbers" name="Realnumbers"></om:OMS><om:OMA><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/constants.mmt#1347.34.40:1353.34.46"/></metadata>
- <om:OMS base="http://cds.omdoc.org/urtheories" module="LambdaPi" name="apply"></om:OMS>
- <om:OMS base="http://mathhub.info/MitM/Models" module="Base" name="comp3"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/constants.mmt#1347.34.40:1351.34.44"/></metadata></om:OMS><om:OMV name="v"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/constants.mmt#1353.34.46:1353.34.46"/></metadata></om:OMV>
- </om:OMA><om:OMLIT type="http://mathhub.info/MitM/Foundation?Literals?nat_lit" value="0"/>
- </om:OMA>
- </om:OMA>
- </om:OMBIND>
- </om:OMBIND></om:OMOBJ></definition>
- <notations><notation dimension="1" precedence="-1" fixity="mixfix" arguments="t2↑ 1"> <scope languages="" priority="0"/> </notation></notations>
- </constant><constant name="lift_function_one_to_three">
- <metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/constants.mmt#1385.36.1:1510.37.45"/></metadata>
- <type><om:OMOBJ xmlns:om="http://www.openmath.org/OpenMath"><om:OMBIND><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/constants.mmt#1414.36.30:1461.36.77"/></metadata>
- <om:OMS base="http://cds.omdoc.org/urtheories" module="LambdaPi" name="Pi"></om:OMS>
- <om:OMBVAR><om:OMV name="P"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/constants.mmt#1415.36.31:1415.36.31"/></metadata><type><om:OMA><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/constants.mmt#1419.36.35:1426.36.42"/></metadata>
- <om:OMS base="http://cds.omdoc.org/urtheories" module="LambdaPi" name="arrow"></om:OMS>
- <om:OMS base="http://mathhub.info/MitM/numberfields" module="realnumbers" name="Realnumbers"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/constants.mmt#1419.36.35:1419.36.35"/></metadata></om:OMS><om:OMS base="http://mathhub.info/MitM/Foundation" module="Logic" name="bool"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/constants.mmt#1423.36.39:1426.36.42"/></metadata></om:OMS>
- </om:OMA></type></om:OMV></om:OMBVAR>
- <om:OMA><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/constants.mmt#1428.36.44:1461.36.77"/></metadata>
- <om:OMS base="http://cds.omdoc.org/urtheories" module="LambdaPi" name="arrow"></om:OMS>
- <om:OMA><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/constants.mmt#1428.36.44:1439.36.55"/></metadata>
- <om:OMS base="http://cds.omdoc.org/urtheories" module="LambdaPi" name="arrow"></om:OMS>
- <om:OMA><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/constants.mmt#1429.36.45:1434.36.50"/></metadata>
- <om:OMS base="http://cds.omdoc.org/urtheories" module="LambdaPi" name="apply"></om:OMS>
- <om:OMS base="http://mathhub.info/MitM/numberfields" module="realarith" name="pred_as_sub"></om:OMS><om:OMV name="P"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/constants.mmt#1434.36.50:1434.36.50"/></metadata></om:OMV>
- </om:OMA><om:OMS base="http://mathhub.info/MitM/numberfields" module="realnumbers" name="Realnumbers"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/constants.mmt#1438.36.54:1438.36.54"/></metadata></om:OMS>
- </om:OMA><om:OMA><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/constants.mmt#1443.36.59:1461.36.77"/></metadata>
- <om:OMS base="http://cds.omdoc.org/urtheories" module="LambdaPi" name="arrow"></om:OMS>
- <om:OMA><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/constants.mmt#1444.36.60:1456.36.72"/></metadata>
- <om:OMS base="http://cds.omdoc.org/urtheories" module="LambdaPi" name="apply"></om:OMS>
- <om:OMS base="http://mathhub.info/MitM/Models" module="Base" name="pred_as_sub3"></om:OMS><om:OMA><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/constants.mmt#1450.36.66:1456.36.72"/></metadata>
- <om:OMS base="http://cds.omdoc.org/urtheories" module="LambdaPi" name="apply"></om:OMS>
- <om:OMS base="http://mathhub.info/MitM/Models" module="Base" name="lift_type_one_to_three"></om:OMS><om:OMV name="P"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/constants.mmt#1455.36.71:1455.36.71"/></metadata></om:OMV>
- </om:OMA>
- </om:OMA><om:OMS base="http://mathhub.info/MitM/numberfields" module="realnumbers" name="Realnumbers"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/constants.mmt#1460.36.76:1460.36.76"/></metadata></om:OMS>
- </om:OMA>
- </om:OMA>
- </om:OMBIND></om:OMOBJ></type>
-
- <notations><notation dimension="1" precedence="0" fixity="mixfix" arguments="f1↑ 2"> <scope languages="" priority="0"/> </notation></notations>
- </constant><constant name="lift_function_two_to_three">
- <metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/constants.mmt#1512.38.1:1650.39.56"/></metadata>
- <type><om:OMOBJ xmlns:om="http://www.openmath.org/OpenMath"><om:OMBIND><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/constants.mmt#1541.38.30:1590.38.79"/></metadata>
- <om:OMS base="http://cds.omdoc.org/urtheories" module="LambdaPi" name="Pi"></om:OMS>
- <om:OMBVAR><om:OMV name="P"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/constants.mmt#1542.38.31:1542.38.31"/></metadata><type><om:OMA><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/constants.mmt#1546.38.35:1554.38.43"/></metadata>
- <om:OMS base="http://cds.omdoc.org/urtheories" module="LambdaPi" name="arrow"></om:OMS>
- <om:OMS base="http://mathhub.info/MitM/Models" module="Base" name="Real_vec_space2"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/constants.mmt#1546.38.35:1547.38.36"/></metadata></om:OMS><om:OMS base="http://mathhub.info/MitM/Foundation" module="Logic" name="bool"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/constants.mmt#1551.38.40:1554.38.43"/></metadata></om:OMS>
- </om:OMA></type></om:OMV></om:OMBVAR>
- <om:OMA><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/constants.mmt#1556.38.45:1590.38.79"/></metadata>
- <om:OMS base="http://cds.omdoc.org/urtheories" module="LambdaPi" name="arrow"></om:OMS>
- <om:OMA><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/constants.mmt#1556.38.45:1568.38.57"/></metadata>
- <om:OMS base="http://cds.omdoc.org/urtheories" module="LambdaPi" name="arrow"></om:OMS>
- <om:OMA><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/constants.mmt#1557.38.46:1563.38.52"/></metadata>
- <om:OMS base="http://cds.omdoc.org/urtheories" module="LambdaPi" name="apply"></om:OMS>
- <om:OMS base="http://mathhub.info/MitM/Models" module="Base" name="pred_as_sub2"></om:OMS><om:OMV name="P"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/constants.mmt#1563.38.52:1563.38.52"/></metadata></om:OMV>
- </om:OMA><om:OMS base="http://mathhub.info/MitM/numberfields" module="realnumbers" name="Realnumbers"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/constants.mmt#1567.38.56:1567.38.56"/></metadata></om:OMS>
- </om:OMA><om:OMA><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/constants.mmt#1572.38.61:1590.38.79"/></metadata>
- <om:OMS base="http://cds.omdoc.org/urtheories" module="LambdaPi" name="arrow"></om:OMS>
- <om:OMA><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/constants.mmt#1573.38.62:1585.38.74"/></metadata>
- <om:OMS base="http://cds.omdoc.org/urtheories" module="LambdaPi" name="apply"></om:OMS>
- <om:OMS base="http://mathhub.info/MitM/Models" module="Base" name="pred_as_sub3"></om:OMS><om:OMA><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/constants.mmt#1579.38.68:1585.38.74"/></metadata>
- <om:OMS base="http://cds.omdoc.org/urtheories" module="LambdaPi" name="apply"></om:OMS>
- <om:OMS base="http://mathhub.info/MitM/Models" module="Base" name="lift_type_two_to_three"></om:OMS><om:OMV name="P"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/constants.mmt#1584.38.73:1584.38.73"/></metadata></om:OMV>
- </om:OMA>
- </om:OMA><om:OMS base="http://mathhub.info/MitM/numberfields" module="realnumbers" name="Realnumbers"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/constants.mmt#1589.38.78:1589.38.78"/></metadata></om:OMS>
- </om:OMA>
- </om:OMA>
- </om:OMBIND></om:OMOBJ></type>
-
- <notations><notation dimension="1" precedence="0" fixity="mixfix" arguments="f2↑ 2"> <scope languages="" priority="0"/> </notation></notations>
- </constant></theory></omdoc>
\ No newline at end of file
+<omdoc xmlns="http://omdoc.org/ns" xmlns:om="http://www.openmath.org/OpenMath"><theory name="Base" base="http://mathhub.info/MitM/Models" meta="http://mathhub.info/MitM/smglom/arithmetics?realarith"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/constants.mmt#704.17.0:877.21.1"/></metadata><import from="http://mathhub.info/MitM/Models?PhysicalConstants"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/constants.mmt#738.18.1:765.18.28"/></metadata></import><import from="http://mathhub.info/MitM/smglom/calculus?derivative"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/constants.mmt#768.19.1:828.19.61"/></metadata></import></theory></omdoc>
\ No newline at end of file
diff --git a/content/http..mathhub.info/MitM/Models/$Physical$Constants.omdoc b/content/http..mathhub.info/MitM/Models/$Physical$Constants.omdoc
index 168e4f0..7f2e215 100644
--- a/content/http..mathhub.info/MitM/Models/$Physical$Constants.omdoc
+++ b/content/http..mathhub.info/MitM/Models/$Physical$Constants.omdoc
@@ -1,16 +1,25 @@
-<omdoc xmlns="http://omdoc.org/ns" xmlns:om="http://www.openmath.org/OpenMath"><theory name="PhysicalConstants" base="http://mathhub.info/MitM/Models" meta="http://mathhub.info/MitM/numberfields?realnumbers"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/constants.mmt#202.5.0:540.12.1"/></metadata><opaque format="text"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/constants.mmt#249.6.1:324.6.76"/></metadata>The vaccuum dielectric permitivity constant (usually denoted by <om:OMOBJ xmlns:om="http://www.openmath.org/OpenMath"><om:OMS base="http://mathhub.info/MitM/Models" module="PhysicalConstants" name="vacuum_dielectric_permitivity"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/constants.mmt#317.-1.-1:319.-1.1"/></metadata></om:OMS></om:OMOBJ>)</opaque><constant name="vacuum_dielectric_permitivity">
- <metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/constants.mmt#326.7.1:369.7.44"/></metadata>
- <type><om:OMOBJ xmlns:om="http://www.openmath.org/OpenMath"><om:OMS base="http://mathhub.info/MitM/numberfields" module="realnumbers" name="Realnumbers"></om:OMS></om:OMOBJ></type>
+<omdoc xmlns="http://omdoc.org/ns" xmlns:om="http://www.openmath.org/OpenMath"><theory name="PhysicalConstants" base="http://mathhub.info/MitM/Models" meta="http://mathhub.info/MMT/physics-units?QEBase"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/constants.mmt#259.6.0:702.15.1"/></metadata><import from="http://mathhub.info/MitM/Models?Permittivity"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/constants.mmt#300.7.1:322.7.23"/></metadata></import><import from="http://mathhub.info/MitM/smglom/arithmetics?realarith"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/constants.mmt#325.8.1:350.8.26"/></metadata></import><opaque format="text"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/constants.mmt#353.9.1:428.9.76"/></metadata>The vaccuum dielectric permitivity constant (usually denoted by <om:OMOBJ xmlns:om="http://www.openmath.org/OpenMath"><om:OMS base="http://mathhub.info/MitM/Models" module="PhysicalConstants" name="vacuum_dielectric_permitivity"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/constants.mmt#421.-1.-1:423.-1.1"/></metadata></om:OMS></om:OMOBJ>)</opaque><constant name="vacuum_dielectric_permitivity">
+ <metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/constants.mmt#430.10.1:488.10.59"/></metadata>
+ <type><om:OMOBJ xmlns:om="http://www.openmath.org/OpenMath"><om:OMS base="http://mathhub.info/MitM/Models" module="Permittivity" name="permittivity_dim"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/constants.mmt#462.10.33:477.10.48"/></metadata></om:OMS></om:OMOBJ></type>
<notations><notation dimension="1" precedence="0" fixity="mixfix" arguments="ε_0"> <scope languages="" priority="0"/> </notation></notations>
- </constant><opaque format="text"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/constants.mmt#372.8.1:415.8.44"/></metadata>The elementary charge (denoted by <om:OMOBJ xmlns:om="http://www.openmath.org/OpenMath"><om:OMS base="http://mathhub.info/MitM/Models" module="PhysicalConstants" name="elementary_charge"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/constants.mmt#410.-1.-1:410.-1.-1"/></metadata></om:OMS></om:OMOBJ>)</opaque><constant name="elementary_charge">
- <metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/constants.mmt#417.9.1:446.9.30"/></metadata>
- <type><om:OMOBJ xmlns:om="http://www.openmath.org/OpenMath"><om:OMS base="http://mathhub.info/MitM/numberfields" module="realnumbers" name="Realnumbers"></om:OMS></om:OMOBJ></type>
+ </constant><opaque format="text"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/constants.mmt#491.11.1:534.11.44"/></metadata>The elementary charge (denoted by <unparsed>None</unparsed>)</opaque><constant name="elementary_charge">
+ <metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/constants.mmt#536.12.1:581.12.46"/></metadata>
+ <type><om:OMOBJ xmlns:om="http://www.openmath.org/OpenMath"><om:OMA><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/constants.mmt#556.12.21:572.12.37"/></metadata>
+ <om:OMS base="http://cds.omdoc.org/urtheories" module="LambdaPi" name="apply"></om:OMS>
+ <om:OMS base="http://mathhub.info/MMT/physics-units" module="QEBase" name="QE"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/constants.mmt#556.12.21:557.12.22"/></metadata></om:OMS><om:OMS base="http://mathhub.info/MMT/physics-units" module="DimensionsExtended" name="ElectricCharge"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/constants.mmt#559.12.24:572.12.37"/></metadata></om:OMS>
+ </om:OMA></om:OMOBJ></type>
<notations><notation dimension="1" precedence="0" fixity="mixfix" arguments="q"> <scope languages="" priority="0"/> </notation></notations>
- </constant><opaque format="text"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/constants.mmt#450.10.3:504.10.57"/></metadata>The Boltzmann constant (usually denoted by <om:OMOBJ xmlns:om="http://www.openmath.org/OpenMath"><om:OMS base="http://mathhub.info/MitM/Models" module="PhysicalConstants" name="Boltzmann_constant"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/constants.mmt#497.-1.-1:499.-1.1"/></metadata></om:OMS></om:OMOBJ>)</opaque><constant name="Boltzmann_constant">
- <metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/constants.mmt#506.11.1:538.11.33"/></metadata>
- <type><om:OMOBJ xmlns:om="http://www.openmath.org/OpenMath"><om:OMS base="http://mathhub.info/MitM/numberfields" module="realnumbers" name="Realnumbers"></om:OMS></om:OMOBJ></type>
+ </constant><opaque format="text"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/constants.mmt#585.13.3:639.13.57"/></metadata>The Boltzmann constant (usually denoted by <unparsed>None</unparsed>)</opaque><constant name="Boltzmann_constant">
+ <metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/constants.mmt#641.14.1:700.14.60"/></metadata>
+ <type><om:OMOBJ xmlns:om="http://www.openmath.org/OpenMath"><om:OMA><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/constants.mmt#662.14.22:689.14.49"/></metadata>
+ <om:OMS base="http://cds.omdoc.org/urtheories" module="LambdaPi" name="apply"></om:OMS>
+ <om:OMS base="http://mathhub.info/MMT/physics-units" module="QEBase" name="QE"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/constants.mmt#662.14.22:663.14.23"/></metadata></om:OMS><om:OMA><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/constants.mmt#665.14.25:689.14.49"/></metadata>
+ <om:OMS base="http://cds.omdoc.org/urtheories" module="LambdaPi" name="apply"></om:OMS>
+ <om:OMS base="http://mathhub.info/MMT/physics-units" module="Dimensions" name="DimDiv"></om:OMS><om:OMS base="http://mathhub.info/MMT/physics-units" module="DimensionsExtended" name="Energy"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/constants.mmt#666.14.26:671.14.31"/></metadata></om:OMS><om:OMS base="http://mathhub.info/MMT/physics-units" module="Dimensions" name="SItemperature"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/constants.mmt#676.14.36:688.14.48"/></metadata></om:OMS>
+ </om:OMA>
+ </om:OMA></om:OMOBJ></type>
<notations><notation dimension="1" precedence="0" fixity="mixfix" arguments="k_B"> <scope languages="" priority="0"/> </notation></notations>
</constant></theory></omdoc>
\ No newline at end of file
diff --git a/content/http..mathhub.info/MitM/Models/VanRoosbroeck/$Van$Roosbroeck.omdoc b/content/http..mathhub.info/MitM/Models/VanRoosbroeck/$Van$Roosbroeck.omdoc
index 89cb089..4c027fc 100644
--- a/content/http..mathhub.info/MitM/Models/VanRoosbroeck/$Van$Roosbroeck.omdoc
+++ b/content/http..mathhub.info/MitM/Models/VanRoosbroeck/$Van$Roosbroeck.omdoc
@@ -1 +1 @@
-<omdoc xmlns="http://omdoc.org/ns" xmlns:om="http://www.openmath.org/OpenMath"><theory name="VanRoosbroeck" base="http://mathhub.info/MitM/Models/VanRoosbroeck" meta="http://mathhub.info/MitM/Models?Base"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/VanRoosbroeck.mmt#666.14.0:1044.22.1"/></metadata><import from="http://mathhub.info/MitM/Models/poisson?PoissonEquation"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/VanRoosbroeck.mmt#702.15.1:734.15.33"/></metadata></import><import from="http://mathhub.info/MitM/Models/poisson?PoissonBoundaryConditions"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/VanRoosbroeck.mmt#737.16.1:779.16.43"/></metadata></import><import from="http://mathhub.info/MitM/Models/continuity?ContinuityEquationElectrons"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/VanRoosbroeck.mmt#782.17.1:829.17.48"/></metadata></import><import from="http://mathhub.info/MitM/Models/continuity?ContinuityEquationHoles"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/VanRoosbroeck.mmt#832.18.1:875.18.44"/></metadata></import><import from="http://mathhub.info/MitM/Models/continuity?ContinuityBoundaryConditionsElectrons"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/VanRoosbroeck.mmt#878.19.1:935.19.58"/></metadata></import><import from="http://mathhub.info/MitM/Models/continuity?ContinuityBoundaryConditionsHoles"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/VanRoosbroeck.mmt#938.20.1:991.20.54"/></metadata></import><import from="http://mathhub.info/MitM/Models/recombination?SpontaneousRecombination"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/VanRoosbroeck.mmt#994.21.1:1041.21.48"/></metadata></import></theory></omdoc>
\ No newline at end of file
+<omdoc xmlns="http://omdoc.org/ns" xmlns:om="http://www.openmath.org/OpenMath"><theory name="VanRoosbroeck" base="http://mathhub.info/MitM/Models/VanRoosbroeck" meta="http://mathhub.info/MitM/Models?Base"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/VanRoosbroeck.mmt#666.14.0:1044.22.1"/></metadata><import from="http://mathhub.info/MitM/Models/poisson?PoissonEquation"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/VanRoosbroeck.mmt#702.15.1:734.15.33"/></metadata></import><import from="http://mathhub.info/MitM/Models/poisson?PoissonBoundaryConditions"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/VanRoosbroeck.mmt#737.16.1:779.16.43"/></metadata></import><import from="http://mathhub.info/MitM/Models/continuity?ContinuityEquationElectrons"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/VanRoosbroeck.mmt#782.17.1:829.17.48"/></metadata></import><import from="http://mathhub.info/MitM/Models/continuity?ContinuityEquationHoles"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/VanRoosbroeck.mmt#832.18.1:875.18.44"/></metadata></import><import from="http://mathhub.info/MitM/Models/continuity?ContinuityBoundaryConditionsElectrons"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/VanRoosbroeck.mmt#878.19.1:935.19.58"/></metadata></import><import from="http://mathhub.info/MitM/Models/continuity?ContinuityBoundaryConditionsHoles"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/VanRoosbroeck.mmt#938.20.1:991.20.54"/></metadata></import><import from="http://mathhub.info/MitM/Models/recombination?SpontaneousRecombination"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/VanRoosbroeck.mmt#994.21.1:1041.21.48"/></metadata></import></theory></omdoc>
\ No newline at end of file
diff --git a/content/http..mathhub.info/MitM/Models/continuity/$Continuity$Boundary$Conditions$Electrons.omdoc b/content/http..mathhub.info/MitM/Models/continuity/$Continuity$Boundary$Conditions$Electrons.omdoc
index 6d2d91d..2489835 100644
--- a/content/http..mathhub.info/MitM/Models/continuity/$Continuity$Boundary$Conditions$Electrons.omdoc
+++ b/content/http..mathhub.info/MitM/Models/continuity/$Continuity$Boundary$Conditions$Electrons.omdoc
@@ -1,11 +1,17 @@
-<omdoc xmlns="http://omdoc.org/ns" xmlns:om="http://www.openmath.org/OpenMath"><theory name="ContinuityBoundaryConditionsElectrons" base="http://mathhub.info/MitM/Models/continuity" meta="http://mathhub.info/MitM/Models?Base"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/continuity.mmt#2925.80.0:3202.86.1"/></metadata><import from="http://mathhub.info/MitM/Models/device?DeviceOperationState"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/continuity.mmt#2985.81.1:3021.81.37"/></metadata></import><opaque format="text"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/continuity.mmt#3025.82.2:3069.82.46"/></metadata>Boundary condition for the top contact.</opaque><constant name="potential_top">
- <metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/continuity.mmt#3071.83.1:3108.83.38"/></metadata>
- <type><om:OMOBJ xmlns:om="http://www.openmath.org/OpenMath"><om:OMS base="http://mathhub.info/MitM/numberfields" module="realnumbers" name="Realnumbers"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/continuity.mmt#3087.83.17:3087.83.17"/></metadata></om:OMS></om:OMOBJ></type>
- <definition><om:OMOBJ xmlns:om="http://www.openmath.org/OpenMath"><om:OMS base="http://mathhub.info/MitM/Models/device" module="DeviceOperationState" name="voltage_bottom"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/continuity.mmt#3093.83.23:3095.83.25"/></metadata></om:OMS></om:OMOBJ></definition>
+<omdoc xmlns="http://omdoc.org/ns" xmlns:om="http://www.openmath.org/OpenMath"><theory name="ContinuityBoundaryConditionsElectrons" base="http://mathhub.info/MitM/Models/continuity" meta="http://mathhub.info/MitM/Models?Base"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/continuity.mmt#1269.42.0:1584.48.1"/></metadata><import from="http://mathhub.info/MitM/Models/device?DeviceOperationState"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/continuity.mmt#1329.43.1:1365.43.37"/></metadata></import><opaque format="text"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/continuity.mmt#1369.44.2:1413.44.46"/></metadata>Boundary condition for the top contact.</opaque><constant name="potential_top">
+ <metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/continuity.mmt#1415.45.1:1471.45.57"/></metadata>
+ <type><om:OMOBJ xmlns:om="http://www.openmath.org/OpenMath"><om:OMA><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/continuity.mmt#1431.45.17:1450.45.36"/></metadata>
+ <om:OMS base="http://cds.omdoc.org/urtheories" module="LambdaPi" name="apply"></om:OMS>
+ <om:OMS base="http://mathhub.info/MMT/physics-units" module="QEBase" name="QE"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/continuity.mmt#1431.45.17:1432.45.18"/></metadata></om:OMS><om:OMS base="http://mathhub.info/MMT/physics-units" module="DimensionsExtended" name="ElectricPotential"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/continuity.mmt#1434.45.20:1450.45.36"/></metadata></om:OMS>
+ </om:OMA></om:OMOBJ></type>
+ <definition><om:OMOBJ xmlns:om="http://www.openmath.org/OpenMath"><om:OMS base="http://mathhub.info/MitM/Models/device" module="DeviceOperationState" name="voltage_bottom"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/continuity.mmt#1456.45.42:1458.45.44"/></metadata></om:OMS></om:OMOBJ></definition>
<notations><notation dimension="1" precedence="0" fixity="mixfix" arguments="φ_n_1"> <scope languages="" priority="0"/> </notation></notations>
- </constant><opaque format="text"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/continuity.mmt#3111.84.2:3158.84.49"/></metadata>Boundary condition for the bottom contact.</opaque><constant name="potential_bottom">
- <metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/continuity.mmt#3160.85.1:3200.85.41"/></metadata>
- <type><om:OMOBJ xmlns:om="http://www.openmath.org/OpenMath"><om:OMS base="http://mathhub.info/MitM/numberfields" module="realnumbers" name="Realnumbers"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/continuity.mmt#3179.85.20:3179.85.20"/></metadata></om:OMS></om:OMOBJ></type>
- <definition><om:OMOBJ xmlns:om="http://www.openmath.org/OpenMath"><om:OMS base="http://mathhub.info/MitM/Models/device" module="DeviceOperationState" name="voltage_top"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/continuity.mmt#3185.85.26:3187.85.28"/></metadata></om:OMS></om:OMOBJ></definition>
+ </constant><opaque format="text"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/continuity.mmt#1474.46.2:1521.46.49"/></metadata>Boundary condition for the bottom contact.</opaque><constant name="potential_bottom">
+ <metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/continuity.mmt#1523.47.1:1582.47.60"/></metadata>
+ <type><om:OMOBJ xmlns:om="http://www.openmath.org/OpenMath"><om:OMA><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/continuity.mmt#1542.47.20:1561.47.39"/></metadata>
+ <om:OMS base="http://cds.omdoc.org/urtheories" module="LambdaPi" name="apply"></om:OMS>
+ <om:OMS base="http://mathhub.info/MMT/physics-units" module="QEBase" name="QE"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/continuity.mmt#1542.47.20:1543.47.21"/></metadata></om:OMS><om:OMS base="http://mathhub.info/MMT/physics-units" module="DimensionsExtended" name="ElectricPotential"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/continuity.mmt#1545.47.23:1561.47.39"/></metadata></om:OMS>
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+ <definition><om:OMOBJ xmlns:om="http://www.openmath.org/OpenMath"><om:OMS base="http://mathhub.info/MitM/Models/device" module="DeviceOperationState" name="voltage_top"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/continuity.mmt#1567.47.45:1569.47.47"/></metadata></om:OMS></om:OMOBJ></definition>
<notations><notation dimension="1" precedence="0" fixity="mixfix" arguments="φ_n_2"> <scope languages="" priority="0"/> </notation></notations>
</constant></theory></omdoc>
\ No newline at end of file
diff --git a/content/http..mathhub.info/MitM/Models/continuity/$Continuity$Boundary$Conditions$Holes.omdoc b/content/http..mathhub.info/MitM/Models/continuity/$Continuity$Boundary$Conditions$Holes.omdoc
index ae0a6c6..0d90356 100644
--- a/content/http..mathhub.info/MitM/Models/continuity/$Continuity$Boundary$Conditions$Holes.omdoc
+++ b/content/http..mathhub.info/MitM/Models/continuity/$Continuity$Boundary$Conditions$Holes.omdoc
@@ -1,11 +1,17 @@
-<omdoc xmlns="http://omdoc.org/ns" xmlns:om="http://www.openmath.org/OpenMath"><theory name="ContinuityBoundaryConditionsHoles" base="http://mathhub.info/MitM/Models/continuity" meta="http://mathhub.info/MitM/Models?Base"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/continuity.mmt#3330.91.0:3601.97.1"/></metadata><import from="http://mathhub.info/MitM/Models/device?DeviceOperationState"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/continuity.mmt#3386.92.1:3422.92.37"/></metadata></import><opaque format="text"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/continuity.mmt#3425.93.1:3469.93.45"/></metadata>Boundary condition for the top contact.</opaque><constant name="potential_top">
- <metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/continuity.mmt#3471.94.1:3508.94.38"/></metadata>
- <type><om:OMOBJ xmlns:om="http://www.openmath.org/OpenMath"><om:OMS base="http://mathhub.info/MitM/numberfields" module="realnumbers" name="Realnumbers"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/continuity.mmt#3487.94.17:3487.94.17"/></metadata></om:OMS></om:OMOBJ></type>
- <definition><om:OMOBJ xmlns:om="http://www.openmath.org/OpenMath"><om:OMS base="http://mathhub.info/MitM/Models/device" module="DeviceOperationState" name="voltage_bottom"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/continuity.mmt#3493.94.23:3495.94.25"/></metadata></om:OMS></om:OMOBJ></definition>
+<omdoc xmlns="http://omdoc.org/ns" xmlns:om="http://www.openmath.org/OpenMath"><theory name="ContinuityBoundaryConditionsHoles" base="http://mathhub.info/MitM/Models/continuity" meta="http://mathhub.info/MitM/Models?Base"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/continuity.mmt#1712.53.0:2021.59.1"/></metadata><import from="http://mathhub.info/MitM/Models/device?DeviceOperationState"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/continuity.mmt#1768.54.1:1804.54.37"/></metadata></import><opaque format="text"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/continuity.mmt#1807.55.1:1851.55.45"/></metadata>Boundary condition for the top contact.</opaque><constant name="potential_top">
+ <metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/continuity.mmt#1853.56.1:1909.56.57"/></metadata>
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+ <definition><om:OMOBJ xmlns:om="http://www.openmath.org/OpenMath"><om:OMS base="http://mathhub.info/MitM/Models/device" module="DeviceOperationState" name="voltage_bottom"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/continuity.mmt#1894.56.42:1896.56.44"/></metadata></om:OMS></om:OMOBJ></definition>
<notations><notation dimension="1" precedence="0" fixity="mixfix" arguments="φ_p_1"> <scope languages="" priority="0"/> </notation></notations>
- </constant><opaque format="text"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/continuity.mmt#3510.95.1:3557.95.48"/></metadata>Boundary condition for the bottom contact.</opaque><constant name="potential_bottom">
- <metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/continuity.mmt#3559.96.1:3599.96.41"/></metadata>
- <type><om:OMOBJ xmlns:om="http://www.openmath.org/OpenMath"><om:OMS base="http://mathhub.info/MitM/numberfields" module="realnumbers" name="Realnumbers"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/continuity.mmt#3578.96.20:3578.96.20"/></metadata></om:OMS></om:OMOBJ></type>
- <definition><om:OMOBJ xmlns:om="http://www.openmath.org/OpenMath"><om:OMS base="http://mathhub.info/MitM/Models/device" module="DeviceOperationState" name="voltage_top"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/continuity.mmt#3584.96.26:3586.96.28"/></metadata></om:OMS></om:OMOBJ></definition>
+ </constant><opaque format="text"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/continuity.mmt#1911.57.1:1958.57.48"/></metadata>Boundary condition for the bottom contact.</opaque><constant name="potential_bottom">
+ <metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/continuity.mmt#1960.58.1:2019.58.60"/></metadata>
+ <type><om:OMOBJ xmlns:om="http://www.openmath.org/OpenMath"><om:OMA><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/continuity.mmt#1979.58.20:1998.58.39"/></metadata>
+ <om:OMS base="http://cds.omdoc.org/urtheories" module="LambdaPi" name="apply"></om:OMS>
+ <om:OMS base="http://mathhub.info/MMT/physics-units" module="QEBase" name="QE"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/continuity.mmt#1979.58.20:1980.58.21"/></metadata></om:OMS><om:OMS base="http://mathhub.info/MMT/physics-units" module="DimensionsExtended" name="ElectricPotential"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/continuity.mmt#1982.58.23:1998.58.39"/></metadata></om:OMS>
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<notations><notation dimension="1" precedence="0" fixity="mixfix" arguments="φ_p_2"> <scope languages="" priority="0"/> </notation></notations>
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\ No newline at end of file
diff --git a/content/http..mathhub.info/MitM/Models/continuity/$Continuity$Equation$Electrons.omdoc b/content/http..mathhub.info/MitM/Models/continuity/$Continuity$Equation$Electrons.omdoc
index d5ac5f5..76dca83 100644
--- a/content/http..mathhub.info/MitM/Models/continuity/$Continuity$Equation$Electrons.omdoc
+++ b/content/http..mathhub.info/MitM/Models/continuity/$Continuity$Equation$Electrons.omdoc
@@ -1,79 +1,78 @@
-<omdoc xmlns="http://omdoc.org/ns" xmlns:om="http://www.openmath.org/OpenMath"><theory name="ContinuityEquationElectrons" base="http://mathhub.info/MitM/Models/continuity" meta="http://mathhub.info/MitM/Models?Base"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/continuity.mmt#1829.49.0:2277.60.1"/></metadata><import from="http://mathhub.info/MitM/Models/continuity?CurrentElectrons"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/continuity.mmt#1879.50.1:1905.50.27"/></metadata></import><import from="http://mathhub.info/MitM/Models/densities?DensityHoles"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/continuity.mmt#1908.51.1:1939.51.32"/></metadata></import><import from="http://mathhub.info/MitM/Models/densities?FermiPotentialHoles"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/continuity.mmt#1942.52.1:1980.52.39"/></metadata></import><import from="http://mathhub.info/MitM/Models/recombination?Recombination"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/continuity.mmt#1983.53.1:2019.53.37"/></metadata></import><import from="http://mathhub.info/MitM/Models/densities?ElectrostaticPotential"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/continuity.mmt#2022.54.1:2063.54.42"/></metadata></import><opaque format="text"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/continuity.mmt#2067.56.1:2144.56.78"/></metadata>Formulation of the continuity equation for electrons in divergence form.</opaque><constant name="continuity_equation_electrons">
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+<omdoc xmlns="http://omdoc.org/ns" xmlns:om="http://www.openmath.org/OpenMath"><theory name="ContinuityEquationElectrons" base="http://mathhub.info/MitM/Models/continuity" meta="http://mathhub.info/MitM/Models?Base"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/continuity.mmt#887.29.0:1140.35.1"/></metadata><opaque format="text"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/continuity.mmt#938.31.1:1015.31.78"/></metadata>Formulation of the continuity equation for electrons in divergence form.</opaque><constant name="continuity_equation">
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</om:OMA>
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\ No newline at end of file
diff --git a/content/http..mathhub.info/MitM/Models/continuity/$Continuity$Equation$Holes.omdoc b/content/http..mathhub.info/MitM/Models/continuity/$Continuity$Equation$Holes.omdoc
index 5048aea..d2e1008 100644
--- a/content/http..mathhub.info/MitM/Models/continuity/$Continuity$Equation$Holes.omdoc
+++ b/content/http..mathhub.info/MitM/Models/continuity/$Continuity$Equation$Holes.omdoc
@@ -1,82 +1,68 @@
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<om:OMS base="http://cds.omdoc.org/urtheories" module="LambdaPi" name="apply"></om:OMS>
- <om:OMS base="http://mathhub.info/MitM/numberfields" module="realarith" name="uminus"></om:OMS><om:OMS base="http://mathhub.info/MitM/Models" module="PhysicalConstants" name="elementary_charge"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/continuity.mmt#2730.74.29:2730.74.29"/></metadata></om:OMS>
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+ <om:OMA>
+ <om:OMS base="http://cds.omdoc.org/mmt" module="mmt" name="oneOf"></om:OMS>
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<om:OMS base="http://cds.omdoc.org/urtheories" module="LambdaPi" name="apply"></om:OMS>
- <om:OMS base="http://mathhub.info/MitM/Models/recombination" module="Recombination" name="recombination_rate"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/continuity.mmt#2735.74.34:2735.74.34"/></metadata></om:OMS><om:OMA><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/continuity.mmt#2737.74.36:2753.74.52"/></metadata>
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<om:OMS base="http://cds.omdoc.org/urtheories" module="LambdaPi" name="apply"></om:OMS>
- <om:OMS base="http://mathhub.info/MitM/Models/densities" module="DensityElectrons" name="density_electrons"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/continuity.mmt#2738.74.37:2738.74.37"/></metadata></om:OMS><om:OMA><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/continuity.mmt#2740.74.39:2744.74.43"/></metadata>
+ <om:OMS base="http://mathhub.info/MitM/Models/densities" module="ElectrostaticPotential" name="electrostatic_potential"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/continuity.mmt#2789.73.40:2789.73.40"/></metadata></om:OMS><om:OMV name="x"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/continuity.mmt#2791.73.42:2791.73.42"/></metadata></om:OMV>
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<om:OMS base="http://cds.omdoc.org/urtheories" module="LambdaPi" name="apply"></om:OMS>
- <om:OMS base="http://mathhub.info/MitM/Models/densities" module="ElectrostaticPotential" name="electrostatic_potential"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/continuity.mmt#2741.74.40:2741.74.40"/></metadata></om:OMS><om:OMV name="x"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/continuity.mmt#2743.74.42:2743.74.42"/></metadata></om:OMV>
- </om:OMA><om:OMA><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/continuity.mmt#2746.74.45:2752.74.51"/></metadata>
- <om:OMS base="http://cds.omdoc.org/urtheories" module="LambdaPi" name="apply"></om:OMS>
- <om:OMS base="http://mathhub.info/MitM/Models/densities" module="FermiPotentialElectrons" name="quasi_Fermi_potential"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/continuity.mmt#2747.74.46:2749.74.48"/></metadata></om:OMS><om:OMV name="x"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/continuity.mmt#2751.74.50:2751.74.50"/></metadata></om:OMV>
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</om:OMA>
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<om:OMS base="http://cds.omdoc.org/urtheories" module="LambdaPi" name="apply"></om:OMS>
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+ <om:OMS base="http://mathhub.info/MitM/Models/densities" module="DensityHoles" name="density_holes"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/continuity.mmt#2804.73.55:2804.73.55"/></metadata></om:OMS><om:OMA><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/continuity.mmt#2806.73.57:2810.73.61"/></metadata>
<om:OMS base="http://cds.omdoc.org/urtheories" module="LambdaPi" name="apply"></om:OMS>
- <om:OMS base="http://mathhub.info/MitM/Models/densities" module="ElectrostaticPotential" name="electrostatic_potential"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/continuity.mmt#2759.74.58:2759.74.58"/></metadata></om:OMS><om:OMV name="x"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/continuity.mmt#2761.74.60:2761.74.60"/></metadata></om:OMV>
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+ <om:OMS base="http://mathhub.info/MitM/Models/densities" module="ElectrostaticPotential" name="electrostatic_potential"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/continuity.mmt#2807.73.58:2807.73.58"/></metadata></om:OMS><om:OMV name="x"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/continuity.mmt#2809.73.60:2809.73.60"/></metadata></om:OMV>
+ </om:OMA><om:OMA><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/continuity.mmt#2812.73.63:2818.73.69"/></metadata>
<om:OMS base="http://cds.omdoc.org/urtheories" module="LambdaPi" name="apply"></om:OMS>
- <om:OMS base="http://mathhub.info/MitM/Models/densities" module="FermiPotentialHoles" name="quasi_Fermi_potential"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/continuity.mmt#2765.74.64:2767.74.66"/></metadata></om:OMS><om:OMV name="x"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/continuity.mmt#2769.74.68:2769.74.68"/></metadata></om:OMV>
+ <om:OMS base="http://mathhub.info/MitM/Models/densities" module="FermiPotentialHoles" name="quasi_Fermi_potential"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/continuity.mmt#2813.73.64:2815.73.66"/></metadata></om:OMS><om:OMV name="x"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/continuity.mmt#2817.73.68:2817.73.68"/></metadata></om:OMV>
</om:OMA>
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+ </om:OMA><om:OMA><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/continuity.mmt#2821.73.72:2827.73.78"/></metadata>
<om:OMS base="http://cds.omdoc.org/urtheories" module="LambdaPi" name="apply"></om:OMS>
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+ <om:OMS base="http://mathhub.info/MitM/Models/densities" module="FermiPotentialElectrons" name="quasi_Fermi_potential"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/continuity.mmt#2822.73.73:2824.73.75"/></metadata></om:OMS><om:OMV name="x"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/continuity.mmt#2826.73.77:2826.73.77"/></metadata></om:OMV>
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<om:OMS base="http://cds.omdoc.org/urtheories" module="LambdaPi" name="apply"></om:OMS>
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+ <om:OMS base="http://mathhub.info/MitM/Models/densities" module="FermiPotentialHoles" name="quasi_Fermi_potential"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/continuity.mmt#2830.73.81:2832.73.83"/></metadata></om:OMS><om:OMV name="x"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/continuity.mmt#2834.73.85:2834.73.85"/></metadata></om:OMV>
</om:OMA>
</om:OMA>
</om:OMA>
</om:OMBIND>
</om:OMA>
- </om:OMA></om:OMOBJ></type>
+ </om:OMA>
+ </om:OMBIND></om:OMOBJ></type>
</constant></theory></omdoc>
\ No newline at end of file
diff --git a/content/http..mathhub.info/MitM/Models/continuity/$Current$Electrons.omdoc b/content/http..mathhub.info/MitM/Models/continuity/$Current$Electrons.omdoc
index e678d4e..3be3039 100644
--- a/content/http..mathhub.info/MitM/Models/continuity/$Current$Electrons.omdoc
+++ b/content/http..mathhub.info/MitM/Models/continuity/$Current$Electrons.omdoc
@@ -1,100 +1,118 @@
-<omdoc xmlns="http://omdoc.org/ns" xmlns:om="http://www.openmath.org/OpenMath"><theory name="CurrentElectrons" base="http://mathhub.info/MitM/Models/continuity" meta="http://mathhub.info/MitM/Models?Base"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/continuity.mmt#492.15.0:1091.28.1"/></metadata><import from="http://mathhub.info/MitM/Models/densities?FermiPotentialElectrons"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/continuity.mmt#531.16.1:573.16.43"/></metadata></import><import from="http://mathhub.info/MitM/Models/densities?ElectrostaticPotential"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/continuity.mmt#576.17.1:617.17.42"/></metadata></import><import from="http://mathhub.info/MitM/Models/densities?DensityElectrons"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/continuity.mmt#620.18.1:655.18.36"/></metadata></import><import from="http://mathhub.info/MitM/Models/continuity?Mobilities"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/continuity.mmt#658.19.1:678.19.21"/></metadata></import><opaque format="text"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/continuity.mmt#683.21.1:862.23.53"/></metadata>Definition of the electron current in gradient form.
+<omdoc xmlns="http://omdoc.org/ns" xmlns:om="http://www.openmath.org/OpenMath"><theory name="CurrentElectrons" base="http://mathhub.info/MitM/Models/continuity" meta="http://mathhub.info/MitM/Models?Base"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/continuity.mmt#572.15.0:1261.29.1"/></metadata><import from="http://mathhub.info/MitM/Models/densities?FermiPotentialElectrons"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/continuity.mmt#611.16.1:653.16.43"/></metadata></import><import from="http://mathhub.info/MitM/Models/densities?ElectrostaticPotential"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/continuity.mmt#656.17.1:697.17.42"/></metadata></import><import from="http://mathhub.info/MitM/Models/densities?DensityElectrons"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/continuity.mmt#700.18.1:735.18.36"/></metadata></import><import from="http://mathhub.info/MitM/Models/continuity?Mobilities"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/continuity.mmt#738.19.1:758.19.21"/></metadata></import><import from="http://mathhub.info/MitM/Models?CurrentDensity"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/continuity.mmt#761.20.1:789.20.29"/></metadata></import><opaque format="text"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/continuity.mmt#794.22.1:973.24.53"/></metadata>Definition of the electron current in gradient form.
The driving force of the current are the negative gradients of
- the quasi-Fermi potential, here denoted by j_n.</opaque><constant name="current_electrons">
- <metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/continuity.mmt#946.26.1:1089.27.64"/></metadata>
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+ the quasi-Fermi potential, here denoted by j_n.</opaque><constant name="current_electrons_law">
+ <metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/continuity.mmt#1057.27.1:1259.28.64"/></metadata>
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<om:OMS base="http://cds.omdoc.org/urtheories" module="LambdaPi" name="Pi"></om:OMS>
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<om:OMS base="http://cds.omdoc.org/urtheories" module="LambdaPi" name="arrow"></om:OMS>
- <om:OMS base="http://mathhub.info/MitM/numberfields" module="realnumbers" name="Realnumbers"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/continuity.mmt#970.26.25:970.26.25"/></metadata></om:OMS><om:OMS base="http://mathhub.info/MitM/Foundation" module="Logic" name="bool"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/continuity.mmt#974.26.29:977.26.32"/></metadata></om:OMS>
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</om:OMA></type></om:OMV></om:OMBVAR>
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<om:OMS base="http://cds.omdoc.org/urtheories" module="LambdaPi" name="arrow"></om:OMS>
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<om:OMS base="http://cds.omdoc.org/urtheories" module="LambdaPi" name="arrow"></om:OMS>
- <om:OMA><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/continuity.mmt#981.26.36:986.26.41"/></metadata>
+ <om:OMA><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/continuity.mmt#1096.27.40:1101.27.45"/></metadata>
<om:OMS base="http://cds.omdoc.org/urtheories" module="LambdaPi" name="apply"></om:OMS>
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</om:OMA>
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<om:OMS base="http://cds.omdoc.org/urtheories" module="LambdaPi" name="apply"></om:OMS>
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</om:OMA>
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<notations><notation dimension="1" precedence="0" fixity="mixfix" arguments="j_n 2 3"> <scope languages="" priority="0"/> </notation></notations>
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diff --git a/content/http..mathhub.info/MitM/Models/continuity/$Current$Holes.omdoc b/content/http..mathhub.info/MitM/Models/continuity/$Current$Holes.omdoc
index 32a26c0..400e37e 100644
--- a/content/http..mathhub.info/MitM/Models/continuity/$Current$Holes.omdoc
+++ b/content/http..mathhub.info/MitM/Models/continuity/$Current$Holes.omdoc
@@ -1,100 +1,118 @@
-<omdoc xmlns="http://omdoc.org/ns" xmlns:om="http://www.openmath.org/OpenMath"><theory name="CurrentHoles" base="http://mathhub.info/MitM/Models/continuity" meta="http://mathhub.info/MitM/Models?Base"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/continuity.mmt#1166.32.0:1747.45.1"/></metadata><import from="http://mathhub.info/MitM/Models/densities?FermiPotentialHoles"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/continuity.mmt#1201.33.1:1239.33.39"/></metadata></import><import from="http://mathhub.info/MitM/Models/densities?ElectrostaticPotential"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/continuity.mmt#1242.34.1:1283.34.42"/></metadata></import><import from="http://mathhub.info/MitM/Models/densities?DensityHoles"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/continuity.mmt#1286.35.1:1317.35.32"/></metadata></import><import from="http://mathhub.info/MitM/Models/continuity?Mobilities"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/continuity.mmt#1320.36.1:1340.36.21"/></metadata></import><opaque format="text"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/continuity.mmt#1344.38.1:1518.40.54"/></metadata>Defintion of the hole current in gradient form.
+<omdoc xmlns="http://omdoc.org/ns" xmlns:om="http://www.openmath.org/OpenMath"><theory name="CurrentHoles" base="http://mathhub.info/MitM/Models/continuity" meta="http://mathhub.info/MitM/Models?Base"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/continuity.mmt#1124.30.0:1795.44.1"/></metadata><import from="http://mathhub.info/MitM/Models/densities?FermiPotentialHoles"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/continuity.mmt#1159.31.1:1197.31.39"/></metadata></import><import from="http://mathhub.info/MitM/Models/densities?ElectrostaticPotential"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/continuity.mmt#1200.32.1:1241.32.42"/></metadata></import><import from="http://mathhub.info/MitM/Models/densities?DensityHoles"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/continuity.mmt#1244.33.1:1275.33.32"/></metadata></import><import from="http://mathhub.info/MitM/Models/continuity?Mobilities"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/continuity.mmt#1278.34.1:1298.34.21"/></metadata></import><import from="http://mathhub.info/MitM/Models?CurrentDensity"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/continuity.mmt#1301.35.1:1329.35.29"/></metadata></import><opaque format="text"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/continuity.mmt#1333.37.1:1507.39.54"/></metadata>Defintion of the hole current in gradient form.
The driving force of the current are the negative gradient of
- the quasi-Fermi potential, here denoted by j_p.</opaque><constant name="current_holes">
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+ the quasi-Fermi potential, here denoted by j_p.</opaque><constant name="current_holes_law">
+ <metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/continuity.mmt#1595.42.1:1793.43.64"/></metadata>
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<om:OMS base="http://cds.omdoc.org/urtheories" module="LambdaPi" name="arrow"></om:OMS>
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</om:OMA>
</om:OMBIND></om:OMOBJ></type>
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diff --git a/content/http..mathhub.info/MitM/Models/continuity/$Mobilities.omdoc b/content/http..mathhub.info/MitM/Models/continuity/$Mobilities.omdoc
index d981753..46deda8 100644
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+++ b/content/http..mathhub.info/MitM/Models/continuity/$Mobilities.omdoc
@@ -1,11 +1,29 @@
-<omdoc xmlns="http://omdoc.org/ns" xmlns:om="http://www.openmath.org/OpenMath"><theory name="Mobilities" base="http://mathhub.info/MitM/Models/continuity" meta="http://mathhub.info/MitM/Models?Base"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/continuity.mmt#190.6.0:411.11.1"/></metadata><opaque format="text"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/continuity.mmt#223.7.1:285.7.63"/></metadata>The electron mobility parameter usually denoted by <om:OMOBJ xmlns:om="http://www.openmath.org/OpenMath"><om:OMS base="http://mathhub.info/MitM/Models/continuity" module="Mobilities" name="mobility_electrons"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/continuity.mmt#278.-1.-1:280.-1.1"/></metadata></om:OMS></om:OMOBJ>.</opaque><constant name="mobility_electrons">
- <metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/continuity.mmt#287.8.1:319.8.33"/></metadata>
- <type><om:OMOBJ xmlns:om="http://www.openmath.org/OpenMath"><om:OMS base="http://mathhub.info/MitM/numberfields" module="realnumbers" name="Realnumbers"></om:OMS></om:OMOBJ></type>
+<omdoc xmlns="http://omdoc.org/ns" xmlns:om="http://www.openmath.org/OpenMath"><theory name="Mobilities" base="http://mathhub.info/MitM/Models/continuity" meta="http://mathhub.info/MitM/Models?Base"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/continuity.mmt#190.6.0:491.11.1"/></metadata><opaque format="text"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/continuity.mmt#223.7.1:285.7.63"/></metadata>The electron mobility parameter usually denoted by <om:OMOBJ xmlns:om="http://www.openmath.org/OpenMath"><om:OMS base="http://mathhub.info/MitM/Models/continuity" module="Mobilities" name="mobility_electrons"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/continuity.mmt#278.-1.-1:280.-1.1"/></metadata></om:OMS></om:OMOBJ>.</opaque><constant name="mobility_electrons">
+ <metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/continuity.mmt#287.8.1:359.8.73"/></metadata>
+ <type><om:OMOBJ xmlns:om="http://www.openmath.org/OpenMath"><om:OMA><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/continuity.mmt#308.8.22:348.8.62"/></metadata>
+ <om:OMS base="http://cds.omdoc.org/urtheories" module="LambdaPi" name="apply"></om:OMS>
+ <om:OMS base="http://mathhub.info/MMT/physics-units" module="QEBase" name="QE"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/continuity.mmt#308.8.22:309.8.23"/></metadata></om:OMS><om:OMA><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/continuity.mmt#311.8.25:348.8.62"/></metadata>
+ <om:OMS base="http://cds.omdoc.org/urtheories" module="LambdaPi" name="apply"></om:OMS>
+ <om:OMS base="http://mathhub.info/MMT/physics-units" module="Dimensions" name="DimDiv"></om:OMS><om:OMS base="http://mathhub.info/MMT/physics-units" module="DimensionsExtended" name="Area"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/continuity.mmt#312.8.26:315.8.29"/></metadata></om:OMS><om:OMA><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/continuity.mmt#320.8.34:347.8.61"/></metadata>
+ <om:OMS base="http://cds.omdoc.org/urtheories" module="LambdaPi" name="apply"></om:OMS>
+ <om:OMS base="http://mathhub.info/MMT/physics-units" module="Dimensions" name="DimTimes"></om:OMS><om:OMS base="http://mathhub.info/MMT/physics-units" module="DimensionsExtended" name="ElectricPotential"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/continuity.mmt#321.8.35:337.8.51"/></metadata></om:OMS><om:OMS base="http://mathhub.info/MMT/physics-units" module="Dimensions" name="SItime"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/continuity.mmt#341.8.55:346.8.60"/></metadata></om:OMS>
+ </om:OMA>
+ </om:OMA>
+ </om:OMA></om:OMOBJ></type>
<notations><notation dimension="1" precedence="0" fixity="mixfix" arguments="μ_n"> <scope languages="" priority="0"/> </notation></notations>
- </constant><opaque format="text"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/continuity.mmt#321.9.1:379.9.59"/></metadata>The hole mobility parameter usually denoted by <om:OMOBJ xmlns:om="http://www.openmath.org/OpenMath"><om:OMS base="http://mathhub.info/MitM/Models/continuity" module="Mobilities" name="mobility_holes"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/continuity.mmt#372.-1.-1:374.-1.1"/></metadata></om:OMS></om:OMOBJ>.</opaque><constant name="mobility_holes">
- <metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/continuity.mmt#381.10.1:409.10.29"/></metadata>
- <type><om:OMOBJ xmlns:om="http://www.openmath.org/OpenMath"><om:OMS base="http://mathhub.info/MitM/numberfields" module="realnumbers" name="Realnumbers"></om:OMS></om:OMOBJ></type>
+ </constant><opaque format="text"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/continuity.mmt#361.9.1:419.9.59"/></metadata>The hole mobility parameter usually denoted by <unparsed>None</unparsed>.</opaque><constant name="mobility_holes">
+ <metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/continuity.mmt#421.10.1:489.10.69"/></metadata>
+ <type><om:OMOBJ xmlns:om="http://www.openmath.org/OpenMath"><om:OMA><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/continuity.mmt#438.10.18:478.10.58"/></metadata>
+ <om:OMS base="http://cds.omdoc.org/urtheories" module="LambdaPi" name="apply"></om:OMS>
+ <om:OMS base="http://mathhub.info/MMT/physics-units" module="QEBase" name="QE"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/continuity.mmt#438.10.18:439.10.19"/></metadata></om:OMS><om:OMA><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/continuity.mmt#441.10.21:478.10.58"/></metadata>
+ <om:OMS base="http://cds.omdoc.org/urtheories" module="LambdaPi" name="apply"></om:OMS>
+ <om:OMS base="http://mathhub.info/MMT/physics-units" module="Dimensions" name="DimDiv"></om:OMS><om:OMS base="http://mathhub.info/MMT/physics-units" module="DimensionsExtended" name="Area"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/continuity.mmt#442.10.22:445.10.25"/></metadata></om:OMS><om:OMA><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/continuity.mmt#450.10.30:477.10.57"/></metadata>
+ <om:OMS base="http://cds.omdoc.org/urtheories" module="LambdaPi" name="apply"></om:OMS>
+ <om:OMS base="http://mathhub.info/MMT/physics-units" module="Dimensions" name="DimTimes"></om:OMS><om:OMS base="http://mathhub.info/MMT/physics-units" module="DimensionsExtended" name="ElectricPotential"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/continuity.mmt#451.10.31:467.10.47"/></metadata></om:OMS><om:OMS base="http://mathhub.info/MMT/physics-units" module="Dimensions" name="SItime"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/continuity.mmt#471.10.51:476.10.56"/></metadata></om:OMS>
+ </om:OMA>
+ </om:OMA>
+ </om:OMA></om:OMOBJ></type>
<notations><notation dimension="1" precedence="0" fixity="mixfix" arguments="μ_p"> <scope languages="" priority="0"/> </notation></notations>
</constant></theory></omdoc>
\ No newline at end of file
diff --git a/content/http..mathhub.info/MitM/Models/densities/$Bandstructure$Parameters.omdoc b/content/http..mathhub.info/MitM/Models/densities/$Bandstructure$Parameters.omdoc
index 49cb357..5c7d442 100644
--- a/content/http..mathhub.info/MitM/Models/densities/$Bandstructure$Parameters.omdoc
+++ b/content/http..mathhub.info/MitM/Models/densities/$Bandstructure$Parameters.omdoc
@@ -1,26 +1,29 @@
-<omdoc xmlns="http://omdoc.org/ns" xmlns:om="http://www.openmath.org/OpenMath"><theory name="BandstructureParameters" base="http://mathhub.info/MitM/Models/densities" meta="http://mathhub.info/MitM/Models?Base"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/densities.mmt#198.6.0:807.18.1"/></metadata><opaque format="text"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/densities.mmt#245.7.1:338.8.32"/></metadata>The effective density of states for the conduction bands
- usually denoted by <om:OMOBJ xmlns:om="http://www.openmath.org/OpenMath"><om:OMS base="http://mathhub.info/MitM/Models/densities" module="BandstructureParameters" name="effective_density_of_states_conduction_bands"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/densities.mmt#331.-1.-1:333.-1.1"/></metadata></om:OMS></om:OMOBJ>.</opaque><constant name="effective_density_of_states_conduction_bands">
- <metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/densities.mmt#340.9.1:398.9.59"/></metadata>
- <type><om:OMOBJ xmlns:om="http://www.openmath.org/OpenMath"><om:OMS base="http://mathhub.info/MitM/numberfields" module="realnumbers" name="Realnumbers"></om:OMS></om:OMOBJ></type>
+<omdoc xmlns="http://omdoc.org/ns" xmlns:om="http://www.openmath.org/OpenMath"><theory name="BandstructureParameters" base="http://mathhub.info/MitM/Models/densities" meta="http://mathhub.info/MitM/Models?Base"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/densities2.mmt#209.6.0:878.19.1"/></metadata><import from="http://mathhub.info/MitM/Models?Density"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/densities2.mmt#256.7.1:277.7.22"/></metadata></import><opaque format="text"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/densities2.mmt#280.8.1:373.9.32"/></metadata>The effective density of states for the conduction bands
+ usually denoted by <om:OMOBJ xmlns:om="http://www.openmath.org/OpenMath"><om:OMS base="http://mathhub.info/MitM/Models/densities" module="BandstructureParameters" name="effective_density_of_states_conduction_bands"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/densities2.mmt#366.-1.-1:368.-1.1"/></metadata></om:OMS></om:OMOBJ>.</opaque><constant name="effective_density_of_states_conduction_bands">
+ <metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/densities2.mmt#375.10.1:443.10.69"/></metadata>
+ <type><om:OMOBJ xmlns:om="http://www.openmath.org/OpenMath"><om:OMS base="http://mathhub.info/MitM/Models" module="Density" name="density_dim"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/densities2.mmt#422.10.48:432.10.58"/></metadata></om:OMS></om:OMOBJ></type>
<notations><notation dimension="1" precedence="0" fixity="mixfix" arguments="N_c"> <scope languages="" priority="0"/> </notation></notations>
- </constant><opaque format="text"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/densities.mmt#401.10.2:491.11.32"/></metadata>The effective density of states for the valence bands
- usually denoted by <om:OMOBJ xmlns:om="http://www.openmath.org/OpenMath"><om:OMS base="http://mathhub.info/MitM/Models/densities" module="BandstructureParameters" name="effective_density_of_states_valence_bands"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/densities.mmt#484.-1.-1:486.-1.1"/></metadata></om:OMS></om:OMOBJ>.</opaque><constant name="effective_density_of_states_valence_bands">
- <metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/densities.mmt#493.12.1:548.12.56"/></metadata>
- <type><om:OMOBJ xmlns:om="http://www.openmath.org/OpenMath"><om:OMS base="http://mathhub.info/MitM/numberfields" module="realnumbers" name="Realnumbers"></om:OMS></om:OMOBJ></type>
+ </constant><opaque format="text"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/densities2.mmt#446.11.2:536.12.32"/></metadata>The effective density of states for the valence bands
+ usually denoted by <unparsed>None</unparsed>.</opaque><constant name="effective_density_of_states_valence_bands">
+ <metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/densities2.mmt#538.13.1:603.13.66"/></metadata>
+ <type><om:OMOBJ xmlns:om="http://www.openmath.org/OpenMath"><om:OMS base="http://mathhub.info/MitM/Models" module="Density" name="density_dim"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/densities2.mmt#582.13.45:592.13.55"/></metadata></om:OMS></om:OMOBJ></type>
<notations><notation dimension="1" precedence="0" fixity="mixfix" arguments="N_v"> <scope languages="" priority="0"/> </notation></notations>
- </constant><opaque format="text"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/densities.mmt#551.13.2:606.13.57"/></metadata>The conduction band edge usually denoted by <om:OMOBJ xmlns:om="http://www.openmath.org/OpenMath"><om:OMS base="http://mathhub.info/MitM/Models/densities" module="BandstructureParameters" name="conduction_band_edge"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/densities.mmt#599.-1.-1:601.-1.1"/></metadata></om:OMS></om:OMOBJ>.</opaque><constant name="conduction_band_edge">
- <metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/densities.mmt#608.14.1:642.14.35"/></metadata>
- <type><om:OMOBJ xmlns:om="http://www.openmath.org/OpenMath"><om:OMS base="http://mathhub.info/MitM/numberfields" module="realnumbers" name="Realnumbers"></om:OMS></om:OMOBJ></type>
+ </constant><opaque format="text"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/densities2.mmt#606.14.2:661.14.57"/></metadata>The conduction band edge usually denoted by <unparsed>None</unparsed>.</opaque><constant name="conduction_band_edge">
+ <metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/densities2.mmt#663.15.1:705.15.43"/></metadata>
+ <type><om:OMOBJ xmlns:om="http://www.openmath.org/OpenMath"><om:OMA><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/densities2.mmt#686.15.24:694.15.32"/></metadata>
+ <om:OMS base="http://cds.omdoc.org/urtheories" module="LambdaPi" name="apply"></om:OMS>
+ <om:OMS base="http://mathhub.info/MMT/physics-units" module="QEBase" name="QE"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/densities2.mmt#686.15.24:687.15.25"/></metadata></om:OMS><om:OMS base="http://mathhub.info/MMT/physics-units" module="DimensionsExtended" name="Energy"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/densities2.mmt#689.15.27:694.15.32"/></metadata></om:OMS>
+ </om:OMA></om:OMOBJ></type>
<notations><notation dimension="1" precedence="0" fixity="mixfix" arguments="E_c"> <scope languages="" priority="0"/> </notation></notations>
- </constant><opaque format="text"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/densities.mmt#645.15.2:697.15.54"/></metadata>The valence band edge usually denoted by <om:OMOBJ xmlns:om="http://www.openmath.org/OpenMath"><om:OMS base="http://mathhub.info/MitM/Models/densities" module="BandstructureParameters" name="valence_band_edge"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/densities.mmt#690.-1.-1:692.-1.1"/></metadata></om:OMS></om:OMOBJ>.</opaque><constant name="valence_band_edge">
- <metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/densities.mmt#699.16.1:730.16.32"/></metadata>
- <type><om:OMOBJ xmlns:om="http://www.openmath.org/OpenMath"><om:OMS base="http://mathhub.info/MitM/numberfields" module="realnumbers" name="Realnumbers"></om:OMS></om:OMOBJ></type>
+ </constant><opaque format="text"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/densities2.mmt#708.16.2:760.16.54"/></metadata>The valence band edge usually denoted by <unparsed>None</unparsed>.</opaque><constant name="valence_band_edge">
+ <metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/densities2.mmt#762.17.1:801.17.40"/></metadata>
+ <type><om:OMOBJ xmlns:om="http://www.openmath.org/OpenMath"><om:OMA><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/densities2.mmt#782.17.21:790.17.29"/></metadata>
+ <om:OMS base="http://cds.omdoc.org/urtheories" module="LambdaPi" name="apply"></om:OMS>
+ <om:OMS base="http://mathhub.info/MMT/physics-units" module="QEBase" name="QE"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/densities2.mmt#782.17.21:783.17.22"/></metadata></om:OMS><om:OMS base="http://mathhub.info/MMT/physics-units" module="DimensionsExtended" name="Energy"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/densities2.mmt#785.17.24:790.17.29"/></metadata></om:OMS>
+ </om:OMA></om:OMOBJ></type>
<notations><notation dimension="1" precedence="0" fixity="mixfix" arguments="E_v"> <scope languages="" priority="0"/> </notation></notations>
- </constant><opaque format="text"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/densities.mmt#733.17.2:805.17.74"/></metadata>N.B.: The band gap of the semiconductor is given by Eg = <om:OMOBJ xmlns:om="http://www.openmath.org/OpenMath"><om:OMA><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/densities.mmt#794.-1.-1:800.-1.5"/></metadata>
- <om:OMS base="http://cds.omdoc.org/urtheories" module="LambdaPi" name="apply"></om:OMS>
- <om:OMS base="http://mathhub.info/MitM/numberfields" module="realarith" name="bin_minus"></om:OMS><om:OMS base="http://mathhub.info/MitM/Models/densities" module="BandstructureParameters" name="conduction_band_edge"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/densities.mmt#794.-1.-1:796.-1.1"/></metadata></om:OMS><om:OMS base="http://mathhub.info/MitM/Models/densities" module="BandstructureParameters" name="valence_band_edge"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/densities.mmt#798.-1.3:800.-1.5"/></metadata></om:OMS>
- </om:OMA></om:OMOBJ>.</opaque></theory></omdoc>
\ No newline at end of file
+ </constant><opaque format="text"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/densities2.mmt#804.18.2:876.18.74"/></metadata>N.B.: The band gap of the semiconductor is given by Eg = <unparsed>None</unparsed>.</opaque></theory></omdoc>
\ No newline at end of file
diff --git a/content/http..mathhub.info/MitM/Models/densities/$Electrostatic$Potential.omdoc b/content/http..mathhub.info/MitM/Models/densities/$Electrostatic$Potential.omdoc
index 187cf22..e9c6c99 100644
--- a/content/http..mathhub.info/MitM/Models/densities/$Electrostatic$Potential.omdoc
+++ b/content/http..mathhub.info/MitM/Models/densities/$Electrostatic$Potential.omdoc
@@ -1,9 +1,12 @@
-<omdoc xmlns="http://omdoc.org/ns" xmlns:om="http://www.openmath.org/OpenMath"><theory name="ElectrostaticPotential" base="http://mathhub.info/MitM/Models/densities" meta="http://mathhub.info/MitM/Models?Base"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/densities.mmt#1721.46.0:1925.52.1"/></metadata><import from="http://mathhub.info/MitM/Models/device?DeviceGeometry"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/densities.mmt#1766.47.1:1796.47.31"/></metadata></import><opaque format="text"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/densities.mmt#1800.49.1:1882.50.29"/></metadata>Spatial variation of the electrostatic potential,
- usually denoted by <om:OMOBJ xmlns:om="http://www.openmath.org/OpenMath"><om:OMS base="http://mathhub.info/MitM/Models/densities" module="ElectrostaticPotential" name="electrostatic_potential"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/densities.mmt#1877.-1.-1:1877.-1.-1"/></metadata></om:OMS></om:OMOBJ>.</opaque><constant name="electrostatic_potential">
- <metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/densities.mmt#1884.51.1:1923.51.40"/></metadata>
- <type><om:OMOBJ xmlns:om="http://www.openmath.org/OpenMath"><om:OMA>
+<omdoc xmlns="http://omdoc.org/ns" xmlns:om="http://www.openmath.org/OpenMath"><theory name="ElectrostaticPotential" base="http://mathhub.info/MitM/Models/densities" meta="http://mathhub.info/MitM/Models?Base"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/densities2.mmt#1432.36.0:1657.42.1"/></metadata><import from="http://mathhub.info/MitM/Models/device?DeviceGeometry"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/densities2.mmt#1477.37.1:1507.37.31"/></metadata></import><opaque format="text"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/densities2.mmt#1511.39.1:1593.40.29"/></metadata>Spatial variation of the electrostatic potential,
+ usually denoted by <om:OMOBJ xmlns:om="http://www.openmath.org/OpenMath"><om:OMS base="http://mathhub.info/MitM/Models/densities" module="ElectrostaticPotential" name="electrostatic_potential"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/densities2.mmt#1588.-1.-1:1588.-1.-1"/></metadata></om:OMS></om:OMOBJ>.</opaque><constant name="electrostatic_potential">
+ <metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/densities2.mmt#1595.41.1:1655.41.61"/></metadata>
+ <type><om:OMOBJ xmlns:om="http://www.openmath.org/OpenMath"><om:OMA><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/densities2.mmt#1621.41.27:1646.41.52"/></metadata>
<om:OMS base="http://cds.omdoc.org/urtheories" module="LambdaPi" name="arrow"></om:OMS>
- <om:OMS base="http://mathhub.info/MitM/Models/device" module="DeviceGeometry" name="domain"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/densities.mmt#1910.51.27:1910.51.27"/></metadata></om:OMS><om:OMS base="http://mathhub.info/MitM/numberfields" module="realnumbers" name="Realnumbers"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/densities.mmt#1914.51.31:1914.51.31"/></metadata></om:OMS>
+ <om:OMS base="http://mathhub.info/MitM/Models/device" module="DeviceGeometry" name="domain"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/densities2.mmt#1621.41.27:1621.41.27"/></metadata></om:OMS><om:OMA><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/densities2.mmt#1625.41.31:1646.41.52"/></metadata>
+ <om:OMS base="http://cds.omdoc.org/urtheories" module="LambdaPi" name="apply"></om:OMS>
+ <om:OMS base="http://mathhub.info/MMT/physics-units" module="QEBase" name="QE"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/densities2.mmt#1626.41.32:1627.41.33"/></metadata></om:OMS><om:OMS base="http://mathhub.info/MMT/physics-units" module="DimensionsExtended" name="ElectricPotential"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/densities2.mmt#1629.41.35:1645.41.51"/></metadata></om:OMS>
+ </om:OMA>
</om:OMA></om:OMOBJ></type>
<notations><notation dimension="1" precedence="0" fixity="mixfix" arguments="ψ"> <scope languages="" priority="0"/> </notation></notations>
diff --git a/content/http..mathhub.info/MitM/Models/densities/$Fermi$Potential$Electrons.omdoc b/content/http..mathhub.info/MitM/Models/densities/$Fermi$Potential$Electrons.omdoc
index a08e288..d884294 100644
--- a/content/http..mathhub.info/MitM/Models/densities/$Fermi$Potential$Electrons.omdoc
+++ b/content/http..mathhub.info/MitM/Models/densities/$Fermi$Potential$Electrons.omdoc
@@ -1,10 +1,21 @@
-<omdoc xmlns="http://omdoc.org/ns" xmlns:om="http://www.openmath.org/OpenMath"><theory name="FermiPotentialElectrons" base="http://mathhub.info/MitM/Models/densities" meta="http://mathhub.info/MitM/Models?Base"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/densities.mmt#965.24.0:1188.29.1"/></metadata><import from="http://mathhub.info/MitM/Models/device?DeviceGeometry"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/densities.mmt#1011.25.1:1041.25.31"/></metadata></import><opaque format="text"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/densities.mmt#1045.26.2:1145.27.31"/></metadata>Spatial variation of the quasi-Fermi potential for the electrons,
- usually denoted by <om:OMOBJ xmlns:om="http://www.openmath.org/OpenMath"><om:OMS base="http://mathhub.info/MitM/Models/densities" module="FermiPotentialElectrons" name="quasi_Fermi_potential"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/densities.mmt#1138.-1.-1:1140.-1.1"/></metadata></om:OMS></om:OMOBJ>.</opaque><constant name="quasi_Fermi_potential">
- <metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/densities.mmt#1147.28.1:1186.28.40"/></metadata>
- <type><om:OMOBJ xmlns:om="http://www.openmath.org/OpenMath"><om:OMA>
+<omdoc xmlns="http://omdoc.org/ns" xmlns:om="http://www.openmath.org/OpenMath"><theory name="FermiPotentialElectrons" base="http://mathhub.info/MitM/Models/densities" meta="http://mathhub.info/MitM/Models?Base"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/densities.mmt#1049.25.0:1293.30.1"/></metadata><import from="http://mathhub.info/MitM/Models/device?DeviceGeometry"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/densities.mmt#1095.26.1:1125.26.31"/></metadata></import><opaque format="text"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/densities.mmt#1129.27.2:1229.28.31"/></metadata>Spatial variation of the quasi-Fermi potential for the electrons,
+ usually denoted by <om:OMOBJ xmlns:om="http://www.openmath.org/OpenMath"><om:OMS base="http://mathhub.info/MitM/Models/densities" module="FermiPotentialElectrons" name="quasi_Fermi_potential"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/densities.mmt#1222.-1.-1:1224.-1.1"/></metadata></om:OMS></om:OMOBJ>.</opaque><constant name="quasi_Fermi_potential">
+ <metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/densities.mmt#1231.29.1:1291.29.61"/></metadata>
+ <type><om:OMOBJ xmlns:om="http://www.openmath.org/OpenMath"><om:OMBIND>
+ <om:OMS base="http://cds.omdoc.org/mmt" module="mmt" name="unknown"></om:OMS>
+ <om:OMBVAR><om:OMV name="/Ω/0"></om:OMV></om:OMBVAR>
+ <om:OMBIND>
+ <om:OMS base="http://cds.omdoc.org/mmt" module="mmt" name="free"></om:OMS>
+ <om:OMBVAR><om:OMV name="Ω"><type><om:OMV name="/Ω/0"></om:OMV></type></om:OMV></om:OMBVAR>
+ <om:OMA><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/densities.mmt#1255.29.25:1280.29.50"/></metadata>
<om:OMS base="http://cds.omdoc.org/urtheories" module="LambdaPi" name="arrow"></om:OMS>
- <om:OMS base="http://mathhub.info/MitM/Models/device" module="DeviceGeometry" name="domain"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/densities.mmt#1171.28.25:1171.28.25"/></metadata></om:OMS><om:OMS base="http://mathhub.info/MitM/numberfields" module="realnumbers" name="Realnumbers"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/densities.mmt#1175.28.29:1175.28.29"/></metadata></om:OMS>
- </om:OMA></om:OMOBJ></type>
+ <om:OMV name="Ω"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/densities.mmt#1255.29.25:1255.29.25"/></metadata></om:OMV><om:OMA><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/densities.mmt#1259.29.29:1280.29.50"/></metadata>
+ <om:OMS base="http://cds.omdoc.org/urtheories" module="LambdaPi" name="apply"></om:OMS>
+ <om:OMS base="http://mathhub.info/MMT/physics-units" module="QEBase" name="QE"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/densities.mmt#1260.29.30:1261.29.31"/></metadata></om:OMS><om:OMS base="http://mathhub.info/MMT/physics-units" module="DimensionsExtended" name="ElectricPotential"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/densities.mmt#1263.29.33:1279.29.49"/></metadata></om:OMS>
+ </om:OMA>
+ </om:OMA>
+ </om:OMBIND>
+ </om:OMBIND></om:OMOBJ></type>
<notations><notation dimension="1" precedence="0" fixity="mixfix" arguments="φ_n"> <scope languages="" priority="0"/> </notation></notations>
</constant></theory></omdoc>
\ No newline at end of file
diff --git a/content/http..mathhub.info/MitM/Models/densities/$Fermi$Potential$Holes.omdoc b/content/http..mathhub.info/MitM/Models/densities/$Fermi$Potential$Holes.omdoc
index c0ed854..559afad 100644
--- a/content/http..mathhub.info/MitM/Models/densities/$Fermi$Potential$Holes.omdoc
+++ b/content/http..mathhub.info/MitM/Models/densities/$Fermi$Potential$Holes.omdoc
@@ -1,10 +1,21 @@
-<omdoc xmlns="http://omdoc.org/ns" xmlns:om="http://www.openmath.org/OpenMath"><theory name="FermiPotentialHoles" base="http://mathhub.info/MitM/Models/densities" meta="http://mathhub.info/MitM/Models?Base"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/densities.mmt#1355.35.0:1569.40.1"/></metadata><import from="http://mathhub.info/MitM/Models/device?DeviceGeometry"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/densities.mmt#1397.36.1:1427.36.31"/></metadata></import><opaque format="text"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/densities.mmt#1430.37.1:1526.38.31"/></metadata>Spatial variation of the quasi-Fermi potential for the holes,
- usually denoted by <om:OMOBJ xmlns:om="http://www.openmath.org/OpenMath"><om:OMS base="http://mathhub.info/MitM/Models/densities" module="FermiPotentialHoles" name="quasi_Fermi_potential"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/densities.mmt#1519.-1.-1:1521.-1.1"/></metadata></om:OMS></om:OMOBJ>.</opaque><constant name="quasi_Fermi_potential">
- <metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/densities.mmt#1528.39.1:1567.39.40"/></metadata>
- <type><om:OMOBJ xmlns:om="http://www.openmath.org/OpenMath"><om:OMA>
+<omdoc xmlns="http://omdoc.org/ns" xmlns:om="http://www.openmath.org/OpenMath"><theory name="FermiPotentialHoles" base="http://mathhub.info/MitM/Models/densities" meta="http://mathhub.info/MitM/Models?Base"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/densities.mmt#1475.36.0:1710.41.1"/></metadata><import from="http://mathhub.info/MitM/Models/device?DeviceGeometry"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/densities.mmt#1517.37.1:1547.37.31"/></metadata></import><opaque format="text"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/densities.mmt#1550.38.1:1646.39.31"/></metadata>Spatial variation of the quasi-Fermi potential for the holes,
+ usually denoted by <om:OMOBJ xmlns:om="http://www.openmath.org/OpenMath"><om:OMS base="http://mathhub.info/MitM/Models/densities" module="FermiPotentialHoles" name="quasi_Fermi_potential"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/densities.mmt#1639.-1.-1:1641.-1.1"/></metadata></om:OMS></om:OMOBJ>.</opaque><constant name="quasi_Fermi_potential">
+ <metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/densities.mmt#1648.40.1:1708.40.61"/></metadata>
+ <type><om:OMOBJ xmlns:om="http://www.openmath.org/OpenMath"><om:OMBIND>
+ <om:OMS base="http://cds.omdoc.org/mmt" module="mmt" name="unknown"></om:OMS>
+ <om:OMBVAR><om:OMV name="/Ω/0"></om:OMV></om:OMBVAR>
+ <om:OMBIND>
+ <om:OMS base="http://cds.omdoc.org/mmt" module="mmt" name="free"></om:OMS>
+ <om:OMBVAR><om:OMV name="Ω"><type><om:OMV name="/Ω/0"></om:OMV></type></om:OMV></om:OMBVAR>
+ <om:OMA><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/densities.mmt#1672.40.25:1697.40.50"/></metadata>
<om:OMS base="http://cds.omdoc.org/urtheories" module="LambdaPi" name="arrow"></om:OMS>
- <om:OMS base="http://mathhub.info/MitM/Models/device" module="DeviceGeometry" name="domain"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/densities.mmt#1552.39.25:1552.39.25"/></metadata></om:OMS><om:OMS base="http://mathhub.info/MitM/numberfields" module="realnumbers" name="Realnumbers"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/densities.mmt#1556.39.29:1556.39.29"/></metadata></om:OMS>
- </om:OMA></om:OMOBJ></type>
+ <om:OMV name="Ω"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/densities.mmt#1672.40.25:1672.40.25"/></metadata></om:OMV><om:OMA><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/densities.mmt#1676.40.29:1697.40.50"/></metadata>
+ <om:OMS base="http://cds.omdoc.org/urtheories" module="LambdaPi" name="apply"></om:OMS>
+ <om:OMS base="http://mathhub.info/MMT/physics-units" module="QEBase" name="QE"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/densities.mmt#1677.40.30:1678.40.31"/></metadata></om:OMS><om:OMS base="http://mathhub.info/MMT/physics-units" module="DimensionsExtended" name="ElectricPotential"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/densities.mmt#1680.40.33:1696.40.49"/></metadata></om:OMS>
+ </om:OMA>
+ </om:OMA>
+ </om:OMBIND>
+ </om:OMBIND></om:OMOBJ></type>
<notations><notation dimension="1" precedence="0" fixity="mixfix" arguments="φ_p"> <scope languages="" priority="0"/> </notation></notations>
</constant></theory></omdoc>
\ No newline at end of file
diff --git a/content/http..mathhub.info/MitM/Models/device/$Device$Geometry.omdoc b/content/http..mathhub.info/MitM/Models/device/$Device$Geometry.omdoc
index a933e9e..c9f1431 100644
--- a/content/http..mathhub.info/MitM/Models/device/$Device$Geometry.omdoc
+++ b/content/http..mathhub.info/MitM/Models/device/$Device$Geometry.omdoc
@@ -1,17 +1,17 @@
-<omdoc xmlns="http://omdoc.org/ns" xmlns:om="http://www.openmath.org/OpenMath"><theory name="DeviceGeometry" base="http://mathhub.info/MitM/Models/device" meta="http://mathhub.info/MitM/Models?Base"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/device.mmt#255.7.0:532.14.1"/></metadata><import from="http://mathhub.info/MitM/Models/device?Device"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/device.mmt#292.8.1:308.8.17"/></metadata></import><constant name="domain_prop">
- <metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/device.mmt#341.10.1:365.10.25"/></metadata>
- <type><om:OMOBJ xmlns:om="http://www.openmath.org/OpenMath"><om:OMA><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/device.mmt#355.10.15:362.10.22"/></metadata>
+<omdoc xmlns="http://omdoc.org/ns" xmlns:om="http://www.openmath.org/OpenMath"><theory name="DeviceGeometry" base="http://mathhub.info/MitM/Models/device" meta="http://mathhub.info/MitM/Models?Base"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/device.mmt#290.9.0:567.16.1"/></metadata><import from="http://mathhub.info/MitM/Models/device?Device"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/device.mmt#327.10.1:343.10.17"/></metadata></import><constant name="domain_prop">
+ <metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/device.mmt#376.12.1:400.12.25"/></metadata>
+ <type><om:OMOBJ xmlns:om="http://www.openmath.org/OpenMath"><om:OMA><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/device.mmt#390.12.15:397.12.22"/></metadata>
<om:OMS base="http://cds.omdoc.org/urtheories" module="LambdaPi" name="arrow"></om:OMS>
- <om:OMS base="http://mathhub.info/MitM/numberfields" module="realnumbers" name="Realnumbers"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/device.mmt#355.10.15:355.10.15"/></metadata></om:OMS><om:OMS base="http://mathhub.info/MitM/Foundation" module="Logic" name="bool"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/device.mmt#359.10.19:362.10.22"/></metadata></om:OMS>
+ <om:OMS base="http://mathhub.info/MitM/Foundation" module="Literals" name="real_lit"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/device.mmt#390.12.15:390.12.15"/></metadata></om:OMS><om:OMS base="http://mathhub.info/MitM/Foundation" module="Logic" name="bool"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/device.mmt#394.12.19:397.12.22"/></metadata></om:OMS>
</om:OMA></om:OMOBJ></type>
- </constant><opaque format="text"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/device.mmt#367.11.1:438.11.72"/></metadata>The one-dimensional spatial domain of the device (denoted by <om:OMOBJ xmlns:om="http://www.openmath.org/OpenMath"><om:OMS base="http://mathhub.info/MitM/Models/device" module="DeviceGeometry" name="domain"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/device.mmt#432.-1.-1:432.-1.-1"/></metadata></om:OMS></om:OMOBJ>).</opaque><constant name="domain">
- <metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/device.mmt#488.13.1:530.13.43"/></metadata>
- <type><om:OMOBJ xmlns:om="http://www.openmath.org/OpenMath"><om:OMS base="http://cds.omdoc.org/urtheories" module="Typed" name="type"></om:OMS></om:OMOBJ></type>
- <definition><om:OMOBJ xmlns:om="http://www.openmath.org/OpenMath"><om:OMA><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/device.mmt#506.13.19:521.13.34"/></metadata>
+ </constant><opaque format="text"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/device.mmt#402.13.1:473.13.72"/></metadata>The one-dimensional spatial domain of the device (denoted by <om:OMOBJ xmlns:om="http://www.openmath.org/OpenMath"><om:OMS base="http://mathhub.info/MitM/Models/device" module="DeviceGeometry" name="domain"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/device.mmt#467.-1.-1:467.-1.-1"/></metadata></om:OMS></om:OMOBJ>).</opaque><constant name="domain">
+ <metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/device.mmt#523.15.1:565.15.43"/></metadata>
+ <type><om:OMOBJ xmlns:om="http://www.openmath.org/OpenMath"><om:OMS base="http://cds.omdoc.org/urtheories" module="Typed" name="type"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/device.mmt#532.15.10:535.15.13"/></metadata></om:OMS></om:OMOBJ></type>
+ <definition><om:OMOBJ xmlns:om="http://www.openmath.org/OpenMath"><om:OMA><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/device.mmt#541.15.19:556.15.34"/></metadata>
<om:OMS base="http://cds.omdoc.org/urtheories" module="LambdaPi" name="apply"></om:OMS>
- <om:OMS base="http://mathhub.info/MitM/numberfields" module="realarith" name="pred_as_sub"></om:OMS><om:OMS base="http://mathhub.info/MitM/Models/device" module="DeviceGeometry" name="domain_prop"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/device.mmt#511.13.24:521.13.34"/></metadata></om:OMS>
+ <om:OMS base="http://mathhub.info/MitM/smglom/arithmetics" module="realarith" name="pred_as_sub"></om:OMS><om:OMS base="http://mathhub.info/MitM/Models/device" module="DeviceGeometry" name="domain_prop"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/device.mmt#546.15.24:556.15.34"/></metadata></om:OMS>
</om:OMA></om:OMOBJ></definition>
<notations><notation dimension="1" precedence="0" fixity="mixfix" arguments="Ω"> <scope languages="" priority="0"/> </notation></notations>
</constant></theory></omdoc>
\ No newline at end of file
diff --git a/content/http..mathhub.info/MitM/Models/device/$Device$Operation$State.omdoc b/content/http..mathhub.info/MitM/Models/device/$Device$Operation$State.omdoc
index 16fb097..fbb8c90 100644
--- a/content/http..mathhub.info/MitM/Models/device/$Device$Operation$State.omdoc
+++ b/content/http..mathhub.info/MitM/Models/device/$Device$Operation$State.omdoc
@@ -1,30 +1,25 @@
-<omdoc xmlns="http://omdoc.org/ns" xmlns:om="http://www.openmath.org/OpenMath"><theory name="DeviceOperationState" base="http://mathhub.info/MitM/Models/device" meta="http://mathhub.info/MitM/Models?Base"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/device.mmt#1367.48.0:1797.60.1"/></metadata><import from="http://mathhub.info/MitM/Models/device?DeviceGeometry"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/device.mmt#1410.49.1:1434.49.25"/></metadata></import><opaque format="text"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/device.mmt#1437.50.1:1494.50.58"/></metadata>The global temperature of the device denoted by <om:OMOBJ xmlns:om="http://www.openmath.org/OpenMath"><om:OMS base="http://mathhub.info/MitM/Models/device" module="DeviceOperationState" name="temperatur"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/device.mmt#1489.-1.-1:1489.-1.-1"/></metadata></om:OMS></om:OMOBJ>.</opaque><constant name="temperatur">
- <metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/device.mmt#1528.52.1:1550.52.23"/></metadata>
- <type><om:OMOBJ xmlns:om="http://www.openmath.org/OpenMath"><om:OMS base="http://mathhub.info/MitM/numberfields" module="realnumbers" name="Realnumbers"></om:OMS></om:OMOBJ></type>
+<omdoc xmlns="http://omdoc.org/ns" xmlns:om="http://www.openmath.org/OpenMath"><theory name="DeviceOperationState" base="http://mathhub.info/MitM/Models/device" meta="http://mathhub.info/MitM/Models?Base"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/device.mmt#1463.51.0:1925.62.1"/></metadata><import from="http://mathhub.info/MitM/Models/device?DeviceGeometry"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/device.mmt#1506.52.1:1530.52.25"/></metadata></import><opaque format="text"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/device.mmt#1533.53.1:1590.53.58"/></metadata>The global temperature of the device denoted by <om:OMOBJ xmlns:om="http://www.openmath.org/OpenMath"><om:OMS base="http://mathhub.info/MitM/Models/device" module="DeviceOperationState" name="temperature"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/device.mmt#1585.-1.-1:1585.-1.-1"/></metadata></om:OMS></om:OMOBJ>.</opaque><constant name="temperature">
+ <metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/device.mmt#1624.55.1:1662.55.39"/></metadata>
+ <type><om:OMOBJ xmlns:om="http://www.openmath.org/OpenMath"><om:OMA><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/device.mmt#1638.55.15:1653.55.30"/></metadata>
+ <om:OMS base="http://cds.omdoc.org/urtheories" module="LambdaPi" name="apply"></om:OMS>
+ <om:OMS base="http://mathhub.info/MMT/physics-units" module="QEBase" name="QE"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/device.mmt#1638.55.15:1639.55.16"/></metadata></om:OMS><om:OMS base="http://mathhub.info/MMT/physics-units" module="Dimensions" name="SItemperature"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/device.mmt#1641.55.18:1653.55.30"/></metadata></om:OMS>
+ </om:OMA></om:OMOBJ></type>
<notations><notation dimension="1" precedence="0" fixity="mixfix" arguments="T"> <scope languages="" priority="0"/> </notation></notations>
- </constant><opaque format="text"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/device.mmt#1552.53.1:1616.53.65"/></metadata>The applied voltage at the bottom contact denoted by <om:OMOBJ xmlns:om="http://www.openmath.org/OpenMath"><om:OMS base="http://mathhub.info/MitM/Models/device" module="DeviceOperationState" name="voltage_bottom"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/device.mmt#1609.-1.-1:1611.-1.1"/></metadata></om:OMS></om:OMOBJ>.</opaque><constant name="voltage_bottom">
- <metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/device.mmt#1618.54.1:1646.54.29"/></metadata>
- <type><om:OMOBJ xmlns:om="http://www.openmath.org/OpenMath"><om:OMS base="http://mathhub.info/MitM/numberfields" module="realnumbers" name="Realnumbers"></om:OMS></om:OMOBJ></type>
+ </constant><opaque format="text"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/device.mmt#1664.56.1:1728.56.65"/></metadata>The applied voltage at the bottom contact denoted by <unparsed>None</unparsed>.</opaque><constant name="voltage_bottom">
+ <metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/device.mmt#1730.57.1:1777.57.48"/></metadata>
+ <type><om:OMOBJ xmlns:om="http://www.openmath.org/OpenMath"><om:OMA><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/device.mmt#1747.57.18:1766.57.37"/></metadata>
+ <om:OMS base="http://cds.omdoc.org/urtheories" module="LambdaPi" name="apply"></om:OMS>
+ <om:OMS base="http://mathhub.info/MMT/physics-units" module="QEBase" name="QE"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/device.mmt#1747.57.18:1748.57.19"/></metadata></om:OMS><om:OMS base="http://mathhub.info/MMT/physics-units" module="DimensionsExtended" name="ElectricPotential"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/device.mmt#1750.57.21:1766.57.37"/></metadata></om:OMS>
+ </om:OMA></om:OMOBJ></type>
<notations><notation dimension="1" precedence="0" fixity="mixfix" arguments="U_1"> <scope languages="" priority="0"/> </notation></notations>
- </constant><opaque format="text"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/device.mmt#1648.55.1:1709.55.62"/></metadata>The applied voltage at the top contact denoted by <om:OMOBJ xmlns:om="http://www.openmath.org/OpenMath"><om:OMS base="http://mathhub.info/MitM/Models/device" module="DeviceOperationState" name="voltage_top"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/device.mmt#1702.-1.-1:1704.-1.1"/></metadata></om:OMS></om:OMOBJ>.</opaque><constant name="voltage_top">
- <metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/device.mmt#1711.56.1:1736.56.26"/></metadata>
- <type><om:OMOBJ xmlns:om="http://www.openmath.org/OpenMath"><om:OMS base="http://mathhub.info/MitM/numberfields" module="realnumbers" name="Realnumbers"></om:OMS></om:OMOBJ></type>
-
- <notations><notation dimension="1" precedence="0" fixity="mixfix" arguments="U_2"> <scope languages="" priority="0"/> </notation></notations>
- </constant><constant name="prf">
- <metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/device.mmt#1774.59.1:1795.59.22"/></metadata>
- <type><om:OMOBJ xmlns:om="http://www.openmath.org/OpenMath"><om:OMA><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/device.mmt#1780.59.7:1792.59.19"/></metadata>
- <om:OMS base="http://cds.omdoc.org/urtheories" module="LambdaPi" name="apply"></om:OMS>
- <om:OMS base="http://mathhub.info/MitM/Foundation" module="Logic" name="ded"></om:OMS><om:OMA><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/device.mmt#1782.59.9:1792.59.19"/></metadata>
- <om:OMS base="http://cds.omdoc.org/urtheories" module="LambdaPi" name="apply"></om:OMS>
- <om:OMS base="http://mathhub.info/MitM/Foundation" module="Logic" name="neq"></om:OMS><om:OMS base="http://mathhub.info/MitM/numberfields" module="realnumbers" name="Realnumbers"></om:OMS><om:OMA><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/device.mmt#1782.59.9:1788.59.15"/></metadata>
+ </constant><opaque format="text"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/device.mmt#1779.58.1:1840.58.62"/></metadata>The applied voltage at the top contact denoted by <unparsed>None</unparsed>.</opaque><constant name="voltage_top">
+ <metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/device.mmt#1842.59.1:1886.59.45"/></metadata>
+ <type><om:OMOBJ xmlns:om="http://www.openmath.org/OpenMath"><om:OMA><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/device.mmt#1856.59.15:1875.59.34"/></metadata>
<om:OMS base="http://cds.omdoc.org/urtheories" module="LambdaPi" name="apply"></om:OMS>
- <om:OMS base="http://mathhub.info/MitM/numberfields" module="realarith" name="multiplication"></om:OMS><om:OMS base="http://mathhub.info/MitM/Models" module="PhysicalConstants" name="Boltzmann_constant"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/device.mmt#1782.59.9:1784.59.11"/></metadata></om:OMS><om:OMS base="http://mathhub.info/MitM/Models/device" module="DeviceOperationState" name="temperatur"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/device.mmt#1788.59.15:1788.59.15"/></metadata></om:OMS>
- </om:OMA><om:OMLIT type="http://mathhub.info/MitM/Foundation?Literals?nat_lit" value="0"/>
- </om:OMA>
+ <om:OMS base="http://mathhub.info/MMT/physics-units" module="QEBase" name="QE"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/device.mmt#1856.59.15:1857.59.16"/></metadata></om:OMS><om:OMS base="http://mathhub.info/MMT/physics-units" module="DimensionsExtended" name="ElectricPotential"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/device.mmt#1859.59.18:1875.59.34"/></metadata></om:OMS>
</om:OMA></om:OMOBJ></type>
-
+ <notations><notation dimension="1" precedence="0" fixity="mixfix" arguments="U_2"> <scope languages="" priority="0"/> </notation></notations>
</constant></theory></omdoc>
\ No newline at end of file
diff --git a/content/http..mathhub.info/MitM/Models/device/$Device.omdoc b/content/http..mathhub.info/MitM/Models/device/$Device.omdoc
index 37c4b44..483fd23 100644
--- a/content/http..mathhub.info/MitM/Models/device/$Device.omdoc
+++ b/content/http..mathhub.info/MitM/Models/device/$Device.omdoc
@@ -1 +1 @@
-<omdoc xmlns="http://omdoc.org/ns" xmlns:om="http://www.openmath.org/OpenMath"><theory name="Device" base="http://mathhub.info/MitM/Models/device"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/device.mmt#169.4.0:186.4.17"/></metadata></theory></omdoc>
\ No newline at end of file
+<omdoc xmlns="http://omdoc.org/ns" xmlns:om="http://www.openmath.org/OpenMath"><theory name="Device" base="http://mathhub.info/MitM/Models/device"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/device.mmt#187.5.0:204.5.17"/></metadata></theory></omdoc>
\ No newline at end of file
diff --git a/content/http..mathhub.info/MitM/Models/device/$Doping$Profile.omdoc b/content/http..mathhub.info/MitM/Models/device/$Doping$Profile.omdoc
index 9e296dd..d387a1f 100644
--- a/content/http..mathhub.info/MitM/Models/device/$Doping$Profile.omdoc
+++ b/content/http..mathhub.info/MitM/Models/device/$Doping$Profile.omdoc
@@ -1,8 +1,8 @@
-<omdoc xmlns="http://omdoc.org/ns" xmlns:om="http://www.openmath.org/OpenMath"><theory name="DopingProfile" base="http://mathhub.info/MitM/Models/device" meta="http://mathhub.info/MitM/Models?Base"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/device.mmt#1092.38.0:1231.42.1"/></metadata><import from="http://mathhub.info/MitM/Models/device?DeviceGeometry"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/device.mmt#1128.39.1:1152.39.25"/></metadata></import><opaque format="text"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/device.mmt#1156.40.2:1196.40.42"/></metadata>The doping profile, denoted by <om:OMOBJ xmlns:om="http://www.openmath.org/OpenMath"><om:OMS base="http://mathhub.info/MitM/Models/device" module="DopingProfile" name="doping_profile"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/device.mmt#1191.-1.-1:1191.-1.-1"/></metadata></om:OMS></om:OMOBJ>.</opaque><constant name="doping_profile">
- <metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/device.mmt#1198.41.1:1229.41.32"/></metadata>
- <type><om:OMOBJ xmlns:om="http://www.openmath.org/OpenMath"><om:OMA>
+<omdoc xmlns="http://omdoc.org/ns" xmlns:om="http://www.openmath.org/OpenMath"><theory name="DopingProfile" base="http://mathhub.info/MitM/Models/device" meta="http://mathhub.info/MitM/Models?Base"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/device.mmt#1138.40.0:1311.45.1"/></metadata><import from="http://mathhub.info/MitM/Models/device?DeviceGeometry"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/device.mmt#1174.41.1:1198.41.25"/></metadata></import><import from="http://mathhub.info/MitM/Models?Density"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/device.mmt#1201.42.1:1222.42.22"/></metadata></import><opaque format="text"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/device.mmt#1226.43.2:1266.43.42"/></metadata>The doping profile, denoted by <om:OMOBJ xmlns:om="http://www.openmath.org/OpenMath"><om:OMS base="http://mathhub.info/MitM/Models/device" module="DopingProfile" name="doping_profile"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/device.mmt#1261.-1.-1:1261.-1.-1"/></metadata></om:OMS></om:OMOBJ>.</opaque><constant name="doping_profile">
+ <metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/device.mmt#1268.44.1:1309.44.42"/></metadata>
+ <type><om:OMOBJ xmlns:om="http://www.openmath.org/OpenMath"><om:OMA><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/device.mmt#1285.44.18:1300.44.33"/></metadata>
<om:OMS base="http://cds.omdoc.org/urtheories" module="LambdaPi" name="arrow"></om:OMS>
- <om:OMS base="http://mathhub.info/MitM/Models/device" module="DeviceGeometry" name="domain"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/device.mmt#1215.41.18:1215.41.18"/></metadata></om:OMS><om:OMS base="http://mathhub.info/MitM/numberfields" module="realnumbers" name="Realnumbers"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/device.mmt#1220.41.23:1220.41.23"/></metadata></om:OMS>
+ <om:OMS base="http://mathhub.info/MitM/Models/device" module="DeviceGeometry" name="domain"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/device.mmt#1285.44.18:1285.44.18"/></metadata></om:OMS><om:OMS base="http://mathhub.info/MitM/Models" module="Density" name="density_dim"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/device.mmt#1290.44.23:1300.44.33"/></metadata></om:OMS>
</om:OMA></om:OMOBJ></type>
<notations><notation dimension="1" precedence="0" fixity="mixfix" arguments="C"> <scope languages="" priority="0"/> </notation></notations>
diff --git a/content/http..mathhub.info/MitM/Models/poisson/$Poisson$Boundary$Conditions.omdoc b/content/http..mathhub.info/MitM/Models/poisson/$Poisson$Boundary$Conditions.omdoc
index c83a676..0b23979 100644
--- a/content/http..mathhub.info/MitM/Models/poisson/$Poisson$Boundary$Conditions.omdoc
+++ b/content/http..mathhub.info/MitM/Models/poisson/$Poisson$Boundary$Conditions.omdoc
@@ -1,23 +1,26 @@
-<omdoc xmlns="http://omdoc.org/ns" xmlns:om="http://www.openmath.org/OpenMath"><theory name="PoissonBoundaryConditions" base="http://mathhub.info/MitM/Models/poisson" meta="http://mathhub.info/MitM/Models?Base"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/poisson.mmt#2391.74.0:2833.83.1"/></metadata><import from="http://mathhub.info/MitM/Models/poisson?ThermodynamicEquilibrium"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/poisson.mmt#2439.75.1:2473.75.35"/></metadata></import><opaque format="text"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/poisson.mmt#2476.76.1:2575.77.37"/></metadata>Boundary value for electrostatic potential at top contact
- for an applied voltage <om:OMOBJ xmlns:om="http://www.openmath.org/OpenMath"><om:OMS base="http://mathhub.info/MitM/Models/device" module="DeviceOperationState" name="voltage_bottom"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/poisson.mmt#2568.-1.-1:2570.-1.1"/></metadata></om:OMS></om:OMOBJ>.</opaque><constant name="potential_top">
- <metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/poisson.mmt#2577.78.1:2620.78.44"/></metadata>
- <type><om:OMOBJ xmlns:om="http://www.openmath.org/OpenMath"><om:OMS base="http://mathhub.info/MitM/numberfields" module="realnumbers" name="Realnumbers"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/poisson.mmt#2593.78.17:2593.78.17"/></metadata></om:OMS></om:OMOBJ></type>
- <definition><om:OMOBJ xmlns:om="http://www.openmath.org/OpenMath"><om:OMA><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/poisson.mmt#2599.78.23:2609.78.33"/></metadata>
+<omdoc xmlns="http://omdoc.org/ns" xmlns:om="http://www.openmath.org/OpenMath"><theory name="PoissonBoundaryConditions" base="http://mathhub.info/MitM/Models/poisson" meta="http://mathhub.info/MitM/Models?Base"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/poisson.mmt#2396.72.0:2876.81.1"/></metadata><import from="http://mathhub.info/MitM/Models/poisson?ThermodynamicEquilibrium"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/poisson.mmt#2444.73.1:2478.73.35"/></metadata></import><opaque format="text"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/poisson.mmt#2481.74.1:2580.75.37"/></metadata>Boundary value for electrostatic potential at top contact
+ for an applied voltage <om:OMOBJ xmlns:om="http://www.openmath.org/OpenMath"><om:OMS base="http://mathhub.info/MitM/Models/device" module="DeviceOperationState" name="voltage_bottom"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/poisson.mmt#2573.-1.-1:2575.-1.1"/></metadata></om:OMS></om:OMOBJ>.</opaque><constant name="potential_top">
+ <metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/poisson.mmt#2582.76.1:2644.76.63"/></metadata>
+ <type><om:OMOBJ xmlns:om="http://www.openmath.org/OpenMath"><om:OMA><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/poisson.mmt#2598.76.17:2617.76.36"/></metadata>
<om:OMS base="http://cds.omdoc.org/urtheories" module="LambdaPi" name="apply"></om:OMS>
- <om:OMS base="http://mathhub.info/MitM/numberfields" module="realarith" name="addition"></om:OMS><om:OMS base="http://mathhub.info/MitM/Models/poisson" module="ThermodynamicEquilibrium" name="equilibrium_potential_bottom"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/poisson.mmt#2599.78.23:2603.78.27"/></metadata></om:OMS><om:OMS base="http://mathhub.info/MitM/Models/device" module="DeviceOperationState" name="voltage_bottom"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/poisson.mmt#2607.78.31:2609.78.33"/></metadata></om:OMS>
+ <om:OMS base="http://mathhub.info/MMT/physics-units" module="QEBase" name="QE"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/poisson.mmt#2598.76.17:2599.76.18"/></metadata></om:OMS><om:OMS base="http://mathhub.info/MMT/physics-units" module="DimensionsExtended" name="ElectricPotential"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/poisson.mmt#2601.76.20:2617.76.36"/></metadata></om:OMS>
+ </om:OMA></om:OMOBJ></type>
+ <definition><om:OMOBJ xmlns:om="http://www.openmath.org/OpenMath"><om:OMA><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/poisson.mmt#2623.76.42:2633.76.52"/></metadata>
+ <om:OMS base="http://cds.omdoc.org/urtheories" module="LambdaPi" name="apply"></om:OMS>
+ <om:OMS base="http://mathhub.info/MitM/smglom/arithmetics" module="realarith" name="addition"></om:OMS><om:OMS base="http://mathhub.info/MitM/Models/poisson" module="ThermodynamicEquilibrium" name="equilibrium_potential_bottom"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/poisson.mmt#2623.76.42:2627.76.46"/></metadata></om:OMS><om:OMS base="http://mathhub.info/MitM/Models/device" module="DeviceOperationState" name="voltage_bottom"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/poisson.mmt#2631.76.50:2633.76.52"/></metadata></om:OMS>
</om:OMA></om:OMOBJ></definition>
<notations><notation dimension="1" precedence="0" fixity="mixfix" arguments="ψ_1"> <scope languages="" priority="0"/> </notation></notations>
- </constant><opaque format="text"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/poisson.mmt#2622.79.1:2783.81.60"/></metadata>Boundary value for electrostatic potential at bottom contact
- for an applied voltage <om:OMOBJ xmlns:om="http://www.openmath.org/OpenMath"><om:OMS base="http://mathhub.info/MitM/Models/device" module="DeviceOperationState" name="voltage_top"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/poisson.mmt#2717.-1.-1:2719.-1.1"/></metadata></om:OMS></om:OMOBJ>.
- N.B.: the applied bias voltage is U_bias = <om:OMOBJ xmlns:om="http://www.openmath.org/OpenMath"><om:OMA><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/poisson.mmt#2773.-1.-1:2779.-1.5"/></metadata>
+ </constant><opaque format="text"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/poisson.mmt#2646.77.1:2807.79.60"/></metadata>Boundary value for electrostatic potential at bottom contact
+ for an applied voltage <unparsed>None</unparsed>.
+ N.B.: the applied bias voltage is U_bias = <unparsed>None</unparsed></opaque><constant name="potential_bottom">
+ <metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/poisson.mmt#2809.80.1:2874.80.66"/></metadata>
+ <type><om:OMOBJ xmlns:om="http://www.openmath.org/OpenMath"><om:OMA><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/poisson.mmt#2828.80.20:2847.80.39"/></metadata>
<om:OMS base="http://cds.omdoc.org/urtheories" module="LambdaPi" name="apply"></om:OMS>
- <om:OMS base="http://mathhub.info/MitM/numberfields" module="realarith" name="bin_minus"></om:OMS><om:OMS base="http://mathhub.info/MitM/Models/device" module="DeviceOperationState" name="voltage_top"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/poisson.mmt#2773.-1.-1:2775.-1.1"/></metadata></om:OMS><om:OMS base="http://mathhub.info/MitM/Models/device" module="DeviceOperationState" name="voltage_bottom"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/poisson.mmt#2777.-1.3:2779.-1.5"/></metadata></om:OMS>
- </om:OMA></om:OMOBJ></opaque><constant name="potential_bottom">
- <metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/poisson.mmt#2785.82.1:2831.82.47"/></metadata>
- <type><om:OMOBJ xmlns:om="http://www.openmath.org/OpenMath"><om:OMS base="http://mathhub.info/MitM/numberfields" module="realnumbers" name="Realnumbers"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/poisson.mmt#2804.82.20:2804.82.20"/></metadata></om:OMS></om:OMOBJ></type>
- <definition><om:OMOBJ xmlns:om="http://www.openmath.org/OpenMath"><om:OMA><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/poisson.mmt#2810.82.26:2820.82.36"/></metadata>
+ <om:OMS base="http://mathhub.info/MMT/physics-units" module="QEBase" name="QE"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/poisson.mmt#2828.80.20:2829.80.21"/></metadata></om:OMS><om:OMS base="http://mathhub.info/MMT/physics-units" module="DimensionsExtended" name="ElectricPotential"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/poisson.mmt#2831.80.23:2847.80.39"/></metadata></om:OMS>
+ </om:OMA></om:OMOBJ></type>
+ <definition><om:OMOBJ xmlns:om="http://www.openmath.org/OpenMath"><om:OMA><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/poisson.mmt#2853.80.45:2863.80.55"/></metadata>
<om:OMS base="http://cds.omdoc.org/urtheories" module="LambdaPi" name="apply"></om:OMS>
- <om:OMS base="http://mathhub.info/MitM/numberfields" module="realarith" name="addition"></om:OMS><om:OMS base="http://mathhub.info/MitM/Models/poisson" module="ThermodynamicEquilibrium" name="equilibrium_potential_top"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/poisson.mmt#2810.82.26:2814.82.30"/></metadata></om:OMS><om:OMS base="http://mathhub.info/MitM/Models/device" module="DeviceOperationState" name="voltage_top"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/poisson.mmt#2818.82.34:2820.82.36"/></metadata></om:OMS>
+ <om:OMS base="http://mathhub.info/MitM/smglom/arithmetics" module="realarith" name="addition"></om:OMS><om:OMS base="http://mathhub.info/MitM/Models/poisson" module="ThermodynamicEquilibrium" name="equilibrium_potential_top"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/poisson.mmt#2853.80.45:2857.80.49"/></metadata></om:OMS><om:OMS base="http://mathhub.info/MitM/Models/device" module="DeviceOperationState" name="voltage_top"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/poisson.mmt#2861.80.53:2863.80.55"/></metadata></om:OMS>
</om:OMA></om:OMOBJ></definition>
<notations><notation dimension="1" precedence="0" fixity="mixfix" arguments="ψ_2"> <scope languages="" priority="0"/> </notation></notations>
</constant></theory></omdoc>
\ No newline at end of file
diff --git a/content/http..mathhub.info/MitM/Models/poisson/$Poisson$Equation.omdoc b/content/http..mathhub.info/MitM/Models/poisson/$Poisson$Equation.omdoc
index d977b11..17d8ce0 100644
--- a/content/http..mathhub.info/MitM/Models/poisson/$Poisson$Equation.omdoc
+++ b/content/http..mathhub.info/MitM/Models/poisson/$Poisson$Equation.omdoc
@@ -1,36 +1,20 @@
-<omdoc xmlns="http://omdoc.org/ns" xmlns:om="http://www.openmath.org/OpenMath"><theory name="PoissonEquation" base="http://mathhub.info/MitM/Models/poisson" meta="http://mathhub.info/MitM/Models?Base"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/poisson.mmt#1562.45.0:1765.53.1"/></metadata><import from="http://mathhub.info/MitM/Models/poisson?Charge"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/poisson.mmt#1600.46.1:1616.46.17"/></metadata></import><import from="http://mathhub.info/MitM/Models/poisson?Displacement"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/poisson.mmt#1619.47.1:1641.47.23"/></metadata></import><opaque format="text"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/poisson.mmt#1646.49.1:1731.50.29"/></metadata>Defintion of the Poisson equation with total charge
+<omdoc xmlns="http://omdoc.org/ns" xmlns:om="http://www.openmath.org/OpenMath"><theory name="PoissonEquation" base="http://mathhub.info/MitM/Models/poisson" meta="http://mathhub.info/MitM/Models?Base"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/poisson.mmt#1529.43.0:1732.51.1"/></metadata><import from="http://mathhub.info/MitM/Models/poisson?Charge"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/poisson.mmt#1567.44.1:1583.44.17"/></metadata></import><import from="http://mathhub.info/MitM/Models/poisson?Displacement"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/poisson.mmt#1586.45.1:1608.45.23"/></metadata></import><opaque format="text"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/poisson.mmt#1613.47.1:1698.48.29"/></metadata>Defintion of the Poisson equation with total charge
as right hand side.</opaque><constant name="poisson_equation">
- <metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/poisson.mmt#1733.51.1:1762.51.30"/></metadata>
- <type><om:OMOBJ xmlns:om="http://www.openmath.org/OpenMath"><om:OMA><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/poisson.mmt#1752.51.20:1760.51.28"/></metadata>
+ <metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/poisson.mmt#1700.49.1:1729.49.30"/></metadata>
+ <type><om:OMOBJ xmlns:om="http://www.openmath.org/OpenMath"><om:OMBIND>
+ <om:OMS base="http://cds.omdoc.org/mmt" module="mmt" name="unknown"></om:OMS>
+ <om:OMBVAR><om:OMV name="/I/2"></om:OMV><om:OMV name="/I/1"></om:OMV><om:OMV name="/I/0"></om:OMV></om:OMBVAR>
+ <om:OMA><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/poisson.mmt#1719.49.20:1727.49.28"/></metadata>
<om:OMS base="http://cds.omdoc.org/urtheories" module="LambdaPi" name="apply"></om:OMS>
- <om:OMS base="http://mathhub.info/MitM/Foundation" module="Logic" name="ded"></om:OMS><om:OMA><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/poisson.mmt#1754.51.22:1760.51.28"/></metadata>
+ <om:OMS base="http://mathhub.info/MitM/Foundation" module="Logic" name="ded"></om:OMS><om:OMA><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/poisson.mmt#1721.49.22:1727.49.28"/></metadata>
<om:OMS base="http://cds.omdoc.org/urtheories" module="LambdaPi" name="apply"></om:OMS>
- <om:OMS base="http://mathhub.info/MitM/Foundation" module="Logic" name="eq"></om:OMS><om:OMA>
- <om:OMS base="http://cds.omdoc.org/urtheories" module="LambdaPi" name="arrow"></om:OMS>
- <om:OMA><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/constants.mmt#686.18.38:691.18.43"/></metadata>
+ <om:OMS base="http://mathhub.info/MitM/Foundation" module="Logic" name="eq"></om:OMS><om:OMV name="/I/2"></om:OMV><om:OMA><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/poisson.mmt#1721.49.22:1723.49.24"/></metadata>
<om:OMS base="http://cds.omdoc.org/urtheories" module="LambdaPi" name="apply"></om:OMS>
- <om:OMS base="http://mathhub.info/MitM/numberfields" module="realarith" name="pred_as_sub"></om:OMS><om:OMBIND>
- <om:OMS base="http://cds.omdoc.org/urtheories" module="LambdaPi" name="lambda"></om:OMS>
- <om:OMBVAR><om:OMV name="z"><type><om:OMS base="http://mathhub.info/MitM/numberfields" module="realnumbers" name="Realnumbers"></om:OMS></type></om:OMV></om:OMBVAR>
- <om:OMA><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/numberfields/numberfields.mmt#7824.214.54:7826.214.56"/></metadata>
- <om:OMS base="http://cds.omdoc.org/urtheories" module="LambdaPi" name="apply"></om:OMS>
- <om:OMS base="http://mathhub.info/MitM/Models/device" module="DeviceGeometry" name="domain_prop"></om:OMS><om:OMV name="z"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/numberfields/numberfields.mmt#7826.214.56:7826.214.56"/></metadata></om:OMV>
- </om:OMA>
- </om:OMBIND>
- </om:OMA><om:OMS base="http://mathhub.info/MitM/numberfields" module="realnumbers" name="Realnumbers"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/constants.mmt#695.18.47:695.18.47"/></metadata></om:OMS>
- </om:OMA><om:OMA><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/poisson.mmt#1754.51.22:1756.51.24"/></metadata>
- <om:OMS base="http://cds.omdoc.org/urtheories" module="LambdaPi" name="apply"></om:OMS>
- <om:OMS base="http://mathhub.info/MitM/Models" module="Base" name="der"></om:OMS><om:OMBIND>
- <om:OMS base="http://cds.omdoc.org/urtheories" module="LambdaPi" name="lambda"></om:OMS>
- <om:OMBVAR><om:OMV name="z"><type><om:OMS base="http://mathhub.info/MitM/numberfields" module="realnumbers" name="Realnumbers"></om:OMS></type></om:OMV></om:OMBVAR>
- <om:OMA><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/numberfields/numberfields.mmt#7824.214.54:7826.214.56"/></metadata>
- <om:OMS base="http://cds.omdoc.org/urtheories" module="LambdaPi" name="apply"></om:OMS>
- <om:OMS base="http://mathhub.info/MitM/Models/device" module="DeviceGeometry" name="domain_prop"></om:OMS><om:OMV name="z"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/numberfields/numberfields.mmt#7826.214.56:7826.214.56"/></metadata></om:OMV>
+ <om:OMS base="http://mathhub.info/MitM/smglom/calculus" module="derivative" name="derivative"></om:OMS><om:OMV name="/I/0"></om:OMV><om:OMS base="http://mathhub.info/MitM/Models/poisson" module="Displacement" name="electric_displacement"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/poisson.mmt#1721.49.22:1721.49.22"/></metadata></om:OMS><om:OMV name="/I/1"></om:OMV>
+ </om:OMA><om:OMS base="http://mathhub.info/MitM/Models/poisson" module="Charge" name="total_charge"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/poisson.mmt#1727.49.28:1727.49.28"/></metadata></om:OMS>
</om:OMA>
- </om:OMBIND><om:OMS base="http://mathhub.info/MitM/Models/poisson" module="Displacement" name="electric_displacement"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/poisson.mmt#1754.51.22:1754.51.22"/></metadata></om:OMS>
- </om:OMA><om:OMS base="http://mathhub.info/MitM/Models/poisson" module="Charge" name="total_charge"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/poisson.mmt#1760.51.28:1760.51.28"/></metadata></om:OMS>
</om:OMA>
- </om:OMA></om:OMOBJ></type>
+ </om:OMBIND></om:OMOBJ></type>
</constant></theory></omdoc>
\ No newline at end of file
diff --git a/content/http..mathhub.info/MitM/Models/poisson/$Poisson$Parameters.omdoc b/content/http..mathhub.info/MitM/Models/poisson/$Poisson$Parameters.omdoc
index 39fee13..0bc40ac 100644
--- a/content/http..mathhub.info/MitM/Models/poisson/$Poisson$Parameters.omdoc
+++ b/content/http..mathhub.info/MitM/Models/poisson/$Poisson$Parameters.omdoc
@@ -1,14 +1,41 @@
-<omdoc xmlns="http://omdoc.org/ns" xmlns:om="http://www.openmath.org/OpenMath"><theory name="PoissonParameters" base="http://mathhub.info/MitM/Models/poisson" meta="http://mathhub.info/MitM/Models?Base"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/poisson.mmt#209.6.0:491.11.1"/></metadata><opaque format="text"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/poisson.mmt#252.7.4:321.7.73"/></metadata>The relative dielelectric permitivity constant denoted by <om:OMOBJ xmlns:om="http://www.openmath.org/OpenMath"><om:OMS base="http://mathhub.info/MitM/Models/poisson" module="PoissonParameters" name="relative_dielectric_permitivity"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/poisson.mmt#314.-1.-1:316.-1.1"/></metadata></om:OMS></om:OMOBJ>.</opaque><constant name="relative_dielectric_permitivity">
- <metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/poisson.mmt#323.8.1:368.8.46"/></metadata>
- <type><om:OMOBJ xmlns:om="http://www.openmath.org/OpenMath"><om:OMS base="http://mathhub.info/MitM/numberfields" module="realnumbers" name="Realnumbers"></om:OMS></om:OMOBJ></type>
+<omdoc xmlns="http://omdoc.org/ns" xmlns:om="http://www.openmath.org/OpenMath"><theory name="PoissonParameters" base="http://mathhub.info/MitM/Models/poisson" meta="http://mathhub.info/MitM/Models?Base"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/poisson.mmt#259.7.0:565.12.1"/></metadata><opaque format="text"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/poisson.mmt#302.8.4:371.8.73"/></metadata>The relative dielelectric permitivity constant denoted by <om:OMOBJ xmlns:om="http://www.openmath.org/OpenMath"><om:OMS base="http://mathhub.info/MitM/Models/poisson" module="PoissonParameters" name="relative_dielectric_permittivity"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/poisson.mmt#364.-1.-1:366.-1.1"/></metadata></om:OMS></om:OMOBJ>.</opaque><constant name="relative_dielectric_permittivity">
+ <metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/poisson.mmt#373.9.1:426.9.54"/></metadata>
+ <type><om:OMOBJ xmlns:om="http://www.openmath.org/OpenMath"><om:OMS base="http://mathhub.info/MitM/Foundation" module="Literals" name="real_lit"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/poisson.mmt#408.9.36:415.9.43"/></metadata></om:OMS></om:OMOBJ></type>
<notations><notation dimension="1" precedence="0" fixity="mixfix" arguments="ε_r"> <scope languages="" priority="0"/> </notation></notations>
- </constant><opaque format="text"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/poisson.mmt#370.9.1:437.9.68"/></metadata>The static dielelectric permitivity constant denoted by <om:OMOBJ xmlns:om="http://www.openmath.org/OpenMath"><om:OMS base="http://mathhub.info/MitM/Models/poisson" module="PoissonParameters" name="dielectric_permitivity"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/poisson.mmt#430.-1.-1:432.-1.1"/></metadata></om:OMS></om:OMOBJ>.</opaque><constant name="dielectric_permitivity">
- <metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/poisson.mmt#439.10.1:489.10.51"/></metadata>
- <type><om:OMOBJ xmlns:om="http://www.openmath.org/OpenMath"><om:OMS base="http://mathhub.info/MitM/numberfields" module="realnumbers" name="Realnumbers"></om:OMS></om:OMOBJ></type>
- <definition><om:OMOBJ xmlns:om="http://www.openmath.org/OpenMath"><om:OMA><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/poisson.mmt#1482.40.9:1484.40.11"/></metadata>
+ </constant><opaque format="text"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/poisson.mmt#428.10.1:495.10.68"/></metadata>The static dielelectric permitivity constant denoted by <unparsed>None</unparsed>.</opaque><constant name="dielectric_permittivity">
+ <metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/poisson.mmt#497.11.1:563.11.67"/></metadata>
+ <type><om:OMOBJ xmlns:om="http://www.openmath.org/OpenMath"><om:OMS base="http://mathhub.info/MitM/Models" module="Permittivity" name="permittivity_dim"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/poisson.mmt#523.11.27:538.11.42"/></metadata></om:OMS></om:OMOBJ></type>
+ <definition><om:OMOBJ xmlns:om="http://www.openmath.org/OpenMath"><om:OMA><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/poisson.mmt#544.11.48:552.11.56"/></metadata>
<om:OMS base="http://cds.omdoc.org/urtheories" module="LambdaPi" name="apply"></om:OMS>
- <om:OMS base="http://mathhub.info/MitM/numberfields" module="realarith" name="multiplication"></om:OMS><om:OMS base="http://mathhub.info/MitM/Models/poisson" module="PoissonParameters" name="relative_dielectric_permitivity"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/poisson.mmt#470.10.32:472.10.34"/></metadata></om:OMS><om:OMS base="http://mathhub.info/MitM/Models" module="PhysicalConstants" name="vacuum_dielectric_permitivity"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/poisson.mmt#476.10.38:478.10.40"/></metadata></om:OMS>
+ <om:OMS base="http://mathhub.info/MMT/physics-units" module="QEBase" name="QENMul"></om:OMS><om:OMA>
+ <om:OMS base="http://cds.omdoc.org/urtheories" module="LambdaPi" name="apply"></om:OMS>
+ <om:OMS base="http://mathhub.info/MMT/physics-units" module="Dimensions" name="DimDiv"></om:OMS><om:OMA><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/constants.mmt#559.12.24:572.12.37"/></metadata>
+ <om:OMS base="http://cds.omdoc.org/urtheories" module="LambdaPi" name="apply"></om:OMS>
+ <om:OMS base="http://mathhub.info/MMT/physics-units" module="Dimensions" name="DimTimes"></om:OMS><om:OMS base="http://mathhub.info/MMT/physics-units" module="Dimensions" name="SIcurrent"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MMT/physics-units/Dimensions.mmt#1207.43.32:1215.43.40"/></metadata></om:OMS><om:OMS base="http://mathhub.info/MMT/physics-units" module="Dimensions" name="SItime"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MMT/physics-units/Dimensions.mmt#1219.43.44:1224.43.49"/></metadata></om:OMS>
+ </om:OMA><om:OMA>
+ <om:OMS base="http://cds.omdoc.org/urtheories" module="LambdaPi" name="apply"></om:OMS>
+ <om:OMS base="http://mathhub.info/MMT/physics-units" module="Dimensions" name="DimTimes"></om:OMS><om:OMA>
+ <om:OMS base="http://cds.omdoc.org/urtheories" module="LambdaPi" name="apply"></om:OMS>
+ <om:OMS base="http://mathhub.info/MMT/physics-units" module="Dimensions" name="DimDiv"></om:OMS><om:OMA>
+ <om:OMS base="http://cds.omdoc.org/urtheories" module="LambdaPi" name="apply"></om:OMS>
+ <om:OMS base="http://mathhub.info/MMT/physics-units" module="Dimensions" name="DimTimes"></om:OMS><om:OMA>
+ <om:OMS base="http://cds.omdoc.org/urtheories" module="LambdaPi" name="apply"></om:OMS>
+ <om:OMS base="http://mathhub.info/MMT/physics-units" module="Dimensions" name="DimTimes"></om:OMS><om:OMS base="http://mathhub.info/MMT/physics-units" module="Dimensions" name="SImass"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MMT/physics-units/Dimensions.mmt#1071.39.32:1076.39.37"/></metadata></om:OMS><om:OMA>
+ <om:OMS base="http://cds.omdoc.org/urtheories" module="LambdaPi" name="apply"></om:OMS>
+ <om:OMS base="http://mathhub.info/MMT/physics-units" module="Dimensions" name="DimDiv"></om:OMS><om:OMA><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MMT/physics-units/Dimensions.mmt#856.32.37:863.32.44"/></metadata>
+ <om:OMS base="http://cds.omdoc.org/urtheories" module="LambdaPi" name="apply"></om:OMS>
+ <om:OMS base="http://mathhub.info/MMT/physics-units" module="Dimensions" name="DimDiv"></om:OMS><om:OMS base="http://mathhub.info/MMT/physics-units" module="Dimensions" name="SIlength"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MMT/physics-units/Dimensions.mmt#802.31.33:809.31.40"/></metadata></om:OMS><om:OMS base="http://mathhub.info/MMT/physics-units" module="Dimensions" name="SItime"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MMT/physics-units/Dimensions.mmt#811.31.42:816.31.47"/></metadata></om:OMS>
+ </om:OMA><om:OMS base="http://mathhub.info/MMT/physics-units" module="Dimensions" name="SItime"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MMT/physics-units/Dimensions.mmt#865.32.46:870.32.51"/></metadata></om:OMS>
+ </om:OMA>
+ </om:OMA><om:OMS base="http://mathhub.info/MMT/physics-units" module="Dimensions" name="SIlength"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MMT/physics-units/Dimensions.mmt#1260.44.32:1267.44.39"/></metadata></om:OMS>
+ </om:OMA><om:OMA><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/constants.mmt#559.12.24:572.12.37"/></metadata>
+ <om:OMS base="http://cds.omdoc.org/urtheories" module="LambdaPi" name="apply"></om:OMS>
+ <om:OMS base="http://mathhub.info/MMT/physics-units" module="Dimensions" name="DimTimes"></om:OMS><om:OMS base="http://mathhub.info/MMT/physics-units" module="Dimensions" name="SIcurrent"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MMT/physics-units/Dimensions.mmt#1207.43.32:1215.43.40"/></metadata></om:OMS><om:OMS base="http://mathhub.info/MMT/physics-units" module="Dimensions" name="SItime"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MMT/physics-units/Dimensions.mmt#1219.43.44:1224.43.49"/></metadata></om:OMS>
+ </om:OMA>
+ </om:OMA><om:OMS base="http://mathhub.info/MMT/physics-units" module="Dimensions" name="SIlength"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/Quantities.mmt#504.13.72:511.13.79"/></metadata></om:OMS>
+ </om:OMA>
+ </om:OMA><om:OMS base="http://mathhub.info/MitM/Models/poisson" module="PoissonParameters" name="relative_dielectric_permittivity"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/poisson.mmt#544.11.48:546.11.50"/></metadata></om:OMS><om:OMS base="http://mathhub.info/MitM/Models" module="PhysicalConstants" name="vacuum_dielectric_permitivity"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/poisson.mmt#550.11.54:552.11.56"/></metadata></om:OMS>
</om:OMA></om:OMOBJ></definition>
<notations><notation dimension="1" precedence="0" fixity="mixfix" arguments="ε_s"> <scope languages="" priority="0"/> </notation></notations>
</constant></theory></omdoc>
\ No newline at end of file
diff --git a/content/http..mathhub.info/MitM/Models/poisson/$Thermodynamic$Equilibrium.omdoc b/content/http..mathhub.info/MitM/Models/poisson/$Thermodynamic$Equilibrium.omdoc
index e5486b5..970fde8 100644
--- a/content/http..mathhub.info/MitM/Models/poisson/$Thermodynamic$Equilibrium.omdoc
+++ b/content/http..mathhub.info/MitM/Models/poisson/$Thermodynamic$Equilibrium.omdoc
@@ -1,17 +1,27 @@
-<omdoc xmlns="http://omdoc.org/ns" xmlns:om="http://www.openmath.org/OpenMath"><theory name="ThermodynamicEquilibrium" base="http://mathhub.info/MitM/Models/poisson" meta="http://mathhub.info/MitM/Models?Base"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/poisson.mmt#1859.58.0:2303.70.1"/></metadata><import from="http://mathhub.info/MitM/Models/poisson?Charge"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/poisson.mmt#1906.59.1:1922.59.17"/></metadata></import><opaque format="text"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/poisson.mmt#1927.61.1:2024.62.34"/></metadata>Value of build-in potential ψ_0 at top contact guranteeing
+<omdoc xmlns="http://omdoc.org/ns" xmlns:om="http://www.openmath.org/OpenMath"><theory name="ThermodynamicEquilibrium" base="http://mathhub.info/MitM/Models/poisson" meta="http://mathhub.info/MitM/Models?Base"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/poisson.mmt#1826.56.0:2308.68.1"/></metadata><import from="http://mathhub.info/MitM/Models/poisson?Charge"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/poisson.mmt#1873.57.1:1889.57.17"/></metadata></import><opaque format="text"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/poisson.mmt#1894.59.1:1991.60.34"/></metadata>Value of build-in potential ψ_0 at top contact guranteeing
local charge neutrality.</opaque><constant name="equilibrium_potential_top">
- <metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/poisson.mmt#2026.63.1:2067.63.42"/></metadata>
- <type><om:OMOBJ xmlns:om="http://www.openmath.org/OpenMath"><om:OMS base="http://mathhub.info/MitM/numberfields" module="realnumbers" name="Realnumbers"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/poisson.mmt#2054.63.29:2054.63.29"/></metadata></om:OMS></om:OMOBJ></type>
+ <metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/poisson.mmt#1993.61.1:2053.61.61"/></metadata>
+ <type><om:OMOBJ xmlns:om="http://www.openmath.org/OpenMath"><om:OMA><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/poisson.mmt#2021.61.29:2040.61.48"/></metadata>
+ <om:OMS base="http://cds.omdoc.org/urtheories" module="LambdaPi" name="apply"></om:OMS>
+ <om:OMS base="http://mathhub.info/MMT/physics-units" module="QEBase" name="QE"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/poisson.mmt#2021.61.29:2022.61.30"/></metadata></om:OMS><om:OMS base="http://mathhub.info/MMT/physics-units" module="DimensionsExtended" name="ElectricPotential"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/poisson.mmt#2024.61.32:2040.61.48"/></metadata></om:OMS>
+ </om:OMA></om:OMOBJ></type>
<notations><notation dimension="1" precedence="0" fixity="mixfix" arguments="ψ_0_2"> <scope languages="" priority="0"/> </notation></notations>
- </constant><opaque format="text"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/poisson.mmt#2071.65.1:2249.67.79"/></metadata>Value of build-in potential ψ_0 at bottom contact guranteeing
+ </constant><opaque format="text"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/poisson.mmt#2057.63.1:2235.65.79"/></metadata>Value of build-in potential ψ_0 at bottom contact guranteeing
local charge neutrality.
- N.B. the build-in potential is given as U_b = <om:OMOBJ xmlns:om="http://www.openmath.org/OpenMath"><om:OMA><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/poisson.mmt#2224.-1.-1:2236.-1.11"/></metadata>
+ N.B. the build-in potential is given as U_b = <om:OMOBJ xmlns:om="http://www.openmath.org/OpenMath"><om:OMBIND>
+ <om:OMS base="http://cds.omdoc.org/mmt" module="mmt" name="unknown"></om:OMS>
+ <om:OMBVAR><om:OMV name="/I/0"></om:OMV></om:OMBVAR>
+ <om:OMA><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/poisson.mmt#2210.-1.-1:2222.-1.11"/></metadata>
+ <om:OMS base="http://cds.omdoc.org/urtheories" module="LambdaPi" name="apply"></om:OMS>
+ <om:OMS base="http://mathhub.info/MMT/physics-units" module="QEBase" name="QESubtract"></om:OMS><om:OMV name="/I/0"></om:OMV><om:OMS base="http://mathhub.info/MitM/Models/poisson" module="ThermodynamicEquilibrium" name="equilibrium_potential_top"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/poisson.mmt#2210.-1.-1:2214.-1.3"/></metadata></om:OMS><om:OMS base="http://mathhub.info/MitM/Models/poisson" module="ThermodynamicEquilibrium" name="equilibrium_potential_bottom"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/poisson.mmt#2218.-1.7:2222.-1.11"/></metadata></om:OMS>
+ </om:OMA>
+ </om:OMBIND></om:OMOBJ> (Check!)</opaque><constant name="equilibrium_potential_bottom">
+ <metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/poisson.mmt#2243.67.1:2306.67.64"/></metadata>
+ <type><om:OMOBJ xmlns:om="http://www.openmath.org/OpenMath"><om:OMA><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/poisson.mmt#2274.67.32:2293.67.51"/></metadata>
<om:OMS base="http://cds.omdoc.org/urtheories" module="LambdaPi" name="apply"></om:OMS>
- <om:OMS base="http://mathhub.info/MitM/numberfields" module="realarith" name="bin_minus"></om:OMS><om:OMS base="http://mathhub.info/MitM/Models/poisson" module="ThermodynamicEquilibrium" name="equilibrium_potential_top"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/poisson.mmt#2224.-1.-1:2228.-1.3"/></metadata></om:OMS><om:OMS base="http://mathhub.info/MitM/Models/poisson" module="ThermodynamicEquilibrium" name="equilibrium_potential_bottom"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/poisson.mmt#2232.-1.7:2236.-1.11"/></metadata></om:OMS>
- </om:OMA></om:OMOBJ> (Check!)</opaque><constant name="equilibrium_potential_bottom">
- <metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/poisson.mmt#2257.69.1:2301.69.45"/></metadata>
- <type><om:OMOBJ xmlns:om="http://www.openmath.org/OpenMath"><om:OMS base="http://mathhub.info/MitM/numberfields" module="realnumbers" name="Realnumbers"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/poisson.mmt#2288.69.32:2288.69.32"/></metadata></om:OMS></om:OMOBJ></type>
+ <om:OMS base="http://mathhub.info/MMT/physics-units" module="QEBase" name="QE"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/poisson.mmt#2274.67.32:2275.67.33"/></metadata></om:OMS><om:OMS base="http://mathhub.info/MMT/physics-units" module="DimensionsExtended" name="ElectricPotential"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/poisson.mmt#2277.67.35:2293.67.51"/></metadata></om:OMS>
+ </om:OMA></om:OMOBJ></type>
<notations><notation dimension="1" precedence="0" fixity="mixfix" arguments="ψ_0_1"> <scope languages="" priority="0"/> </notation></notations>
</constant></theory></omdoc>
\ No newline at end of file
diff --git a/content/http..mathhub.info/MitM/Models/recombination/$Recombination.omdoc b/content/http..mathhub.info/MitM/Models/recombination/$Recombination.omdoc
index 506d733..ce5181e 100644
--- a/content/http..mathhub.info/MitM/Models/recombination/$Recombination.omdoc
+++ b/content/http..mathhub.info/MitM/Models/recombination/$Recombination.omdoc
@@ -1,52 +1,120 @@
-<omdoc xmlns="http://omdoc.org/ns" xmlns:om="http://www.openmath.org/OpenMath"><theory name="Recombination" base="http://mathhub.info/MitM/Models/recombination" meta="http://mathhub.info/MitM/Models?Base"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/recombination.mmt#199.6.0:703.19.1"/></metadata><import from="http://mathhub.info/MitM/Models/device?DeviceOperationState"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/recombination.mmt#236.7.2:272.7.38"/></metadata></import><import from="http://mathhub.info/MitM/Models/densities?DensityElectrons"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/recombination.mmt#276.8.1:311.8.36"/></metadata></import><import from="http://mathhub.info/MitM/Models/densities?DensityHoles"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/recombination.mmt#314.9.1:345.9.32"/></metadata></import><opaque format="text"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/recombination.mmt#351.11.2:440.12.38"/></metadata>The kernel of the recombination rate depending
- on electron and hole densities.</opaque><constant name="recombination_coefficient">
- <metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/recombination.mmt#442.13.1:487.13.46"/></metadata>
- <type><om:OMOBJ xmlns:om="http://www.openmath.org/OpenMath"><om:OMA>
- <om:OMS base="http://cds.omdoc.org/urtheories" module="LambdaPi" name="arrow"></om:OMS>
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- <notations><notation dimension="1" precedence="0" fixity="mixfix" arguments="r"> <scope languages="" priority="0"/> </notation></notations>
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+<omdoc xmlns="http://omdoc.org/ns" xmlns:om="http://www.openmath.org/OpenMath"><theory name="Recombination" base="http://mathhub.info/MitM/Models/recombination" meta="http://mathhub.info/MitM/Models?Base"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/recombination.mmt#206.8.0:694.16.1"/></metadata><import from="http://mathhub.info/MitM/Models/Species?ElectronsAndHoles"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/recombination.mmt#243.9.2:282.9.41"/></metadata></import><import from="http://mathhub.info/MitM/Models?RecombinationCoefficient"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/recombination.mmt#286.10.2:324.10.40"/></metadata></import><import from="http://mathhub.info/MitM/Models?RecombinationRate"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/recombination.mmt#328.11.2:359.11.33"/></metadata></import><opaque format="text"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/recombination.mmt#363.12.2:431.12.70"/></metadata>Recombination rate for right hand side of continuity equations.</opaque><constant name="recombination_rate">
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+ </om:OMA><om:OMA>
+ <om:OMS base="http://cds.omdoc.org/urtheories" module="LambdaPi" name="apply"></om:OMS>
+ <om:OMV name="/I/10"></om:OMV><om:OMV name="x"></om:OMV>
+ </om:OMA><om:OMA><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/recombination.mmt#612.15.23:674.15.85"/></metadata>
+ <om:OMS base="http://cds.omdoc.org/urtheories" module="LambdaPi" name="apply"></om:OMS>
+ <om:OMS base="http://mathhub.info/MMT/physics-units" module="QEBase" name="QEMul"></om:OMS><om:OMA>
+ <om:OMS base="http://cds.omdoc.org/urtheories" module="LambdaPi" name="apply"></om:OMS>
+ <om:OMV name="/I/5"></om:OMV><om:OMV name="x"></om:OMV>
+ </om:OMA><om:OMA>
+ <om:OMS base="http://cds.omdoc.org/urtheories" module="LambdaPi" name="apply"></om:OMS>
+ <om:OMV name="/I/6"></om:OMV><om:OMV name="x"></om:OMV>
+ </om:OMA><om:OMS base="http://mathhub.info/MitM/Models" module="PhysicalConstants" name="elementary_charge"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/recombination.mmt#612.15.23:612.15.23"/></metadata></om:OMS><om:OMA><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/recombination.mmt#616.15.27:674.15.85"/></metadata>
+ <om:OMS base="http://cds.omdoc.org/urtheories" module="LambdaPi" name="apply"></om:OMS>
+ <om:OMS base="http://mathhub.info/MMT/physics-units" module="QEBase" name="QESubtract"></om:OMS><om:OMA>
+ <om:OMS base="http://cds.omdoc.org/urtheories" module="LambdaPi" name="apply"></om:OMS>
+ <om:OMV name="/I/4"></om:OMV><om:OMV name="x"></om:OMV>
+ </om:OMA><om:OMA><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/recombination.mmt#617.15.28:645.15.56"/></metadata>
+ <om:OMS base="http://cds.omdoc.org/urtheories" module="LambdaPi" name="apply"></om:OMS>
+ <om:OMSF><om:text format="unknown"><![CDATA[electrons/fermi/potential]]></om:text></om:OMSF><om:OMV name="x"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/recombination.mmt#644.15.55:644.15.55"/></metadata></om:OMV>
+ </om:OMA><om:OMA><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/recombination.mmt#649.15.60:673.15.84"/></metadata>
+ <om:OMS base="http://cds.omdoc.org/urtheories" module="LambdaPi" name="apply"></om:OMS>
+ <om:OMSF><om:text format="unknown"><![CDATA[holes/fermi/potential]]></om:text></om:OMSF><om:OMV name="x"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/recombination.mmt#672.15.83:672.15.83"/></metadata></om:OMV>
+ </om:OMA>
+ </om:OMA>
+ </om:OMA><om:OMA><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/recombination.mmt#678.15.89:686.15.97"/></metadata>
+ <om:OMS base="http://cds.omdoc.org/urtheories" module="LambdaPi" name="apply"></om:OMS>
+ <om:OMS base="http://mathhub.info/MMT/physics-units" module="QEBase" name="QEMul"></om:OMS><om:OMA>
+ <om:OMS base="http://cds.omdoc.org/urtheories" module="LambdaPi" name="apply"></om:OMS>
+ <om:OMV name="/I/7"></om:OMV><om:OMV name="x"></om:OMV>
+ </om:OMA><om:OMA>
+ <om:OMS base="http://cds.omdoc.org/urtheories" module="LambdaPi" name="apply"></om:OMS>
+ <om:OMV name="/I/8"></om:OMV><om:OMV name="x"></om:OMV>
+ </om:OMA><om:OMS base="http://mathhub.info/MitM/Models" module="PhysicalConstants" name="Boltzmann_constant"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/recombination.mmt#679.15.90:681.15.92"/></metadata></om:OMS><om:OMV name="T"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/recombination.mmt#685.15.96:685.15.96"/></metadata></om:OMV>
</om:OMA>
</om:OMA>
</om:OMA>
</om:OMA>
- </om:OMBIND></om:OMOBJ></definition>
- <notations><notation dimension="1" precedence="0" fixity="mixfix" arguments="R"> <scope languages="" priority="0"/> </notation></notations>
+ </om:OMA>
+ </om:OMA>
+ </om:OMA>
+ </om:OMBIND>
+ </om:OMBIND>
+ </om:OMBIND></om:OMOBJ></type>
+
+ <notations></notations>
</constant></theory></omdoc>
\ No newline at end of file
diff --git a/content/http..mathhub.info/MitM/Models/recombination/$Spontaneous$Recombination.omdoc b/content/http..mathhub.info/MitM/Models/recombination/$Spontaneous$Recombination.omdoc
index c5a979c..108724c 100644
--- a/content/http..mathhub.info/MitM/Models/recombination/$Spontaneous$Recombination.omdoc
+++ b/content/http..mathhub.info/MitM/Models/recombination/$Spontaneous$Recombination.omdoc
@@ -1,24 +1,42 @@
-<omdoc xmlns="http://omdoc.org/ns" xmlns:om="http://www.openmath.org/OpenMath"><theory name="SpontaneousRecombination" base="http://mathhub.info/MitM/Models/recombination" meta="http://mathhub.info/MitM/Models?Base"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/recombination.mmt#769.22.0:1091.29.1"/></metadata><import from="http://mathhub.info/MitM/Models/recombination?Recombination"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/recombination.mmt#816.23.1:839.23.24"/></metadata></import><opaque format="text"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/recombination.mmt#844.25.1:921.25.78"/></metadata>The coefficient for the sponanteous recombination rate is denoted by <om:OMOBJ xmlns:om="http://www.openmath.org/OpenMath"><om:OMS base="http://mathhub.info/MitM/Models/recombination" module="SpontaneousRecombination" name="spontaneous_recombination_coefficient"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/recombination.mmt#917.-1.-1:917.-1.-1"/></metadata></om:OMS></om:OMOBJ></opaque><constant name="spontaneous_recombination_coefficient">
- <metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/recombination.mmt#923.26.1:971.26.49"/></metadata>
- <type><om:OMOBJ xmlns:om="http://www.openmath.org/OpenMath"><om:OMS base="http://mathhub.info/MitM/numberfields" module="realnumbers" name="Realnumbers"></om:OMS></om:OMOBJ></type>
+<omdoc xmlns="http://omdoc.org/ns" xmlns:om="http://www.openmath.org/OpenMath"><theory name="SpontaneousRecombination" base="http://mathhub.info/MitM/Models/recombination" meta="http://mathhub.info/MitM/Models?Base"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/recombination.mmt#760.19.0:1104.26.1"/></metadata><import from="http://mathhub.info/MitM/Models/recombination?Recombination"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/recombination.mmt#807.20.1:830.20.24"/></metadata></import><opaque format="text"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/recombination.mmt#835.22.1:912.22.78"/></metadata>The coefficient for the sponanteous recombination rate is denoted by <om:OMOBJ xmlns:om="http://www.openmath.org/OpenMath"><om:OMS base="http://mathhub.info/MitM/Models/recombination" module="SpontaneousRecombination" name="spontaneous_recombination_coefficient"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/recombination.mmt#908.-1.-1:908.-1.-1"/></metadata></om:OMS></om:OMOBJ></opaque><constant name="spontaneous_recombination_coefficient">
+ <metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/recombination.mmt#914.23.1:982.23.69"/></metadata>
+ <type><om:OMOBJ xmlns:om="http://www.openmath.org/OpenMath"><om:OMA><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/recombination.mmt#954.23.41:974.23.61"/></metadata>
+ <om:OMS base="http://cds.omdoc.org/urtheories" module="LambdaPi" name="apply"></om:OMS>
+ <om:OMS base="http://mathhub.info/MMT/physics-units" module="QEBase" name="QE"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/recombination.mmt#954.23.41:955.23.42"/></metadata></om:OMS><om:OMA><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/recombination.mmt#957.23.44:974.23.61"/></metadata>
+ <om:OMS base="http://cds.omdoc.org/urtheories" module="LambdaPi" name="apply"></om:OMS>
+ <om:OMS base="http://mathhub.info/MMT/physics-units" module="Dimensions" name="DimDiv"></om:OMS><om:OMS base="http://mathhub.info/MMT/physics-units" module="DimensionsExtended" name="Volume"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/recombination.mmt#958.23.45:963.23.50"/></metadata></om:OMS><om:OMS base="http://mathhub.info/MMT/physics-units" module="Dimensions" name="SItime"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/recombination.mmt#968.23.55:973.23.60"/></metadata></om:OMS>
+ </om:OMA>
+ </om:OMA></om:OMOBJ></type>
<notations><notation dimension="1" precedence="0" fixity="mixfix" arguments="B"> <scope languages="" priority="0"/> </notation></notations>
- </constant><opaque format="text"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/recombination.mmt#973.27.1:1034.27.62"/></metadata>Formula for sponanteous recombination <om:OMOBJ xmlns:om="http://www.openmath.org/OpenMath"><om:OMS base="http://mathhub.info/MitM/Models/recombination" module="Recombination" name="recombination_coefficient"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/recombination.mmt#1015.-1.-1:1015.-1.-1"/></metadata></om:OMS></om:OMOBJ>(<om:OMOBJ xmlns:om="http://www.openmath.org/OpenMath"><om:OMS base="http://mathhub.info/MitM/Models/densities" module="DensityElectrons" name="density_electrons"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/recombination.mmt#1019.-1.-1:1019.-1.-1"/></metadata></om:OMS></om:OMOBJ>,<om:OMOBJ xmlns:om="http://www.openmath.org/OpenMath"><om:OMS base="http://mathhub.info/MitM/Models/densities" module="DensityHoles" name="density_holes"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/recombination.mmt#1023.-1.-1:1023.-1.-1"/></metadata></om:OMS></om:OMOBJ>) = <om:OMOBJ xmlns:om="http://www.openmath.org/OpenMath"><om:OMS base="http://mathhub.info/MitM/Models/recombination" module="SpontaneousRecombination" name="spontaneous_recombination_coefficient"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/recombination.mmt#1030.-1.-1:1030.-1.-1"/></metadata></om:OMS></om:OMOBJ></opaque><constant name="axiom_spontaneous" role="Simplify">
- <metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/recombination.mmt#1036.28.1:1089.28.54"/></metadata>
- <type><om:OMOBJ xmlns:om="http://www.openmath.org/OpenMath"><om:OMA><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/recombination.mmt#1056.28.21:1070.28.35"/></metadata>
+ </constant><opaque format="text"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/recombination.mmt#984.24.1:1045.24.62"/></metadata>Formula for sponanteous recombination <unparsed>None</unparsed>(<unparsed>None</unparsed>,<unparsed>None</unparsed>) = <unparsed>None</unparsed></opaque><constant name="axiom_spontaneous" role="Simplify">
+ <metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/recombination.mmt#1047.25.1:1102.25.56"/></metadata>
+ <type><om:OMOBJ xmlns:om="http://www.openmath.org/OpenMath"><om:OMBIND><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/recombination.mmt#1067.25.21:1083.25.37"/></metadata>
+ <om:OMS base="http://cds.omdoc.org/urtheories" module="LambdaPi" name="Pi"></om:OMS>
+ <om:OMBVAR><om:OMV name="x"><metadata><tag property="http://cds.omdoc.org/mmt?mmt?inferred-type"/><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/recombination.mmt#1068.25.22:1068.25.22"/></metadata><type><om:OMA>
<om:OMS base="http://cds.omdoc.org/urtheories" module="LambdaPi" name="apply"></om:OMS>
- <om:OMS base="http://mathhub.info/MitM/Foundation" module="Logic" name="ded"></om:OMS><om:OMA><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/recombination.mmt#1058.28.23:1070.28.35"/></metadata>
+ <om:OMS base="http://mathhub.info/MMT/physics-units" module="QEBase" name="QE"></om:OMS><om:OMS base="http://mathhub.info/MitM/Models" module="Density" name="density_dim"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/Quantities.mmt#1269.38.32:1279.38.42"/></metadata></om:OMS>
+ </om:OMA></type></om:OMV><om:OMV name="y"><metadata><tag property="http://cds.omdoc.org/mmt?mmt?inferred-type"/><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/recombination.mmt#1070.25.24:1070.25.24"/></metadata><type><om:OMA>
+ <om:OMS base="http://cds.omdoc.org/urtheories" module="LambdaPi" name="apply"></om:OMS>
+ <om:OMS base="http://mathhub.info/MMT/physics-units" module="QEBase" name="QE"></om:OMS><om:OMS base="http://mathhub.info/MitM/Models" module="Density" name="density_dim"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/Quantities.mmt#1286.38.49:1296.38.59"/></metadata></om:OMS>
+ </om:OMA></type></om:OMV></om:OMBVAR>
+ <om:OMA><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/recombination.mmt#1073.25.27:1083.25.37"/></metadata>
+ <om:OMS base="http://cds.omdoc.org/urtheories" module="LambdaPi" name="apply"></om:OMS>
+ <om:OMS base="http://mathhub.info/MitM/Foundation" module="Logic" name="ded"></om:OMS><om:OMA><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/recombination.mmt#1075.25.29:1083.25.37"/></metadata>
<om:OMS base="http://cds.omdoc.org/urtheories" module="LambdaPi" name="apply"></om:OMS>
<om:OMS base="http://mathhub.info/MitM/Foundation" module="Logic" name="eq"></om:OMS><om:OMA>
- <om:OMS base="http://cds.omdoc.org/urtheories" module="LambdaPi" name="arrow"></om:OMS>
- <om:OMS base="http://mathhub.info/MitM/numberfields" module="realnumbers" name="Realnumbers"></om:OMS><om:OMS base="http://mathhub.info/MitM/numberfields" module="realnumbers" name="Realnumbers"></om:OMS><om:OMS base="http://mathhub.info/MitM/numberfields" module="realnumbers" name="Realnumbers"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/recombination.mmt#478.13.37:478.13.37"/></metadata></om:OMS>
- </om:OMA><om:OMS base="http://mathhub.info/MitM/Models/recombination" module="Recombination" name="recombination_coefficient"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/recombination.mmt#1058.28.23:1058.28.23"/></metadata></om:OMS><om:OMBIND><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/recombination.mmt#1062.28.27:1070.28.35"/></metadata>
- <om:OMS base="http://cds.omdoc.org/urtheories" module="LambdaPi" name="lambda"></om:OMS>
- <om:OMBVAR><om:OMV name="x"><metadata><tag property="http://cds.omdoc.org/mmt?mmt?inferred-type"/><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/recombination.mmt#1064.28.29:1064.28.29"/></metadata><type><om:OMS base="http://mathhub.info/MitM/numberfields" module="realnumbers" name="Realnumbers"></om:OMS></type></om:OMV><om:OMV name="y"><metadata><tag property="http://cds.omdoc.org/mmt?mmt?inferred-type"/><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/recombination.mmt#1066.28.31:1066.28.31"/></metadata><type><om:OMS base="http://mathhub.info/MitM/numberfields" module="realnumbers" name="Realnumbers"></om:OMS></type></om:OMV></om:OMBVAR>
- <om:OMS base="http://mathhub.info/MitM/Models/recombination" module="SpontaneousRecombination" name="spontaneous_recombination_coefficient"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/recombination.mmt#1069.28.34:1069.28.34"/></metadata></om:OMS>
- </om:OMBIND>
+ <om:OMS base="http://cds.omdoc.org/urtheories" module="LambdaPi" name="apply"></om:OMS>
+ <om:OMS base="http://mathhub.info/MMT/physics-units" module="QEBase" name="QE"></om:OMS><om:OMA><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/Quantities.mmt#1303.38.66:1320.38.83"/></metadata>
+ <om:OMS base="http://cds.omdoc.org/urtheories" module="LambdaPi" name="apply"></om:OMS>
+ <om:OMS base="http://mathhub.info/MMT/physics-units" module="Dimensions" name="DimDiv"></om:OMS><om:OMS base="http://mathhub.info/MMT/physics-units" module="DimensionsExtended" name="Volume"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/Quantities.mmt#1304.38.67:1309.38.72"/></metadata></om:OMS><om:OMS base="http://mathhub.info/MMT/physics-units" module="Dimensions" name="SItime"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/Quantities.mmt#1314.38.77:1319.38.82"/></metadata></om:OMS>
</om:OMA>
- </om:OMA></om:OMOBJ></type>
-
+ </om:OMA><om:OMA><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/recombination.mmt#1075.25.29:1079.25.33"/></metadata>
+ <om:OMS base="http://cds.omdoc.org/urtheories" module="LambdaPi" name="apply"></om:OMS>
+ <om:OMS base="http://mathhub.info/MitM/Models" module="RecombinationCoefficient" name="recombination_coefficient"></om:OMS><om:OMV name="x"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/recombination.mmt#1077.25.31:1077.25.31"/></metadata></om:OMV><om:OMV name="y"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/recombination.mmt#1079.25.33:1079.25.33"/></metadata></om:OMV>
+ </om:OMA><om:OMS base="http://mathhub.info/MitM/Models/recombination" module="SpontaneousRecombination" name="spontaneous_recombination_coefficient"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/recombination.mmt#1083.25.37:1083.25.37"/></metadata></om:OMS>
+ </om:OMA>
+ </om:OMA>
+ </om:OMBIND></om:OMOBJ></type>
+ <notations></notations>
</constant></theory></omdoc>
\ No newline at end of file
diff --git a/relational/http..mathhub.info/MitM/Models/$Base.rel b/relational/http..mathhub.info/MitM/Models/$Base.rel
index 256ed47..1258db7 100644
--- a/relational/http..mathhub.info/MitM/Models/$Base.rel
+++ b/relational/http..mathhub.info/MitM/Models/$Base.rel
@@ -1,44 +1,4 @@
theory http://mathhub.info/MitM/Models?Base
-HasMeta http://mathhub.info/MitM/Models?Base http://mathhub.info/MitM/numberfields?realarith
+HasMeta http://mathhub.info/MitM/Models?Base http://mathhub.info/MitM/smglom/arithmetics?realarith
Includes http://mathhub.info/MitM/Models?Base http://mathhub.info/MitM/Models?PhysicalConstants
-Includes http://mathhub.info/MitM/Models?Base http://gl.mathhub.info/MMT/LFX/Sigma?LFSigma
-Includes http://mathhub.info/MitM/Models?Base http://gl.mathhub.info/MMT/LFX/Sigma?TypedSigma
-Includes http://mathhub.info/MitM/Models?Base http://gl.mathhub.info/MMT/LFX/Sigma?Symbols
-Includes http://mathhub.info/MitM/Models?Base http://gl.mathhub.info/MMT/LFX/Sigma?Rules
-Includes http://mathhub.info/MitM/Models?Base http://cds.omdoc.org/urtheories?LF
-Includes http://mathhub.info/MitM/Models?Base http://cds.omdoc.org/urtheories?TermsTypesKinds
-Includes http://mathhub.info/MitM/Models?Base http://cds.omdoc.org/mmt?Errors
-Includes http://mathhub.info/MitM/Models?Base http://cds.omdoc.org/mmt?ModExp
-Includes http://mathhub.info/MitM/Models?Base http://cds.omdoc.org/mmt?mmt
-Includes http://mathhub.info/MitM/Models?Base http://cds.omdoc.org/urtheories?Typed
-Includes http://mathhub.info/MitM/Models?Base http://cds.omdoc.org/urtheories?Kinded
-Includes http://mathhub.info/MitM/Models?Base http://cds.omdoc.org/urtheories?TypedConstants
-Includes http://mathhub.info/MitM/Models?Base http://cds.omdoc.org/urtheories?KindedConstants
-Includes http://mathhub.info/MitM/Models?Base http://cds.omdoc.org/urtheories?LambdaPi
-Includes http://mathhub.info/MitM/Models?Base http://cds.omdoc.org/urtheories?LFRules
-Declares http://mathhub.info/MitM/Models?Base http://mathhub.info/MitM/Models?Base?exp
-constant http://mathhub.info/MitM/Models?Base?exp
-Declares http://mathhub.info/MitM/Models?Base http://mathhub.info/MitM/Models?Base?der
-constant http://mathhub.info/MitM/Models?Base?der
-Declares http://mathhub.info/MitM/Models?Base http://mathhub.info/MitM/Models?Base?Real_vec_space2
-constant http://mathhub.info/MitM/Models?Base?Real_vec_space2
-Declares http://mathhub.info/MitM/Models?Base http://mathhub.info/MitM/Models?Base?Real_vec_space3
-constant http://mathhub.info/MitM/Models?Base?Real_vec_space3
-Declares http://mathhub.info/MitM/Models?Base http://mathhub.info/MitM/Models?Base?comp1
-constant http://mathhub.info/MitM/Models?Base?comp1
-Declares http://mathhub.info/MitM/Models?Base http://mathhub.info/MitM/Models?Base?comp2
-constant http://mathhub.info/MitM/Models?Base?comp2
-Declares http://mathhub.info/MitM/Models?Base http://mathhub.info/MitM/Models?Base?comp3
-constant http://mathhub.info/MitM/Models?Base?comp3
-Declares http://mathhub.info/MitM/Models?Base http://mathhub.info/MitM/Models?Base?pred_as_sub2
-constant http://mathhub.info/MitM/Models?Base?pred_as_sub2
-Declares http://mathhub.info/MitM/Models?Base http://mathhub.info/MitM/Models?Base?pred_as_sub3
-constant http://mathhub.info/MitM/Models?Base?pred_as_sub3
-Declares http://mathhub.info/MitM/Models?Base http://mathhub.info/MitM/Models?Base?lift_type_one_to_three
-constant http://mathhub.info/MitM/Models?Base?lift_type_one_to_three
-Declares http://mathhub.info/MitM/Models?Base http://mathhub.info/MitM/Models?Base?lift_type_two_to_three
-constant http://mathhub.info/MitM/Models?Base?lift_type_two_to_three
-Declares http://mathhub.info/MitM/Models?Base http://mathhub.info/MitM/Models?Base?lift_function_one_to_three
-constant http://mathhub.info/MitM/Models?Base?lift_function_one_to_three
-Declares http://mathhub.info/MitM/Models?Base http://mathhub.info/MitM/Models?Base?lift_function_two_to_three
-constant http://mathhub.info/MitM/Models?Base?lift_function_two_to_three
+Includes http://mathhub.info/MitM/Models?Base http://mathhub.info/MitM/smglom/calculus?derivative
diff --git a/relational/http..mathhub.info/MitM/Models/$Physical$Constants.rel b/relational/http..mathhub.info/MitM/Models/$Physical$Constants.rel
index d7ad3c9..44a1003 100644
--- a/relational/http..mathhub.info/MitM/Models/$Physical$Constants.rel
+++ b/relational/http..mathhub.info/MitM/Models/$Physical$Constants.rel
@@ -1,5 +1,14 @@
theory http://mathhub.info/MitM/Models?PhysicalConstants
-HasMeta http://mathhub.info/MitM/Models?PhysicalConstants http://mathhub.info/MitM/numberfields?realnumbers
+HasMeta http://mathhub.info/MitM/Models?PhysicalConstants http://mathhub.info/MMT/physics-units?QEBase
+Includes http://mathhub.info/MitM/Models?PhysicalConstants http://mathhub.info/MitM/Models?Permittivity
+Includes http://mathhub.info/MitM/Models?PhysicalConstants http://mathhub.info/MitM/smglom/arithmetics?realarith
+Includes http://mathhub.info/MitM/Models?PhysicalConstants http://mathhub.info/MitM/smglom/arithmetics?realnumbers
+Includes http://mathhub.info/MitM/Models?PhysicalConstants http://mathhub.info/MitM/smglom/arithmetics?rationalnumbers
+Includes http://mathhub.info/MitM/Models?PhysicalConstants http://mathhub.info/MitM/smglom/arithmetics?integernumbers
+Includes http://mathhub.info/MitM/Models?PhysicalConstants http://mathhub.info/MitM/smglom/arithmetics?naturalnumbers
+Includes http://mathhub.info/MitM/Models?PhysicalConstants http://mathhub.info/MitM/smglom/arithmetics?ratarith
+Includes http://mathhub.info/MitM/Models?PhysicalConstants http://mathhub.info/MitM/smglom/arithmetics?intarith
+Includes http://mathhub.info/MitM/Models?PhysicalConstants http://mathhub.info/MitM/smglom/arithmetics?natarith
Declares http://mathhub.info/MitM/Models?PhysicalConstants http://mathhub.info/MitM/Models?PhysicalConstants?vacuum_dielectric_permitivity
constant http://mathhub.info/MitM/Models?PhysicalConstants?vacuum_dielectric_permitivity
Declares http://mathhub.info/MitM/Models?PhysicalConstants http://mathhub.info/MitM/Models?PhysicalConstants?elementary_charge
diff --git a/relational/http..mathhub.info/MitM/Models/continuity/$Continuity$Equation$Electrons.rel b/relational/http..mathhub.info/MitM/Models/continuity/$Continuity$Equation$Electrons.rel
index 2a9961d..5b7e869 100644
--- a/relational/http..mathhub.info/MitM/Models/continuity/$Continuity$Equation$Electrons.rel
+++ b/relational/http..mathhub.info/MitM/Models/continuity/$Continuity$Equation$Electrons.rel
@@ -1,17 +1,4 @@
theory http://mathhub.info/MitM/Models/continuity?ContinuityEquationElectrons
HasMeta http://mathhub.info/MitM/Models/continuity?ContinuityEquationElectrons http://mathhub.info/MitM/Models?Base
-Includes http://mathhub.info/MitM/Models/continuity?ContinuityEquationElectrons http://mathhub.info/MitM/Models/continuity?CurrentElectrons
-Includes http://mathhub.info/MitM/Models/continuity?ContinuityEquationElectrons http://mathhub.info/MitM/Models/densities?FermiPotentialElectrons
-Includes http://mathhub.info/MitM/Models/continuity?ContinuityEquationElectrons http://mathhub.info/MitM/Models/device?DeviceGeometry
-Includes http://mathhub.info/MitM/Models/continuity?ContinuityEquationElectrons http://mathhub.info/MitM/Models/device?Device
-Includes http://mathhub.info/MitM/Models/continuity?ContinuityEquationElectrons http://mathhub.info/MitM/Models/densities?DensityElectrons
-Includes http://mathhub.info/MitM/Models/continuity?ContinuityEquationElectrons http://mathhub.info/MitM/Models/device?DeviceOperationState
-Includes http://mathhub.info/MitM/Models/continuity?ContinuityEquationElectrons http://mathhub.info/MitM/Models?PhysicalConstants
-Includes http://mathhub.info/MitM/Models/continuity?ContinuityEquationElectrons http://mathhub.info/MitM/Models/densities?BandstructureParameters
-Includes http://mathhub.info/MitM/Models/continuity?ContinuityEquationElectrons http://mathhub.info/MitM/Models/continuity?Mobilities
-Includes http://mathhub.info/MitM/Models/continuity?ContinuityEquationElectrons http://mathhub.info/MitM/Models/densities?DensityHoles
-Includes http://mathhub.info/MitM/Models/continuity?ContinuityEquationElectrons http://mathhub.info/MitM/Models/densities?FermiPotentialHoles
-Includes http://mathhub.info/MitM/Models/continuity?ContinuityEquationElectrons http://mathhub.info/MitM/Models/recombination?Recombination
-Includes http://mathhub.info/MitM/Models/continuity?ContinuityEquationElectrons http://mathhub.info/MitM/Models/densities?ElectrostaticPotential
-Declares http://mathhub.info/MitM/Models/continuity?ContinuityEquationElectrons http://mathhub.info/MitM/Models/continuity?ContinuityEquationElectrons?continuity_equation_electrons
-constant http://mathhub.info/MitM/Models/continuity?ContinuityEquationElectrons?continuity_equation_electrons
+Declares http://mathhub.info/MitM/Models/continuity?ContinuityEquationElectrons http://mathhub.info/MitM/Models/continuity?ContinuityEquationElectrons?continuity_equation
+constant http://mathhub.info/MitM/Models/continuity?ContinuityEquationElectrons?continuity_equation
diff --git a/relational/http..mathhub.info/MitM/Models/continuity/$Continuity$Equation$Holes.rel b/relational/http..mathhub.info/MitM/Models/continuity/$Continuity$Equation$Holes.rel
index eacdaae..df666b1 100644
--- a/relational/http..mathhub.info/MitM/Models/continuity/$Continuity$Equation$Holes.rel
+++ b/relational/http..mathhub.info/MitM/Models/continuity/$Continuity$Equation$Holes.rel
@@ -7,11 +7,23 @@ Includes http://mathhub.info/MitM/Models/continuity?ContinuityEquationHoles http
Includes http://mathhub.info/MitM/Models/continuity?ContinuityEquationHoles http://mathhub.info/MitM/Models/densities?DensityHoles
Includes http://mathhub.info/MitM/Models/continuity?ContinuityEquationHoles http://mathhub.info/MitM/Models/device?DeviceOperationState
Includes http://mathhub.info/MitM/Models/continuity?ContinuityEquationHoles http://mathhub.info/MitM/Models?PhysicalConstants
+Includes http://mathhub.info/MitM/Models/continuity?ContinuityEquationHoles http://mathhub.info/MitM/Models?Permittivity
+Includes http://mathhub.info/MitM/Models/continuity?ContinuityEquationHoles http://mathhub.info/MitM/smglom/arithmetics?realarith
+Includes http://mathhub.info/MitM/Models/continuity?ContinuityEquationHoles http://mathhub.info/MitM/smglom/arithmetics?realnumbers
+Includes http://mathhub.info/MitM/Models/continuity?ContinuityEquationHoles http://mathhub.info/MitM/smglom/arithmetics?rationalnumbers
+Includes http://mathhub.info/MitM/Models/continuity?ContinuityEquationHoles http://mathhub.info/MitM/smglom/arithmetics?integernumbers
+Includes http://mathhub.info/MitM/Models/continuity?ContinuityEquationHoles http://mathhub.info/MitM/smglom/arithmetics?naturalnumbers
+Includes http://mathhub.info/MitM/Models/continuity?ContinuityEquationHoles http://mathhub.info/MitM/smglom/arithmetics?ratarith
+Includes http://mathhub.info/MitM/Models/continuity?ContinuityEquationHoles http://mathhub.info/MitM/smglom/arithmetics?intarith
+Includes http://mathhub.info/MitM/Models/continuity?ContinuityEquationHoles http://mathhub.info/MitM/smglom/arithmetics?natarith
Includes http://mathhub.info/MitM/Models/continuity?ContinuityEquationHoles http://mathhub.info/MitM/Models/densities?BandstructureParameters
+Includes http://mathhub.info/MitM/Models/continuity?ContinuityEquationHoles http://mathhub.info/MitM/Models?Density
Includes http://mathhub.info/MitM/Models/continuity?ContinuityEquationHoles http://mathhub.info/MitM/Models/continuity?Mobilities
+Includes http://mathhub.info/MitM/Models/continuity?ContinuityEquationHoles http://mathhub.info/MitM/Models?CurrentDensity
Includes http://mathhub.info/MitM/Models/continuity?ContinuityEquationHoles http://mathhub.info/MitM/Models/densities?DensityElectrons
Includes http://mathhub.info/MitM/Models/continuity?ContinuityEquationHoles http://mathhub.info/MitM/Models/densities?FermiPotentialElectrons
Includes http://mathhub.info/MitM/Models/continuity?ContinuityEquationHoles http://mathhub.info/MitM/Models/recombination?Recombination
+Includes http://mathhub.info/MitM/Models/continuity?ContinuityEquationHoles http://mathhub.info/MitM/Models?RecombinationRate
Includes http://mathhub.info/MitM/Models/continuity?ContinuityEquationHoles http://mathhub.info/MitM/Models/densities?ElectrostaticPotential
Declares http://mathhub.info/MitM/Models/continuity?ContinuityEquationHoles http://mathhub.info/MitM/Models/continuity?ContinuityEquationHoles?continuity_equation_holes
constant http://mathhub.info/MitM/Models/continuity?ContinuityEquationHoles?continuity_equation_holes
diff --git a/relational/http..mathhub.info/MitM/Models/continuity/$Current$Electrons.rel b/relational/http..mathhub.info/MitM/Models/continuity/$Current$Electrons.rel
index 7cea8a9..5b0910d 100644
--- a/relational/http..mathhub.info/MitM/Models/continuity/$Current$Electrons.rel
+++ b/relational/http..mathhub.info/MitM/Models/continuity/$Current$Electrons.rel
@@ -1,13 +1,21 @@
theory http://mathhub.info/MitM/Models/continuity?CurrentElectrons
HasMeta http://mathhub.info/MitM/Models/continuity?CurrentElectrons http://mathhub.info/MitM/Models?Base
Includes http://mathhub.info/MitM/Models/continuity?CurrentElectrons http://mathhub.info/MitM/Models/densities?FermiPotentialElectrons
-Includes http://mathhub.info/MitM/Models/continuity?CurrentElectrons http://mathhub.info/MitM/Models/device?DeviceGeometry
-Includes http://mathhub.info/MitM/Models/continuity?CurrentElectrons http://mathhub.info/MitM/Models/device?Device
Includes http://mathhub.info/MitM/Models/continuity?CurrentElectrons http://mathhub.info/MitM/Models/densities?ElectrostaticPotential
Includes http://mathhub.info/MitM/Models/continuity?CurrentElectrons http://mathhub.info/MitM/Models/densities?DensityElectrons
Includes http://mathhub.info/MitM/Models/continuity?CurrentElectrons http://mathhub.info/MitM/Models/device?DeviceOperationState
Includes http://mathhub.info/MitM/Models/continuity?CurrentElectrons http://mathhub.info/MitM/Models?PhysicalConstants
+Includes http://mathhub.info/MitM/Models/continuity?CurrentElectrons http://mathhub.info/MitM/Models?Permittivity
+Includes http://mathhub.info/MitM/Models/continuity?CurrentElectrons http://mathhub.info/MitM/smglom/arithmetics?realarith
+Includes http://mathhub.info/MitM/Models/continuity?CurrentElectrons http://mathhub.info/MitM/smglom/arithmetics?realnumbers
+Includes http://mathhub.info/MitM/Models/continuity?CurrentElectrons http://mathhub.info/MitM/smglom/arithmetics?rationalnumbers
+Includes http://mathhub.info/MitM/Models/continuity?CurrentElectrons http://mathhub.info/MitM/smglom/arithmetics?integernumbers
+Includes http://mathhub.info/MitM/Models/continuity?CurrentElectrons http://mathhub.info/MitM/smglom/arithmetics?naturalnumbers
+Includes http://mathhub.info/MitM/Models/continuity?CurrentElectrons http://mathhub.info/MitM/smglom/arithmetics?ratarith
+Includes http://mathhub.info/MitM/Models/continuity?CurrentElectrons http://mathhub.info/MitM/smglom/arithmetics?intarith
+Includes http://mathhub.info/MitM/Models/continuity?CurrentElectrons http://mathhub.info/MitM/smglom/arithmetics?natarith
Includes http://mathhub.info/MitM/Models/continuity?CurrentElectrons http://mathhub.info/MitM/Models/densities?BandstructureParameters
Includes http://mathhub.info/MitM/Models/continuity?CurrentElectrons http://mathhub.info/MitM/Models/continuity?Mobilities
-Declares http://mathhub.info/MitM/Models/continuity?CurrentElectrons http://mathhub.info/MitM/Models/continuity?CurrentElectrons?current_electrons
-constant http://mathhub.info/MitM/Models/continuity?CurrentElectrons?current_electrons
+Includes http://mathhub.info/MitM/Models/continuity?CurrentElectrons http://mathhub.info/MitM/Models?CurrentDensity
+Declares http://mathhub.info/MitM/Models/continuity?CurrentElectrons http://mathhub.info/MitM/Models/continuity?CurrentElectrons?current_electrons_law
+constant http://mathhub.info/MitM/Models/continuity?CurrentElectrons?current_electrons_law
diff --git a/relational/http..mathhub.info/MitM/Models/continuity/$Current$Holes.rel b/relational/http..mathhub.info/MitM/Models/continuity/$Current$Holes.rel
index f6f43f6..42a3d8e 100644
--- a/relational/http..mathhub.info/MitM/Models/continuity/$Current$Holes.rel
+++ b/relational/http..mathhub.info/MitM/Models/continuity/$Current$Holes.rel
@@ -7,7 +7,18 @@ Includes http://mathhub.info/MitM/Models/continuity?CurrentHoles http://mathhub.
Includes http://mathhub.info/MitM/Models/continuity?CurrentHoles http://mathhub.info/MitM/Models/densities?DensityHoles
Includes http://mathhub.info/MitM/Models/continuity?CurrentHoles http://mathhub.info/MitM/Models/device?DeviceOperationState
Includes http://mathhub.info/MitM/Models/continuity?CurrentHoles http://mathhub.info/MitM/Models?PhysicalConstants
+Includes http://mathhub.info/MitM/Models/continuity?CurrentHoles http://mathhub.info/MitM/Models?Permittivity
+Includes http://mathhub.info/MitM/Models/continuity?CurrentHoles http://mathhub.info/MitM/smglom/arithmetics?realarith
+Includes http://mathhub.info/MitM/Models/continuity?CurrentHoles http://mathhub.info/MitM/smglom/arithmetics?realnumbers
+Includes http://mathhub.info/MitM/Models/continuity?CurrentHoles http://mathhub.info/MitM/smglom/arithmetics?rationalnumbers
+Includes http://mathhub.info/MitM/Models/continuity?CurrentHoles http://mathhub.info/MitM/smglom/arithmetics?integernumbers
+Includes http://mathhub.info/MitM/Models/continuity?CurrentHoles http://mathhub.info/MitM/smglom/arithmetics?naturalnumbers
+Includes http://mathhub.info/MitM/Models/continuity?CurrentHoles http://mathhub.info/MitM/smglom/arithmetics?ratarith
+Includes http://mathhub.info/MitM/Models/continuity?CurrentHoles http://mathhub.info/MitM/smglom/arithmetics?intarith
+Includes http://mathhub.info/MitM/Models/continuity?CurrentHoles http://mathhub.info/MitM/smglom/arithmetics?natarith
Includes http://mathhub.info/MitM/Models/continuity?CurrentHoles http://mathhub.info/MitM/Models/densities?BandstructureParameters
+Includes http://mathhub.info/MitM/Models/continuity?CurrentHoles http://mathhub.info/MitM/Models?Density
Includes http://mathhub.info/MitM/Models/continuity?CurrentHoles http://mathhub.info/MitM/Models/continuity?Mobilities
-Declares http://mathhub.info/MitM/Models/continuity?CurrentHoles http://mathhub.info/MitM/Models/continuity?CurrentHoles?current_holes
-constant http://mathhub.info/MitM/Models/continuity?CurrentHoles?current_holes
+Includes http://mathhub.info/MitM/Models/continuity?CurrentHoles http://mathhub.info/MitM/Models?CurrentDensity
+Declares http://mathhub.info/MitM/Models/continuity?CurrentHoles http://mathhub.info/MitM/Models/continuity?CurrentHoles?current_holes_law
+constant http://mathhub.info/MitM/Models/continuity?CurrentHoles?current_holes_law
diff --git a/relational/http..mathhub.info/MitM/Models/densities/$Bandstructure$Parameters.rel b/relational/http..mathhub.info/MitM/Models/densities/$Bandstructure$Parameters.rel
index 96ee1d0..fb1bb49 100644
--- a/relational/http..mathhub.info/MitM/Models/densities/$Bandstructure$Parameters.rel
+++ b/relational/http..mathhub.info/MitM/Models/densities/$Bandstructure$Parameters.rel
@@ -1,5 +1,6 @@
theory http://mathhub.info/MitM/Models/densities?BandstructureParameters
HasMeta http://mathhub.info/MitM/Models/densities?BandstructureParameters http://mathhub.info/MitM/Models?Base
+Includes http://mathhub.info/MitM/Models/densities?BandstructureParameters http://mathhub.info/MitM/Models?Density
Declares http://mathhub.info/MitM/Models/densities?BandstructureParameters http://mathhub.info/MitM/Models/densities?BandstructureParameters?effective_density_of_states_conduction_bands
constant http://mathhub.info/MitM/Models/densities?BandstructureParameters?effective_density_of_states_conduction_bands
Declares http://mathhub.info/MitM/Models/densities?BandstructureParameters http://mathhub.info/MitM/Models/densities?BandstructureParameters?effective_density_of_states_valence_bands
diff --git a/relational/http..mathhub.info/MitM/Models/densities/$Fermi$Potential$Electrons.rel b/relational/http..mathhub.info/MitM/Models/densities/$Fermi$Potential$Electrons.rel
index fe90500..f11fa2e 100644
--- a/relational/http..mathhub.info/MitM/Models/densities/$Fermi$Potential$Electrons.rel
+++ b/relational/http..mathhub.info/MitM/Models/densities/$Fermi$Potential$Electrons.rel
@@ -1,6 +1,5 @@
theory http://mathhub.info/MitM/Models/densities?FermiPotentialElectrons
HasMeta http://mathhub.info/MitM/Models/densities?FermiPotentialElectrons http://mathhub.info/MitM/Models?Base
Includes http://mathhub.info/MitM/Models/densities?FermiPotentialElectrons http://mathhub.info/MitM/Models/device?DeviceGeometry
-Includes http://mathhub.info/MitM/Models/densities?FermiPotentialElectrons http://mathhub.info/MitM/Models/device?Device
Declares http://mathhub.info/MitM/Models/densities?FermiPotentialElectrons http://mathhub.info/MitM/Models/densities?FermiPotentialElectrons?quasi_Fermi_potential
constant http://mathhub.info/MitM/Models/densities?FermiPotentialElectrons?quasi_Fermi_potential
diff --git a/relational/http..mathhub.info/MitM/Models/densities/$Fermi$Potential$Holes.rel b/relational/http..mathhub.info/MitM/Models/densities/$Fermi$Potential$Holes.rel
index 616a46b..684a98a 100644
--- a/relational/http..mathhub.info/MitM/Models/densities/$Fermi$Potential$Holes.rel
+++ b/relational/http..mathhub.info/MitM/Models/densities/$Fermi$Potential$Holes.rel
@@ -1,6 +1,5 @@
theory http://mathhub.info/MitM/Models/densities?FermiPotentialHoles
HasMeta http://mathhub.info/MitM/Models/densities?FermiPotentialHoles http://mathhub.info/MitM/Models?Base
Includes http://mathhub.info/MitM/Models/densities?FermiPotentialHoles http://mathhub.info/MitM/Models/device?DeviceGeometry
-Includes http://mathhub.info/MitM/Models/densities?FermiPotentialHoles http://mathhub.info/MitM/Models/device?Device
Declares http://mathhub.info/MitM/Models/densities?FermiPotentialHoles http://mathhub.info/MitM/Models/densities?FermiPotentialHoles?quasi_Fermi_potential
constant http://mathhub.info/MitM/Models/densities?FermiPotentialHoles?quasi_Fermi_potential
diff --git a/relational/http..mathhub.info/MitM/Models/device/$Device$Operation$State.rel b/relational/http..mathhub.info/MitM/Models/device/$Device$Operation$State.rel
index 48d7ea4..cccf188 100644
--- a/relational/http..mathhub.info/MitM/Models/device/$Device$Operation$State.rel
+++ b/relational/http..mathhub.info/MitM/Models/device/$Device$Operation$State.rel
@@ -2,11 +2,9 @@ theory http://mathhub.info/MitM/Models/device?DeviceOperationState
HasMeta http://mathhub.info/MitM/Models/device?DeviceOperationState http://mathhub.info/MitM/Models?Base
Includes http://mathhub.info/MitM/Models/device?DeviceOperationState http://mathhub.info/MitM/Models/device?DeviceGeometry
Includes http://mathhub.info/MitM/Models/device?DeviceOperationState http://mathhub.info/MitM/Models/device?Device
-Declares http://mathhub.info/MitM/Models/device?DeviceOperationState http://mathhub.info/MitM/Models/device?DeviceOperationState?temperatur
-constant http://mathhub.info/MitM/Models/device?DeviceOperationState?temperatur
+Declares http://mathhub.info/MitM/Models/device?DeviceOperationState http://mathhub.info/MitM/Models/device?DeviceOperationState?temperature
+constant http://mathhub.info/MitM/Models/device?DeviceOperationState?temperature
Declares http://mathhub.info/MitM/Models/device?DeviceOperationState http://mathhub.info/MitM/Models/device?DeviceOperationState?voltage_bottom
constant http://mathhub.info/MitM/Models/device?DeviceOperationState?voltage_bottom
Declares http://mathhub.info/MitM/Models/device?DeviceOperationState http://mathhub.info/MitM/Models/device?DeviceOperationState?voltage_top
constant http://mathhub.info/MitM/Models/device?DeviceOperationState?voltage_top
-Declares http://mathhub.info/MitM/Models/device?DeviceOperationState http://mathhub.info/MitM/Models/device?DeviceOperationState?prf
-constant http://mathhub.info/MitM/Models/device?DeviceOperationState?prf
diff --git a/relational/http..mathhub.info/MitM/Models/device/$Doping$Profile.rel b/relational/http..mathhub.info/MitM/Models/device/$Doping$Profile.rel
index bb28248..753a7b8 100644
--- a/relational/http..mathhub.info/MitM/Models/device/$Doping$Profile.rel
+++ b/relational/http..mathhub.info/MitM/Models/device/$Doping$Profile.rel
@@ -2,5 +2,6 @@ theory http://mathhub.info/MitM/Models/device?DopingProfile
HasMeta http://mathhub.info/MitM/Models/device?DopingProfile http://mathhub.info/MitM/Models?Base
Includes http://mathhub.info/MitM/Models/device?DopingProfile http://mathhub.info/MitM/Models/device?DeviceGeometry
Includes http://mathhub.info/MitM/Models/device?DopingProfile http://mathhub.info/MitM/Models/device?Device
+Includes http://mathhub.info/MitM/Models/device?DopingProfile http://mathhub.info/MitM/Models?Density
Declares http://mathhub.info/MitM/Models/device?DopingProfile http://mathhub.info/MitM/Models/device?DopingProfile?doping_profile
constant http://mathhub.info/MitM/Models/device?DopingProfile?doping_profile
diff --git a/relational/http..mathhub.info/MitM/Models/poisson/$Poisson$Boundary$Conditions.rel b/relational/http..mathhub.info/MitM/Models/poisson/$Poisson$Boundary$Conditions.rel
index bec83d9..41a2a9f 100644
--- a/relational/http..mathhub.info/MitM/Models/poisson/$Poisson$Boundary$Conditions.rel
+++ b/relational/http..mathhub.info/MitM/Models/poisson/$Poisson$Boundary$Conditions.rel
@@ -5,10 +5,20 @@ Includes http://mathhub.info/MitM/Models/poisson?PoissonBoundaryConditions http:
Includes http://mathhub.info/MitM/Models/poisson?PoissonBoundaryConditions http://mathhub.info/MitM/Models/device?DeviceGeometry
Includes http://mathhub.info/MitM/Models/poisson?PoissonBoundaryConditions http://mathhub.info/MitM/Models/device?Device
Includes http://mathhub.info/MitM/Models/poisson?PoissonBoundaryConditions http://mathhub.info/MitM/Models/device?DopingProfile
+Includes http://mathhub.info/MitM/Models/poisson?PoissonBoundaryConditions http://mathhub.info/MitM/Models?Density
Includes http://mathhub.info/MitM/Models/poisson?PoissonBoundaryConditions http://mathhub.info/MitM/Models/poisson?PoissonParameters
Includes http://mathhub.info/MitM/Models/poisson?PoissonBoundaryConditions http://mathhub.info/MitM/Models/densities?DensityElectrons
Includes http://mathhub.info/MitM/Models/poisson?PoissonBoundaryConditions http://mathhub.info/MitM/Models/device?DeviceOperationState
Includes http://mathhub.info/MitM/Models/poisson?PoissonBoundaryConditions http://mathhub.info/MitM/Models?PhysicalConstants
+Includes http://mathhub.info/MitM/Models/poisson?PoissonBoundaryConditions http://mathhub.info/MitM/Models?Permittivity
+Includes http://mathhub.info/MitM/Models/poisson?PoissonBoundaryConditions http://mathhub.info/MitM/smglom/arithmetics?realarith
+Includes http://mathhub.info/MitM/Models/poisson?PoissonBoundaryConditions http://mathhub.info/MitM/smglom/arithmetics?realnumbers
+Includes http://mathhub.info/MitM/Models/poisson?PoissonBoundaryConditions http://mathhub.info/MitM/smglom/arithmetics?rationalnumbers
+Includes http://mathhub.info/MitM/Models/poisson?PoissonBoundaryConditions http://mathhub.info/MitM/smglom/arithmetics?integernumbers
+Includes http://mathhub.info/MitM/Models/poisson?PoissonBoundaryConditions http://mathhub.info/MitM/smglom/arithmetics?naturalnumbers
+Includes http://mathhub.info/MitM/Models/poisson?PoissonBoundaryConditions http://mathhub.info/MitM/smglom/arithmetics?ratarith
+Includes http://mathhub.info/MitM/Models/poisson?PoissonBoundaryConditions http://mathhub.info/MitM/smglom/arithmetics?intarith
+Includes http://mathhub.info/MitM/Models/poisson?PoissonBoundaryConditions http://mathhub.info/MitM/smglom/arithmetics?natarith
Includes http://mathhub.info/MitM/Models/poisson?PoissonBoundaryConditions http://mathhub.info/MitM/Models/densities?BandstructureParameters
Includes http://mathhub.info/MitM/Models/poisson?PoissonBoundaryConditions http://mathhub.info/MitM/Models/densities?FermiPotentialElectrons
Includes http://mathhub.info/MitM/Models/poisson?PoissonBoundaryConditions http://mathhub.info/MitM/Models/densities?ElectrostaticPotential
diff --git a/relational/http..mathhub.info/MitM/Models/poisson/$Poisson$Equation.rel b/relational/http..mathhub.info/MitM/Models/poisson/$Poisson$Equation.rel
index 0583215..f14102e 100644
--- a/relational/http..mathhub.info/MitM/Models/poisson/$Poisson$Equation.rel
+++ b/relational/http..mathhub.info/MitM/Models/poisson/$Poisson$Equation.rel
@@ -4,10 +4,20 @@ Includes http://mathhub.info/MitM/Models/poisson?PoissonEquation http://mathhub.
Includes http://mathhub.info/MitM/Models/poisson?PoissonEquation http://mathhub.info/MitM/Models/device?DeviceGeometry
Includes http://mathhub.info/MitM/Models/poisson?PoissonEquation http://mathhub.info/MitM/Models/device?Device
Includes http://mathhub.info/MitM/Models/poisson?PoissonEquation http://mathhub.info/MitM/Models/device?DopingProfile
+Includes http://mathhub.info/MitM/Models/poisson?PoissonEquation http://mathhub.info/MitM/Models?Density
Includes http://mathhub.info/MitM/Models/poisson?PoissonEquation http://mathhub.info/MitM/Models/poisson?PoissonParameters
Includes http://mathhub.info/MitM/Models/poisson?PoissonEquation http://mathhub.info/MitM/Models/densities?DensityElectrons
Includes http://mathhub.info/MitM/Models/poisson?PoissonEquation http://mathhub.info/MitM/Models/device?DeviceOperationState
Includes http://mathhub.info/MitM/Models/poisson?PoissonEquation http://mathhub.info/MitM/Models?PhysicalConstants
+Includes http://mathhub.info/MitM/Models/poisson?PoissonEquation http://mathhub.info/MitM/Models?Permittivity
+Includes http://mathhub.info/MitM/Models/poisson?PoissonEquation http://mathhub.info/MitM/smglom/arithmetics?realarith
+Includes http://mathhub.info/MitM/Models/poisson?PoissonEquation http://mathhub.info/MitM/smglom/arithmetics?realnumbers
+Includes http://mathhub.info/MitM/Models/poisson?PoissonEquation http://mathhub.info/MitM/smglom/arithmetics?rationalnumbers
+Includes http://mathhub.info/MitM/Models/poisson?PoissonEquation http://mathhub.info/MitM/smglom/arithmetics?integernumbers
+Includes http://mathhub.info/MitM/Models/poisson?PoissonEquation http://mathhub.info/MitM/smglom/arithmetics?naturalnumbers
+Includes http://mathhub.info/MitM/Models/poisson?PoissonEquation http://mathhub.info/MitM/smglom/arithmetics?ratarith
+Includes http://mathhub.info/MitM/Models/poisson?PoissonEquation http://mathhub.info/MitM/smglom/arithmetics?intarith
+Includes http://mathhub.info/MitM/Models/poisson?PoissonEquation http://mathhub.info/MitM/smglom/arithmetics?natarith
Includes http://mathhub.info/MitM/Models/poisson?PoissonEquation http://mathhub.info/MitM/Models/densities?BandstructureParameters
Includes http://mathhub.info/MitM/Models/poisson?PoissonEquation http://mathhub.info/MitM/Models/densities?FermiPotentialElectrons
Includes http://mathhub.info/MitM/Models/poisson?PoissonEquation http://mathhub.info/MitM/Models/densities?ElectrostaticPotential
diff --git a/relational/http..mathhub.info/MitM/Models/poisson/$Poisson$Parameters.rel b/relational/http..mathhub.info/MitM/Models/poisson/$Poisson$Parameters.rel
index abf5dc7..4c26e19 100644
--- a/relational/http..mathhub.info/MitM/Models/poisson/$Poisson$Parameters.rel
+++ b/relational/http..mathhub.info/MitM/Models/poisson/$Poisson$Parameters.rel
@@ -1,6 +1,6 @@
theory http://mathhub.info/MitM/Models/poisson?PoissonParameters
HasMeta http://mathhub.info/MitM/Models/poisson?PoissonParameters http://mathhub.info/MitM/Models?Base
-Declares http://mathhub.info/MitM/Models/poisson?PoissonParameters http://mathhub.info/MitM/Models/poisson?PoissonParameters?relative_dielectric_permitivity
-constant http://mathhub.info/MitM/Models/poisson?PoissonParameters?relative_dielectric_permitivity
-Declares http://mathhub.info/MitM/Models/poisson?PoissonParameters http://mathhub.info/MitM/Models/poisson?PoissonParameters?dielectric_permitivity
-constant http://mathhub.info/MitM/Models/poisson?PoissonParameters?dielectric_permitivity
+Declares http://mathhub.info/MitM/Models/poisson?PoissonParameters http://mathhub.info/MitM/Models/poisson?PoissonParameters?relative_dielectric_permittivity
+constant http://mathhub.info/MitM/Models/poisson?PoissonParameters?relative_dielectric_permittivity
+Declares http://mathhub.info/MitM/Models/poisson?PoissonParameters http://mathhub.info/MitM/Models/poisson?PoissonParameters?dielectric_permittivity
+constant http://mathhub.info/MitM/Models/poisson?PoissonParameters?dielectric_permittivity
diff --git a/relational/http..mathhub.info/MitM/Models/poisson/$Thermodynamic$Equilibrium.rel b/relational/http..mathhub.info/MitM/Models/poisson/$Thermodynamic$Equilibrium.rel
index 3e5e4f4..55b2fc3 100644
--- a/relational/http..mathhub.info/MitM/Models/poisson/$Thermodynamic$Equilibrium.rel
+++ b/relational/http..mathhub.info/MitM/Models/poisson/$Thermodynamic$Equilibrium.rel
@@ -4,10 +4,20 @@ Includes http://mathhub.info/MitM/Models/poisson?ThermodynamicEquilibrium http:/
Includes http://mathhub.info/MitM/Models/poisson?ThermodynamicEquilibrium http://mathhub.info/MitM/Models/device?DeviceGeometry
Includes http://mathhub.info/MitM/Models/poisson?ThermodynamicEquilibrium http://mathhub.info/MitM/Models/device?Device
Includes http://mathhub.info/MitM/Models/poisson?ThermodynamicEquilibrium http://mathhub.info/MitM/Models/device?DopingProfile
+Includes http://mathhub.info/MitM/Models/poisson?ThermodynamicEquilibrium http://mathhub.info/MitM/Models?Density
Includes http://mathhub.info/MitM/Models/poisson?ThermodynamicEquilibrium http://mathhub.info/MitM/Models/poisson?PoissonParameters
Includes http://mathhub.info/MitM/Models/poisson?ThermodynamicEquilibrium http://mathhub.info/MitM/Models/densities?DensityElectrons
Includes http://mathhub.info/MitM/Models/poisson?ThermodynamicEquilibrium http://mathhub.info/MitM/Models/device?DeviceOperationState
Includes http://mathhub.info/MitM/Models/poisson?ThermodynamicEquilibrium http://mathhub.info/MitM/Models?PhysicalConstants
+Includes http://mathhub.info/MitM/Models/poisson?ThermodynamicEquilibrium http://mathhub.info/MitM/Models?Permittivity
+Includes http://mathhub.info/MitM/Models/poisson?ThermodynamicEquilibrium http://mathhub.info/MitM/smglom/arithmetics?realarith
+Includes http://mathhub.info/MitM/Models/poisson?ThermodynamicEquilibrium http://mathhub.info/MitM/smglom/arithmetics?realnumbers
+Includes http://mathhub.info/MitM/Models/poisson?ThermodynamicEquilibrium http://mathhub.info/MitM/smglom/arithmetics?rationalnumbers
+Includes http://mathhub.info/MitM/Models/poisson?ThermodynamicEquilibrium http://mathhub.info/MitM/smglom/arithmetics?integernumbers
+Includes http://mathhub.info/MitM/Models/poisson?ThermodynamicEquilibrium http://mathhub.info/MitM/smglom/arithmetics?naturalnumbers
+Includes http://mathhub.info/MitM/Models/poisson?ThermodynamicEquilibrium http://mathhub.info/MitM/smglom/arithmetics?ratarith
+Includes http://mathhub.info/MitM/Models/poisson?ThermodynamicEquilibrium http://mathhub.info/MitM/smglom/arithmetics?intarith
+Includes http://mathhub.info/MitM/Models/poisson?ThermodynamicEquilibrium http://mathhub.info/MitM/smglom/arithmetics?natarith
Includes http://mathhub.info/MitM/Models/poisson?ThermodynamicEquilibrium http://mathhub.info/MitM/Models/densities?BandstructureParameters
Includes http://mathhub.info/MitM/Models/poisson?ThermodynamicEquilibrium http://mathhub.info/MitM/Models/densities?FermiPotentialElectrons
Includes http://mathhub.info/MitM/Models/poisson?ThermodynamicEquilibrium http://mathhub.info/MitM/Models/densities?ElectrostaticPotential
diff --git a/relational/http..mathhub.info/MitM/Models/recombination/$Recombination.rel b/relational/http..mathhub.info/MitM/Models/recombination/$Recombination.rel
index 0f02f9d..feace0f 100644
--- a/relational/http..mathhub.info/MitM/Models/recombination/$Recombination.rel
+++ b/relational/http..mathhub.info/MitM/Models/recombination/$Recombination.rel
@@ -1,13 +1,12 @@
theory http://mathhub.info/MitM/Models/recombination?Recombination
HasMeta http://mathhub.info/MitM/Models/recombination?Recombination http://mathhub.info/MitM/Models?Base
-Includes http://mathhub.info/MitM/Models/recombination?Recombination http://mathhub.info/MitM/Models/device?DeviceOperationState
+Includes http://mathhub.info/MitM/Models/recombination?Recombination http://mathhub.info/MitM/Models/Species?ElectronsAndHoles
+Includes http://mathhub.info/MitM/Models/recombination?Recombination http://mathhub.info/MitM/Models/Species?Electrons
+Includes http://mathhub.info/MitM/Models/recombination?Recombination http://mathhub.info/MitM/Models/Species?Holes
+Includes http://mathhub.info/MitM/Models/recombination?Recombination http://mathhub.info/MitM/Models?RecombinationCoefficient
+Includes http://mathhub.info/MitM/Models/recombination?Recombination http://mathhub.info/MitM/Models?Density
+Includes http://mathhub.info/MitM/Models/recombination?Recombination http://mathhub.info/MitM/Models?RecombinationRate
Includes http://mathhub.info/MitM/Models/recombination?Recombination http://mathhub.info/MitM/Models/device?DeviceGeometry
Includes http://mathhub.info/MitM/Models/recombination?Recombination http://mathhub.info/MitM/Models/device?Device
-Includes http://mathhub.info/MitM/Models/recombination?Recombination http://mathhub.info/MitM/Models/densities?DensityElectrons
-Includes http://mathhub.info/MitM/Models/recombination?Recombination http://mathhub.info/MitM/Models?PhysicalConstants
-Includes http://mathhub.info/MitM/Models/recombination?Recombination http://mathhub.info/MitM/Models/densities?BandstructureParameters
-Includes http://mathhub.info/MitM/Models/recombination?Recombination http://mathhub.info/MitM/Models/densities?DensityHoles
-Declares http://mathhub.info/MitM/Models/recombination?Recombination http://mathhub.info/MitM/Models/recombination?Recombination?recombination_coefficient
-constant http://mathhub.info/MitM/Models/recombination?Recombination?recombination_coefficient
Declares http://mathhub.info/MitM/Models/recombination?Recombination http://mathhub.info/MitM/Models/recombination?Recombination?recombination_rate
constant http://mathhub.info/MitM/Models/recombination?Recombination?recombination_rate
diff --git a/relational/http..mathhub.info/MitM/Models/recombination/$Spontaneous$Recombination.rel b/relational/http..mathhub.info/MitM/Models/recombination/$Spontaneous$Recombination.rel
index 5c191de..30c755a 100644
--- a/relational/http..mathhub.info/MitM/Models/recombination/$Spontaneous$Recombination.rel
+++ b/relational/http..mathhub.info/MitM/Models/recombination/$Spontaneous$Recombination.rel
@@ -1,13 +1,14 @@
theory http://mathhub.info/MitM/Models/recombination?SpontaneousRecombination
HasMeta http://mathhub.info/MitM/Models/recombination?SpontaneousRecombination http://mathhub.info/MitM/Models?Base
Includes http://mathhub.info/MitM/Models/recombination?SpontaneousRecombination http://mathhub.info/MitM/Models/recombination?Recombination
-Includes http://mathhub.info/MitM/Models/recombination?SpontaneousRecombination http://mathhub.info/MitM/Models/device?DeviceOperationState
+Includes http://mathhub.info/MitM/Models/recombination?SpontaneousRecombination http://mathhub.info/MitM/Models/Species?ElectronsAndHoles
+Includes http://mathhub.info/MitM/Models/recombination?SpontaneousRecombination http://mathhub.info/MitM/Models/Species?Electrons
+Includes http://mathhub.info/MitM/Models/recombination?SpontaneousRecombination http://mathhub.info/MitM/Models/Species?Holes
+Includes http://mathhub.info/MitM/Models/recombination?SpontaneousRecombination http://mathhub.info/MitM/Models?RecombinationCoefficient
+Includes http://mathhub.info/MitM/Models/recombination?SpontaneousRecombination http://mathhub.info/MitM/Models?Density
+Includes http://mathhub.info/MitM/Models/recombination?SpontaneousRecombination http://mathhub.info/MitM/Models?RecombinationRate
Includes http://mathhub.info/MitM/Models/recombination?SpontaneousRecombination http://mathhub.info/MitM/Models/device?DeviceGeometry
Includes http://mathhub.info/MitM/Models/recombination?SpontaneousRecombination http://mathhub.info/MitM/Models/device?Device
-Includes http://mathhub.info/MitM/Models/recombination?SpontaneousRecombination http://mathhub.info/MitM/Models/densities?DensityElectrons
-Includes http://mathhub.info/MitM/Models/recombination?SpontaneousRecombination http://mathhub.info/MitM/Models?PhysicalConstants
-Includes http://mathhub.info/MitM/Models/recombination?SpontaneousRecombination http://mathhub.info/MitM/Models/densities?BandstructureParameters
-Includes http://mathhub.info/MitM/Models/recombination?SpontaneousRecombination http://mathhub.info/MitM/Models/densities?DensityHoles
Declares http://mathhub.info/MitM/Models/recombination?SpontaneousRecombination http://mathhub.info/MitM/Models/recombination?SpontaneousRecombination?spontaneous_recombination_coefficient
constant http://mathhub.info/MitM/Models/recombination?SpontaneousRecombination?spontaneous_recombination_coefficient
Declares http://mathhub.info/MitM/Models/recombination?SpontaneousRecombination http://mathhub.info/MitM/Models/recombination?SpontaneousRecombination?axiom_spontaneous
diff --git a/source/mmt/Quantities.mmt b/source/mmt/Quantities.mmt
index 75cd587..028342c 100644
--- a/source/mmt/Quantities.mmt
+++ b/source/mmt/Quantities.mmt
@@ -4,31 +4,67 @@ import qe http://mathhub.info/MMT/physics-units
/T This is a theory containing the electric displacement.
theory Displacement : qe:?QEBase =
- meta modeltype physical_quantity
+ // meta modeltype physical_quantity
displacement_dim : type = QE (ElectricCharge /' (SIlength * SIlength))
displacement : displacement_dim # D
theory Permittivity : qe:?QEBase =
- meta modeltype physical_quantity
+ // meta modeltype physical_quantity
permittivity_dim : type = QE (ElectricCharge /' (ElectricPotential * SIlength))
permittivity : permittivity_dim # εs
theory Density : qe:?QEBase =
- meta modeltype physical_quantity
- density_dim : type = QE (DimNone /' (SIlength * SIlength * SIlength))
- density : density_dim
+ // meta modeltype physical_quantity
+ density_dim : dimension = (DimNone /' (SIlength * SIlength * SIlength))
+ density : QE density_dim
theory CurrentDensity : qe:?QEBase =
- meta modeltype physical_quantity
- currentdensity_dim : type = QE (SIcurrent /' Area)
- currentdensity : currentdensity_dim
+ // meta modeltype physical_quantity
+ currentdensity_dim : dimension = (SIcurrent /' Area)
+ currentdensity : QE currentdensity_dim
theory RecombinationRate : qe:?QEBase =
- meta modeltype physical_quantity
- recombinationrate_dim : type = QE (DimNone /' (Volume * SItime))
- recombinationrate : recombinationrate_dim # R
+ include Models/device?DeviceGeometry
+ // meta modeltype physical_quantity
+ recombinationrate_dim : type = DimNone /' (Volume * SItime)
+ recombinationrate : Ω → QE recombinationrate_dim # R
+
+theory RecombinationCoefficient : top:?Base =
+ include ?Density
+ recombination_coefficient : QE density_dim → QE density_dim → QE (Volume /' SItime) # r 1 2
+
+
+
+theory Energy : qe:?QEBase =
+ energy : QE Energy
+
+
+theory SpatialDensity : qe:?QEBase =
+ include Models/device?DeviceGeometry
+ include ?Density
+ spatialdensity : Ω → QE density_dim # n 1
+
+
+theory SpatialPotential : top:?Base =
+ include Models/device?DeviceGeometry
+ /T Spatial variation of the potential,
+ usually denoted by $φ$.
+ potential : Ω → (QE ElectricPotential) # φ 1
+
+
+theory SpatialChargeDensity : top:?Base =
+ include Models/device?DeviceGeometry
+ include ?Density
+ charge : Ω → QE (ElectricCharge * density_dim) # Q 1
+
+
+theory SpatialCurrentDensity : top:?Base =
+ include Models/device?DeviceGeometry
+ include ?CurrentDensity
+ spatialcurrentdensity : Ω → QE currentdensity_dim # j 1
+
\ No newline at end of file
diff --git a/source/mmt/band.mmt b/source/mmt/band.mmt
new file mode 100644
index 0000000..86ebb54
--- /dev/null
+++ b/source/mmt/band.mmt
@@ -0,0 +1,24 @@
+namespace http://mathhub.info/MitM/Models
+
+/T This is a theory containing the bandstructure parameters of
+ the semiconductor.
+/T Parameter
+theory BandstructureParameters : top:?Base =
+ structure effective_density : top:?Density =
+ density @ effective_density_of_states # N
+
+ /T The effective density of states for the conduction bands
+ usually denoted by $N$.
+ /T The conduction band edge usually denoted by $E$.
+ band_edge : QE Energy # E
+ /T Charge number (for electrons -1, for holes 1)
+ charge_number : ℤ # z
+ mobility : QE (Area /' (ElectricPotential * SItime)) # μ
+
+
+theory Band : top:?Base =
+ include ?BandstructureParameters
+ structure fermi : top:?SpatialPotential =
+ potential # φ 1
+
+
\ No newline at end of file
diff --git a/source/mmt/continuity.mmt b/source/mmt/continuity.mmt
index 88624dc..d88668f 100644
--- a/source/mmt/continuity.mmt
+++ b/source/mmt/continuity.mmt
@@ -4,79 +4,39 @@ import top http://mathhub.info/MitM/Models
/T This is a theory containing the mobilitiy parameters of
the semiconductor.
-theory Mobilities : top:?Base =
- /T The electron mobility parameter usually denoted by $μ_n$.
- mobility_electrons : QE (Area /' (ElectricPotential * SItime)) # μ_n
- /T The hole mobility parameter usually denoted by $μ_p$.
- mobility_holes : QE (Area /' (ElectricPotential * SItime)) # μ_p
+theory Mobility : top:?Base =
+ /T The mobility parameter usually denoted by $μ$.
-/T This is a theory containing the expression for the electron current.
-
-theory CurrentElectrons : top:?Base =
- include densities?FermiPotentialElectrons
- include densities?ElectrostaticPotential
- include densities?DensityElectrons
- include ?Mobilities
- include top:?CurrentDensity
-
- /T Definition of the electron current in gradient form.
- The driving force of the current are the negative gradients of
- the quasi-Fermi potential, here denoted by j_n.
- // TODO: change to more natural formulation later, e.g. f-> xψ, g-> xφ_n?
-
- current_electrons_law : {P: ℠→ bool} (pred P → QE ElectricPotential) → (pred P → QE ElectricPotential) → (pred P → currentdensity_dim)
- = [P][f,g][x] -q ⋅ μ_n ⋅ (n (f x) (g x)) ⋅ (g' x) # j_n 2 3
-
/T This is a theory containing the expression for the hole current.
-theory CurrentHoles : top:?Base =
- include densities?FermiPotentialHoles
- include densities?ElectrostaticPotential
- include densities?DensityHoles
- include ?Mobilities
- include top:?CurrentDensity
+theory CurrentLaw : top:?Base =
+ include top:?Band
+ include top:?BandstructureParameters
+ include top:?SpatialCurrentDensity
+
/T Defintion of the hole current in gradient form.
The driving force of the current are the negative gradient of
the quasi-Fermi potential, here denoted by j_p.
// TODO: change to more natural formulation later, e.g. f-> xψ, g-> xφ_p?
- current_holes_law : {P: ℠→ bool} (pred P → QE ElectricPotential) → (pred P → QE ElectricPotential) → (pred P → currentdensity_dim)
- = [P][f,g][x] -q ⋅ μ_p ⋅ (p (f x) (g x)) ⋅ (g' x) # j_p 2 3
+ current_law : {x : Ω} ⊦ j x ≠-q ⋅ μ ⋅ (n x) ⋅ (φ' x)
/T This is a theory containing the continuity equation for the electrons.
-theory ContinuityEquationElectrons : top:?Base =
- include ?CurrentElectrons
- include densities?DensityHoles
- include densities?FermiPotentialHoles
- include recombination?Recombination
- include densities?ElectrostaticPotential
+theory ContinuityEquation : top:?Base =
+ include top:/Species?Species
+ include top:?RecombinationRate
/T Formulation of the continuity equation for electrons in divergence form.
- continuity_equation_electrons :
- ⊦ (j_n ψ φ_n) ' ≠[x : Ω] q ⋅ (R (n (ψ x) (φ_n x)) (p (ψ x) (φ_p x)) (φ_n x) (φ_p x))
+ continuity_equation :
+ {x : Ω} ⊦ (j ') x ≠-z (R x)
-
-/T This is a theory containing the continuity equation for the holes.
-
-theory ContinuityEquationHoles : top:?Base =
- include ?CurrentHoles
- include densities?DensityElectrons
- include densities?FermiPotentialElectrons
- include recombination?Recombination
- include densities?ElectrostaticPotential
-
- /T Formulation of the continuity equation for holes in divergence form.
- continuity_equation_holes :
- ⊦ (j_p ψ φ_p) ' ≠[x : Ω] -q ⋅ (R (n (ψ x) (φ_n x)) (p (ψ x) (φ_p x)) (φ_n x) (φ_p x))
-
-
/T This is a theory containing the boundary conditions for the
electron continuity equation modeling Ohmic contacts.
diff --git a/source/mmt/densities.mmt b/source/mmt/densities.mmt
index 6aae1db..fc7faa4 100644
--- a/source/mmt/densities.mmt
+++ b/source/mmt/densities.mmt
@@ -1,80 +1,19 @@
namespace http://mathhub.info/MitM/Models/densities
import top http://mathhub.info/MitM/Models
-/T This is a theory containing the bandstructure parameters of
- the semiconductor.
-/T Parameter
-theory BandstructureParameters : top:?Base =
- include top:?Density
- /T The effective density of states for the conduction bands
- usually denoted by $N_c$.
- effective_density_of_states_conduction_bands : density_dim # N_c
- /T The effective density of states for the valence bands
- usually denoted by $N_v$.
- effective_density_of_states_valence_bands : density_dim # N_v
- /T The conduction band edge usually denoted by $E_c$.
- conduction_band_edge : QE Energy # E_c
- /T The valence band edge usually denoted by $E_v$.
- valence_band_edge : QE Energy # E_v
- /T N.B.: The band gap of the semiconductor is given by Eg = $E_c-E_v$.
-
-
-/T This is a theory containing spatial variation of the
- quasi-Fermi potential for the electrons.
- This is a basic variable of the system
-/T Solution
-theory FermiPotentialElectrons : top:?Base =
- include device?DeviceGeometry
- /T Spatial variation of the quasi-Fermi potential for the electrons,
- usually denoted by $φ_n$.
- quasi_Fermi_potential : Ω → (QE ElectricPotential) # φ_n
-
-
-/T This is a theory containing spatial variation of the
- quasi-Fermi potential for the holes.
- This is a basic variable (unknown) of the system.
-/T Solution
-theory FermiPotentialHoles : top:?Base =
- include device?DeviceGeometry
- /T Spatial variation of the quasi-Fermi potential for the holes,
- usually denoted by $φ_p$.
- quasi_Fermi_potential : Ω → (QE ElectricPotential) # φ_p
-
-
-/T This is a theory containing spatial variation of the
- electrostatic potential.
- This is a basic variable (unknown) of the system.
-/T Solution
-theory ElectrostaticPotential : top:?Base =
- include device?DeviceGeometry
-
- /T Spatial variation of the electrostatic potential,
- usually denoted by $ψ$.
- electrostatic_potential : Ω → (QE ElectricPotential) # ψ
-
-
/T This is a theory containing state equation for the
- electron density for the Boltzmann approximation (exp).
+ density for the Boltzmann approximation (exp).
/T Solution
-theory DensityElectrons : top:?Base =
+theory DensityLaw : top:?Base =
+// meta model_type physical_law
include device?DeviceOperationState
include top:?PhysicalConstants
- include ?BandstructureParameters
-
+ include top:?Density
+ structure electrostatic : top:?SpatialPotential =
+ domain = `top:/device?DeviceGeometry?domain
+ potential # ψ
+ // should be an include, but...
+ structure band : top:?Band =
/T Formula for the electron density for the Boltzmann approximation.
- density_electrons : (QE ElectricPotential) → (QE ElectricPotential) → density_dim # n
- = [x,y] N_c â‹… exponentiation (scalar ((q â‹… (x - y) - E_c) / k_B â‹… T))
-
-
-
-/T This is a theory containing state equation for the
- hole density for the Boltzmann approximation (exp).
-/T Solution
-theory DensityHoles : top:?Base =
- include device?DeviceOperationState
- include top:?PhysicalConstants
- include ?BandstructureParameters
- /T Formula for the hole density for the Boltzmann approximation.
- density_holes : (QE ElectricPotential) → (QE ElectricPotential) → density_dim # p
- = [x,y] N_v â‹… exponentiation (scalar ((q â‹… (y - x) + E_v) / k_B â‹… T))
-
+ density_law : {x : Ω} ⊦ n x ≠N ⋅ exponentiation (scalar (((- q) ⋅ z ⋅ ((ψ x) - (φ x)) - E) / k_B ⋅ T))
+
\ No newline at end of file
diff --git a/source/mmt/poisson.mmt b/source/mmt/poisson.mmt
index e77dacb..9a5c8f7 100644
--- a/source/mmt/poisson.mmt
+++ b/source/mmt/poisson.mmt
@@ -18,17 +18,13 @@ theory ChargeLaw : top:?Base =
include device?DeviceGeometry
include device?DopingProfile
include ?PoissonParameters
- include densities?DensityElectrons
- include densities?FermiPotentialElectrons
- include densities?ElectrostaticPotential
- include densities?DensityHoles
- include densities?FermiPotentialHoles
+ include top:/Species?ElectronsAndHoles
+ include top:?SpatialChargeDensity
/T The total charge denoted by $Q$ composed of doping profile $C$ and
electron and hole densities $n$ and $p$, defined by
$Q$ = $q$($C$+$p$ - $n$).
- total_charge_density : Ω → QE (ElectricCharge /' Volume) # Q
- = [x : Ω] -q ⋅ ((C x) + (p (ψ x) (φ_p x)) - (n (ψ x) (φ_n x)))
+ total_charge_density : {x : Ω} ⊦ Q x ≠-q ⋅ ((C x) + (holes/z ⋅ (holes/density x)) + (electrons/z ⋅ (electrons/density x))
theory DisplacementLaw : top:?Base =
diff --git a/source/mmt/recombination.mmt b/source/mmt/recombination.mmt
index f94861f..50e33d3 100644
--- a/source/mmt/recombination.mmt
+++ b/source/mmt/recombination.mmt
@@ -4,22 +4,16 @@ import top http://mathhub.info/MitM/Models
/T This is a theory containing the general structure for
a recombination rate.
+
+
theory Recombination : top:?Base =
- include device?DeviceOperationState
- include densities?DensityElectrons
- include densities?DensityHoles
- include top:?Density
- include top:?RecombinationRate
-
- /T The kernel of the recombination rate depending
- on electron and hole densities.
- recombination_coefficient : density_dim → density_dim → QE (Volume /' SItime) # r
-
+ include top:/Species?ElectronsAndHoles
+ include top:?RecombinationCoefficient
+ include top:?RecombinationRate
/T Recombination rate for right hand side of continuity equations.
- recombination_rate : Ω → (QE ElectricPotential) → (QE ElectricPotential) → (QE ElectricPotential) → â„
- = [ x, ψ, xφ_n, xφ_p] (r (n (ψ x) (xφ_n x)) (p (ψ x) (xφ_p x))) ⋅ (n (ψ x) (xφ_n x)) ⋅ (p (ψ x) (xφ_p x)) ⋅
- (1 - exponentiation scalar (((q ⋅(xφ_n - xφ_p)) / k_B ⋅ T)))
- # R
+ recombination_rate : {x : Ω} ⊦ R x â‰
+ (r (electrons/spatialdensity x) (holes/spatialdensity x)) â‹… (electrons/spatialdensity x) â‹… (holes/spatialdensity x)
+ â‹… (1 - (exponential (q â‹… ((electrons/fermi/potential x) - (holes/fermi/potential x)) / (k_B â‹… T))))
/T Kernel for spontaneous recombination with coefficient B.
@@ -29,5 +23,5 @@ theory SpontaneousRecombination : top:?Base =
/T The coefficient for the sponanteous recombination rate is denoted by $B$
spontaneous_recombination_coefficient : QE (Volume /' SItime) # B
/T Formula for sponanteous recombination $r$($n$,$p$) = $B$
- axiom_spontaneous : ⊦ r ≠([x,y] B) role Simplify
+ axiom_spontaneous : {x,y} ⊦ r x y ≠B role Simplify
diff --git a/source/mmt/species.mmt b/source/mmt/species.mmt
new file mode 100644
index 0000000..16fbdb1
--- /dev/null
+++ b/source/mmt/species.mmt
@@ -0,0 +1,21 @@
+namespace http://mathhub.info/MitM/Models/Species
+import top http://mathhub.info/MitM/Models
+
+theory Species : top:?Base =
+ include densities?DensityLaw
+ include top:?SpatialCurrentDensity
+ // include CurrentLaw
+
+
+theory Electrons : top:?Base =
+ structure electron : ?Species =
+
+
+theory Holes : top:?Base =
+ structure hole : ?Species =
+
+
+theory ElectronsAndHoles : top:?Base =
+ include ?Electrons
+ include ?Holes
+
\ No newline at end of file
--
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