From 03cd1e87a3aaa7b5eb84576133788d243948c1c8 Mon Sep 17 00:00:00 2001
From: Ben Ryan <brryan@lanl.gov>
Date: Tue, 7 Jan 2025 20:12:03 -0700
Subject: [PATCH] still working

---
 README.md | 21 +++++++++++----------
 1 file changed, 11 insertions(+), 10 deletions(-)

diff --git a/README.md b/README.md
index 61ec67c..39eec5d 100644
--- a/README.md
+++ b/README.md
@@ -7,20 +7,21 @@ Performance Portable Opacity and Emissivity library for simulation codes
 
 ## API
 
-singularity-opac provides a uniform API for all opacity models. The following functions are provided
+singularity-opac provides a uniform API for all opacity models, in two forms: frequency-averaged
+(Plank or Rosseland means) and frewquency-dependent. The following functions are provided
 (here, $\sigma$ is the frequency- and angle-dependent cross section in units of ${\rm cm}^2$):
 | Function              | Expression | Description            | Units   |
 | --------------------- | ---------- | ---------------------  | ------- |
-| AbsorptionCoefficient | $n \sigma$ | Absorption coefficient | $cm^{-1}$ |
+| 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 | ${\rm erg~cm}^{-3} {\rm s}^{-1}$ |
-| 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 | ${\rm erg~cm}^{-2} {\rm s}^{-1}$ |
+| 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 | ${\rm erg~cm}^{-3}~{\rm s}^{-1}$ |
+| 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 | ${\rm erg~cm}^{-2}~{\rm s}^{-1}$ |
 
 Note that the thermal radiation energy density `u = 1/c ThermalDistributionOfT` and the thermal radiation number density `n = 1/c ThermalNumberDistributionOfT`.