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brryan committed Jan 8, 2025
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22 changes: 13 additions & 9 deletions README.md
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Expand Up @@ -15,19 +15,20 @@ For frequency-dependent absorption opacities, the following functions are provid
| --------------------- | ---------- | --------------------- | ------- |
| AbsorptionCoefficient | $n \sigma$ | Absorption coefficient | ${\rm cm}^{-1}$ |
| AngleAveragedAbsorptionCoefficient | $\frac{1}{4 \pi}\int n \sigma d\Omega$ | Absorption coefficient averaged over solid angle | ${\rm cm}^{-1}$ |
| EmissivityPerNuOmega | $j_{\nu} = \frac{dE}{d^3x dt d\Omega d\nu}$ | Frequency- and angle-dependent emissivity | ${\rm erg~cm}^{-3}~{\rm s}^{-1}~{\rm Sr}^{-1}~{\rm Hz}^{-1}$ |
| EmissivityPerNu | $\int j_{\nu} d\Omega$ | Frequency-dependent emissivity | ${\rm erg~cm}^{-3}~{\rm s}^{-1}~{\rm Hz}^{-1}$ |
| Emissivity | $\int j_{\nu} d\nu d\Omega$ | Total emissivity | ${\rm erg~cm}^{-3}~{\rm s}^{-1}$ |
| EmissivityPerNuOmega | $j_{\nu} = \frac{dE}{d^3x dt d\Omega d\nu}$ | Frequency- and angle-dependent emissivity | ${\rm erg}~{\rm cm}^{-3}~{\rm s}^{-1}~{\rm Sr}^{-1}~{\rm Hz}^{-1}$ |
| EmissivityPerNu | $\int j_{\nu} d\Omega$ | Frequency-dependent emissivity | ${\rm erg}~{\rm cm}^{-3}~{\rm s}^{-1}~{\rm Hz}^{-1}$ |
| Emissivity | $\int j_{\nu} d\nu d\Omega$ | Total emissivity | ${\rm erg}~{\rm cm}^{-3}~{\rm s}^{-1}$ |
| NumberEmissivity | $\int \frac{1}{h \nu} j_{\nu} d\Omega d\nu$ | Total number emissivity | ${\rm cm}^{-3}~{\rm s}^{-1}$ |
| ThermalDistributionOfTNu | $B_{\nu} = \frac{dE}{dA dt d\Omega d\nu}$ | Specific intensity of thermal distribution | ${\rm erg~cm}^{-2}~{\rm s}^{-1}~{\rm Sr}^{-1}~{\rm Hz}^{-1}$ |
| DThermalDistributionOfTNuDT | $dB_{\nu}/dT$ | Temperature derivative of specific intensity of thermal distribution | ${\rm erg~cm}^{-2}~{\rm s}^{-1}~{\rm Sr}^{-1}~{\rm Hz}^{-1}~{\rm K}^{-1}$ |
| ThermalDistributionOfT | $B = \int B_{\nu} d\Omega d\nu$ | Frequency- and angle-integrated intensity of thermal distribution | ${\rm erg~cm}^{-2}~{\rm s}^{-1}$ |
| ThermalNumberDistributionOfT | $B = \int \frac{1}{h \nu} B_{\nu} d\Omega d\nu$ | Frequency- and angle-integrated intensity of thermal distribution | ${\rm erg~cm}^{-2}~{\rm s}^{-1}$ |
| EnergyDensityFromTemperature | $E_{\rm R}$ | Radiation energy density | ${\rm erg~cm}^{-3}$ |
| ThermalDistributionOfTNu | $B_{\nu} = \frac{dE}{dA dt d\Omega d\nu}$ | Specific intensity of thermal distribution | ${\rm erg}~{\rm cm}^{-2}~{\rm s}^{-1}~{\rm Sr}^{-1}~{\rm Hz}^{-1}$ |
| DThermalDistributionOfTNuDT | $dB_{\nu}/dT$ | Temperature derivative of specific intensity of thermal distribution | ${\rm erg}~{\rm cm}^{-2}~{\rm s}^{-1}~{\rm Sr}^{-1}~{\rm Hz}^{-1}~{\rm K}^{-1}$ |
| ThermalDistributionOfT | $B = \int B_{\nu} d\Omega d\nu$ | Frequency- and angle-integrated intensity of thermal distribution | ${\rm erg}~{\rm cm}^{-2}~{\rm s}^{-1}$ |
| ThermalNumberDistributionOfT | $B = \int \frac{1}{h \nu} B_{\nu} d\Omega d\nu$ | Frequency- and angle-integrated intensity of thermal distribution | ${\rm erg}~{\rm cm}^{-2}~{\rm s}^{-1}$ |
| EnergyDensityFromTemperature | $E_{\rm R}$ | Radiation energy density | ${\rm erg}~{\rm cm}^{-3}$ |
| TemperatureFromEnergyDensity | $T_{\rm R}$ | Radiation temperature | ${\rm K}$ |
| NumberDensityFromTemperature | $n_{\rm R}$ | Radiation number density | ${\rm cm}^{-3}$ |

with the following function signatures:

AbsorptionCoefficient(density, temperature, frequency)
AngleAveragedAbsorptionCoefficient(density, temperature, frequency)
EmissivityPerNuOmega(density, temperature, frequency)
Expand All @@ -48,9 +49,10 @@ For mean absorption opacities, the following functions are provided:
| PlankMeanAbsorptionCoefficient | $n \sigma$ | Absorption coefficient | ${\rm cm}^{-1}$ |
| RosselandMeanAbsorptionCoefficient | $n \sigma$ | Absorption coefficient | ${\rm cm}^{-1}$ |
| AbsorptionCoefficient | $n \sigma$ | Absorption coefficient | ${\rm cm}^{-1}$ |
| Emissivity | $\int j_{\nu} d\nu d\Omega$ | Total emissivity | ${\rm erg~cm}^{-3}~{\rm s}^{-1}$ |
| Emissivity | $\int j_{\nu} d\nu d\Omega$ | Total emissivity | ${\rm erg}~{\rm cm}^{-3}~{\rm s}^{-1}$ |

with the following function signatures:

PlanckMeanAbsorptionCoefficient(density, temperature)
RosselandMeanAbsorptionCoefficient(density, temperature)
AbsorptionCoefficient(density, temperature, gmode [Planck, Rosseland])
Expand All @@ -64,6 +66,7 @@ For frequency-dependent scattering opacities, the following functions are provid
| TotalScatteringCoefficient | $ n \sigma $ | Scattering coefficient | ${\rm cm}^{-1}$ |

with the following function signatures:

TotalCrossSection(density, temperature, frequency)
DifferentialCrossSection(density, temperature, frequency, cos(theta))
TotalScatteringCoefficient(density, temperature, frequency)
Expand All @@ -75,6 +78,7 @@ For mean scattering opacities, the following functions are provided:
| RosselandMeanScatteringCoefficient | $n \sigma$ | Rosseland mean scattering coefficient | ${\rm cm}^{-1}$ |

with the following function signatures:

PlanckMeanScatteringCoefficient(density, temperature)
RosselandMeanScatteringCoefficient(density, temperature)

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