diff --git a/content/http..mathhub.info/MitM/Models/poisson/$Displacement$Law.omdoc b/content/http..mathhub.info/MitM/Models/poisson/$Displacement$Law.omdoc index 1ff8b452d220290fb8b079ace9e014071f0b1a58..321919a705660585d67bc400a99c648b0b75b15b 100644 --- a/content/http..mathhub.info/MitM/Models/poisson/$Displacement$Law.omdoc +++ b/content/http..mathhub.info/MitM/Models/poisson/$Displacement$Law.omdoc @@ -1,6 +1,6 @@ <omdoc xmlns="http://omdoc.org/ns" xmlns:om="http://www.openmath.org/OpenMath"><theory name="DisplacementLaw" 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#1171.29.0:1469.38.1"/></metadata><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/poisson.mmt#1209.30.1:1250.30.42"/></metadata></import><import from="http://mathhub.info/MitM/Models/poisson?PoissonParameters"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/poisson.mmt#1253.31.1:1280.31.28"/></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#1283.32.1:1305.32.23"/></metadata></import><opaque format="text"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/poisson.mmt#1310.34.1:1386.34.77"/></metadata>Expression for electric displacement denoted by <unparsed>None</unparsed> = <unparsed>None</unparsed> d/dx <unparsed>None</unparsed></opaque><constant name="electric_displacement"> <metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/mmt/poisson.mmt#1390.36.1:1467.37.30"/></metadata> - <type><om:OMOBJ xmlns:om="http://www.openmath.org/OpenMath"><om:OMSF><om:text format="unparsed"><![CDATA[Ω → displacement_dim]]></om:text></om:OMSF></om:OMOBJ></type> + <type><om:OMOBJ xmlns:om="http://www.openmath.org/OpenMath"><om:OMSF><om:text format="unparsed"><![CDATA[Ω ⟶ displacement_dim]]></om:text></om:OMSF></om:OMOBJ></type> <definition><om:OMOBJ xmlns:om="http://www.openmath.org/OpenMath"><om:OMSF><om:text format="unparsed"><![CDATA[[x] -ε_s â‹… (ψ ' x)]]></om:text></om:OMSF></om:OMOBJ></definition> <notations><notation dimension="1" precedence="0" fixity="mixfix" arguments="D"> <scope languages="" priority="0"/> </notation></notations> </constant></theory></omdoc> \ No newline at end of file diff --git a/content/http..mathhub.info/MitM/Models/thermistor/$Spatial$Reference$Electrical$Field.omdoc b/content/http..mathhub.info/MitM/Models/thermistor/$Spatial$Reference$Electrical$Field.omdoc index 78cd8532cbf05803b1700d15acaac4b6854bba9a..5ad6858730657c0f80ded642a6af081892433b3a 100644 --- a/content/http..mathhub.info/MitM/Models/thermistor/$Spatial$Reference$Electrical$Field.omdoc +++ b/content/http..mathhub.info/MitM/Models/thermistor/$Spatial$Reference$Electrical$Field.omdoc @@ -1,6 +1,6 @@ <omdoc xmlns="http://omdoc.org/ns" xmlns:om="http://www.openmath.org/OpenMath"><theory name="SpatialReferenceElectricalField" base="http://mathhub.info/MitM/Models/thermistor" meta="http://mathhub.info/MitM/Models?Base"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/thermistor/quantities.mmt#2155.71.0:2342.75.-1"/></metadata><import from="http://mathhub.info/MitM/Models/thermistor?DeviceGeometry"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/thermistor/quantities.mmt#2210.72.2:2234.72.26"/></metadata></import><import from="http://mathhub.info/MitM/Models/thermistor?ElectricalFieldStrength"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/thermistor/quantities.mmt#2238.73.2:2271.73.35"/></metadata></import><constant name="referebceelectricfield"> <metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/MitM/Models/thermistor/quantities.mmt#2275.74.2:2341.74.68"/></metadata> - <type><om:OMOBJ xmlns:om="http://www.openmath.org/OpenMath"><om:OMSF><om:text format="unparsed"><![CDATA[Ω → (electricfieldstrength_dim)]]></om:text></om:OMSF></om:OMOBJ></type> + <type><om:OMOBJ xmlns:om="http://www.openmath.org/OpenMath"><om:OMSF><om:text format="unparsed"><![CDATA[Ω ⟶ (electricfieldstrength_dim)]]></om:text></om:OMSF></om:OMOBJ></type> <notations><notation dimension="1" precedence="0" fixity="mixfix" arguments="Eref"> <scope languages="" priority="0"/> </notation></notations> </constant></theory></omdoc> \ No newline at end of file diff --git a/source/mmt/Quantities.mmt b/source/mmt/Quantities.mmt index 5691860a1c9c5496cc96af2ede0eb3a840534994..62112664321cd1c1a26af963084d28ed81fe9e10 100644 --- a/source/mmt/Quantities.mmt +++ b/source/mmt/Quantities.mmt @@ -31,12 +31,12 @@ theory RecombinationRate : qe:?SIUnits = include Models/device?DeviceGeometry â™ // meta modeltype physical_quantity â™ recombinationrate_dim : dimension ☠= DimNone /' (Volume *' Time) â™ - recombinationrate : Ω → QE recombinationrate_dim ☠# R ☠role Quantity â™ + recombinationrate : Ω ⟶ QE recombinationrate_dim ☠# R ☠role Quantity â™ âš theory RecombinationCoefficient : qe:?SIUnits = include ?Density â™ - recombination_coefficient : QE density_dim → QE density_dim → QE (Volume /' Time) ☠# r ☠role Quantity â™ + recombination_coefficient : QE density_dim ⟶ QE density_dim ⟶ QE (Volume /' Time) ☠# r ☠role Quantity â™ âš theory Energy : qe:?SIUnits = @@ -46,7 +46,7 @@ theory Energy : qe:?SIUnits = theory SpatialDensity : qe:?SIUnits = include Models/device?DeviceGeometry â™ include ?Density â™ - spatialdensity : Ω → QE density_dim ☠# n ☠role Quantity â™ + spatialdensity : Ω ⟶ QE density_dim ☠# n ☠role Quantity â™ âš theory SpatialPotential : qe:?SIUnits = @@ -54,17 +54,17 @@ theory SpatialPotential : qe:?SIUnits = /T Spatial variation of the potential, usually denoted by $φ$. â™ - potential : Ω → (QE ElectricPotential) ☠# φ ☠role Quantity â™ + potential : Ω ⟶ (QE ElectricPotential) ☠# φ ☠role Quantity â™ âš theory SpatialChargeDensity : qe:?SIUnits = include Models/device?DeviceGeometry â™ include ?Density â™ - charge : Ω → QE (ElectricCharge *' density_dim) ☠# Q ☠role Quantity â™ + charge : Ω ⟶ QE (ElectricCharge *' density_dim) ☠# Q ☠role Quantity â™ âš theory SpatialCurrentDensity : qe:?SIUnits = include Models/device?DeviceGeometry â™ include ?CurrentDensity â™ - spatialcurrentdensity : Ω → QE currentdensity_dim ☠# j ☠role Quantity â™ + spatialcurrentdensity : Ω ⟶ QE currentdensity_dim ☠# j ☠role Quantity â™ âš diff --git a/source/mmt/constants.mmt b/source/mmt/constants.mmt index dc989a9985cc4fc0bcfe05d89bb42e80390d8dc9..92cd845c20e66804d879b2512e608f83e31b79bf 100644 --- a/source/mmt/constants.mmt +++ b/source/mmt/constants.mmt @@ -19,17 +19,17 @@ theory Base : mitm:/smglom/arithmetics?realarith = include ?PhysicalConstants â™ include http://mathhub.info/MitM/smglom/calculus?derivative â™ // TODO anständige ableitung (Einheiten!!) â™ - unit_pred : {D : dimension, P : ℠→ bool} type ☠+ unit_pred : {D : dimension, P : ℠⟶ bool} type ☠= [D,P] ⟨ QE D | [x] ⊦ P (scalar x) ⟩ ☠# dpred 1 2 â™ - inof : {D : dimension, u : unit D, P : ℠→ bool, r : pred P}dpred D P ☠# 4 inof 2 â™ // TODO â™ - scalarp : {D : dimension, P : ℠→ bool} dpred D P → pred P ☠# scalarp 3 â™ + inof : {D : dimension, u : unit D, P : ℠⟶ bool, r : pred P}dpred D P ☠# 4 inof 2 â™ // TODO â™ + scalarp : {D : dimension, P : ℠⟶ bool} dpred D P ⟶ pred P ☠# scalarp 3 â™ rule rules?QuantityRule â™ rule rules?LawRule â™ rule rules?ModelRule â™ // TODO â™ - // unit_derivative : {P : ℠→ bool, Da : dimension, Db : dimension, u : unit Da, f : (dpred Da P) → QE Db, p : ⊦ diff [x : pred P] scalar (f (x inof u))} dpred Da P → QE Db ☠+ // unit_derivative : {P : ℠⟶ bool, Da : dimension, Db : dimension, u : unit Da, f : (dpred Da P) ⟶ QE Db, p : ⊦ diff [x : pred P] scalar (f (x inof u))} dpred Da P ⟶ QE Db ☠= [P,Da,Db,u,f,p] ([y] ([x : pred P] (scalar (f (x inof u)))' (scalarp y)) of (unitof y) ) â™ // Ω = kompakte, einfach zusammenhängende teilmenge des â„^n für n â€âˆˆ 4 â™ diff --git a/source/mmt/device.mmt b/source/mmt/device.mmt index dfb5f888b75dadde7170d4359c69bb6adf5e5dcc..4e3b9b0e9af6d8bfbcc7c80ed89ed9f3f87e5c5a 100644 --- a/source/mmt/device.mmt +++ b/source/mmt/device.mmt @@ -9,8 +9,8 @@ theory Device = âš /T Parameter âš theory DeviceGeometry : top:?Base = include ?Device â™ - // domain_prop : â„3 → bool â™ - domain_prop : ℠→ bool â™ + // domain_prop : â„3 ⟶ bool â™ + domain_prop : ℠⟶ bool â™ /T The one-dimensional spatial domain of the device (denoted by $Ω$). â™ // domain : type ☠= pred3 domain_prop ☠# Ω â™ domain : type ☠= pred domain_prop ☠# Ω â™ @@ -19,7 +19,7 @@ theory DeviceGeometry : top:?Base = // theory OneDimDeviceGeometry : top:?Base = bottom : â„ â™ top : â„ â™ - Interval_pred : ℠→ bool ☠= [r] bottom ≤ r ∧ r ≤ top â™ + Interval_pred : ℠⟶ bool ☠= [r] bottom ≤ r ∧ r ≤ top â™ Omega_Interval : type ☠= pred Interval_pred ☠# I â™ structure Geometry : ?DeviceGeometry = @@ -28,7 +28,7 @@ theory DeviceGeometry : top:?Base = // âš // theory TwoDimDeviceGeometry : top:?Base = - Plane_pred : â„2 → bool â™ + Plane_pred : â„2 ⟶ bool â™ Omega_Plane : type ☠= pred2 Plane_pred ☠# G â™ structure Geometry : ?DeviceGeometry = @@ -42,7 +42,7 @@ theory DopingProfile : top:?Base = include ?DeviceGeometry â™ include top:?Density â™ /T The doping profile, denoted by $C$. â™ - doping_profile : Ω → QE density_dim ☠# C â™ + doping_profile : Ω ⟶ QE density_dim ☠# C â™ âš @@ -52,7 +52,7 @@ theory DopingProfile : top:?Base = theory DeviceOperationState : top:?Base = include ?DeviceGeometry â™ /T The global temperature of the device denoted by $T$. â™ - // temperature : Ω → ℠☠# T â™ + // temperature : Ω ⟶ ℠☠# T â™ temperature : QE Temperature ☠# T â™ /T The applied voltage at the bottom contact denoted by $U_1$. â™ voltage_bottom : QE ElectricPotential ☠# U_1 â™ diff --git a/source/mmt/poisson.mmt b/source/mmt/poisson.mmt index 7f77a038445b6bc3488f36238761d74ae185d84a..59429f2a1dab914565a74caa8f45be9feb7e0777 100644 --- a/source/mmt/poisson.mmt +++ b/source/mmt/poisson.mmt @@ -34,7 +34,7 @@ theory ChargeLaw : top:?Base = /T Expression for electric displacement denoted by $D$ = $- ε_s$ d/dx $ψ$ â™ - electric_displacement : Ω → displacement_dim ☠+ electric_displacement : Ω ⟶ displacement_dim ☠= [x] -ε_s â‹… (ψ ' x) ☠# D â™ âš diff --git a/source/thermistor/quantities.mmt b/source/thermistor/quantities.mmt index 9010f75ad71e633dd013d2ebe8c796d2f6f1c0dd..cf6e4dc0462740922d1e7bd0ee991ac02b41ebf2 100644 --- a/source/thermistor/quantities.mmt +++ b/source/thermistor/quantities.mmt @@ -10,8 +10,8 @@ theory Device = âš /T Parameter âš theory DeviceGeometry : top:?Base = include ?Device â™ - // domain_prop : â„3 → bool â™ - domain_prop : ℠→ bool â™ + // domain_prop : â„3 ⟶ bool â™ + domain_prop : ℠⟶ bool â™ /T The one-dimensional spatial domain of the device (denoted by $Ω$). â™ domain : type ☠= pred domain_prop ☠# Ω â™ âš @@ -20,7 +20,7 @@ theory SpatialPotential : top:?Base = include ?DeviceGeometry â™ /T Spatial variation of the potential, usually denoted by $φ$. â™ - potential : Ω → (QE ElectricPotential) ☠# φ♠+ potential : Ω ⟶ (QE ElectricPotential) ☠# φ♠⚠theory ElectricFieldStrength : qe:?QEBase = @@ -34,7 +34,7 @@ theory SpatialElectricField : top:?Base = include ?ElectricFieldStrength â™ /T Spatial variation of the electric field strength, usually denoted by $E$. â™ - electricfield : Ω → (electricfieldstrength_dim) ☠# Eâ™ + electricfield : Ω ⟶ (electricfieldstrength_dim) ☠# Eâ™ âš theory CurrentDensity : qe:?QEBase = @@ -47,7 +47,7 @@ theory CurrentDensity : qe:?QEBase = theory SpatialCurrentDensity : top:?Base = include ?DeviceGeometry â™ include ?CurrentDensity â™ - currentdensity : Ω → (currentdensity_dim) ☠# j 1 â™ + currentdensity : Ω ⟶ (currentdensity_dim) ☠# j 1 â™ âš theory ElectricalConductivity : qe:?QEBase = @@ -60,34 +60,34 @@ theory ElectricalConductivity : qe:?QEBase = theory SpatialElectricalConductivity : top:?Base = include ?DeviceGeometry â™ include ?ElectricalConductivity â™ - spatialelectricalconductivity : Ω → (electricalconductitvity_dim) ☠# σ 1 â™ + spatialelectricalconductivity : Ω ⟶ (electricalconductitvity_dim) ☠# σ 1 â™ âš theory SpatialReferenceConductivity : top:?Base = include ?DeviceGeometry â™ include ?ElectricalConductivity â™ - spatialreferenceconductivity : Ω → (electricalconductitvity_dim) ☠# σ_0 1 â™ + spatialreferenceconductivity : Ω ⟶ (electricalconductitvity_dim) ☠# σ_0 1 â™ âš theory SpatialReferenceElectricalField : top:?Base = include ?DeviceGeometry â™ include ?ElectricalFieldStrength â™ - referebceelectricfield : Ω → (electricfieldstrength_dim) ☠# Erefâ™ + referebceelectricfield : Ω ⟶ (electricfieldstrength_dim) ☠# Erefâ™ âš theory SpatialFieldEnhancement : top:?Base = include ?DeviceGeometry â™ - spatialfieldenhancement : Ω → ℠☠# Gâ™ + spatialfieldenhancement : Ω ⟶ ℠☠# Gâ™ âš theory SpatialLaplacep : top:?Base = include ?DeviceGeometry â™ - spatiallaplacep : Ω → ℠☠# pâ™ + spatiallaplacep : Ω ⟶ ℠☠# pâ™ âš theory SpatialArrheniusFaktor : top:?Base = include ?DeviceGeometry â™ - spatialarrheniusfaktor : Ω → ℠☠# Fâ™ + spatialarrheniusfaktor : Ω ⟶ ℠☠# Fâ™ âš theory Heat : qe:?QEBase = @@ -99,13 +99,13 @@ theory Heat : qe:?QEBase = theory SpatialHeatSource : top:?Base = include ?DeviceGeometry â™ include ?Heat â™ - spatialheatsource : Ω → (heat_dim) ☠# Q 1 â™ + spatialheatsource : Ω ⟶ (heat_dim) ☠# Q 1 â™ âš theory SpatialJouleHeat : top:?Base = include ?DeviceGeometry â™ include ?Heat â™ - spatialheatsource : Ω → (heat_dim) ☠# Q_Joule 1 â™ + spatialheatsource : Ω ⟶ (heat_dim) ☠# Q_Joule 1 â™ âš theory ThermalConductivity : qe:?QEBase = @@ -118,7 +118,7 @@ theory ThermalConductivity : qe:?QEBase = theory SpatialThermalConductivity : top:?Base = include ?DeviceGeometry â™ include ?ThermalConductivity â™ - spatialthermalconductivity : Ω → (thermalconductitvity_dim) ☠# λ 1 â™ + spatialthermalconductivity : Ω ⟶ (thermalconductitvity_dim) ☠# λ 1 â™ âš theory ThermalHeatFlux : qe:?QEBase = @@ -130,14 +130,14 @@ theory ThermalHeatFlux : qe:?QEBase = theory SpatialHeatFluxDensity : top:?Base = include ?DeviceGeometry â™ include ?ThermalHeatFlux â™ - heatfluxdensity : Ω → (thermalheatflux_dim) ☠# q 1 â™ + heatfluxdensity : Ω ⟶ (thermalheatflux_dim) ☠# q 1 â™ âš theory SpatialTemperature : top:?Base = include ?DeviceGeometry â™ /T Spatial variation of the potential, usually denoted by $φ$. â™ - potential : Ω → (QE SItemperature) ☠# Tâ™ + potential : Ω ⟶ (QE SItemperature) ☠# Tâ™ âš theory ReferenceTemperature : top:?Base =