Editing Appendix/Ramblings/Radiation/CodeUnits (section)

===Corrected Logic===
Taking all of the above into consideration, the expressions that should be used to convert from Dominic's code units to real units are the following:


<table border="1" align="center" cellpadding="8">
<tr>
  <td colspan="1" align="center">
<font color="blue"><b>General Relations (taking {{Math/MP_MeanMolecularWeight}} into account)</b></font>
  </td>
</tr>

<tr><td align="center"><table border="0" cellpadding="3" cellspacing="10">

<tr>
  <td align="right">
<math>
\frac{T_\mathrm{cgs}}{T_\mathrm{code}}
</math>
  </td>
  <td align="center">
<math>
=
</math>
  </td>
  <td align="left">
<math>
\frac{c^2}{(\Re/\bar{\mu})} \biggl( \frac{\tilde{r}}{\tilde{c}^2} \biggr)
</math>
  </td>
  <td align="center">
<math>
=
</math>
  </td>
  <td align="left">
<math>
1.083\times 10^{13}~\mathrm{K} \biggl( \frac{\tilde{r} \bar{\mu}}{\tilde{c}^2} \biggr)
</math>
  </td>
</tr>

<tr>
  <td align="right">
<math>
\frac{\ell_\mathrm{cgs}}{\ell_\mathrm{code}}
</math>
  </td>
  <td align="center">
<math>
=
</math>
  </td>
  <td align="left">
<math>
\frac{\Lambda}{ c^2 \bar{\mu}^2} \biggl( \frac{\tilde{c}^4 \tilde{g} \tilde{a} }{\tilde{r}^4} \biggr)^{1/2}
</math>
  </td>
  <td align="center">
<math>
=
</math>
  </td>
  <td align="left">
<math>
3.418\times 10^{5}~\mathrm{cm} \biggl( \frac{\tilde{c}^4 \tilde{g} \tilde{a} }{\tilde{r}^4 \bar{\mu}^4} \biggr)^{1/2}
</math>
  </td>
</tr>

<tr>
  <td align="right">
<math>
\frac{t_\mathrm{cgs}}{t_\mathrm{code}}
</math>
  </td>
  <td align="center">
<math>
=
</math>
  </td>
  <td align="left">
<math>
\frac{\Lambda}{ c^3 \bar{\mu}^2} \biggl( \frac{\tilde{c}^6 \tilde{g} \tilde{a} }{\tilde{r}^4} \biggr)^{1/2}
</math>
  </td>
  <td align="center">
<math>
=
</math>
  </td>
  <td align="left">
<math>
1.139\times 10^{-5}~\mathrm{s} \biggl( \frac{\tilde{c}^6 \tilde{g} \tilde{a} }{\tilde{r}^4 \bar{\mu}^4} \biggr)^{1/2}
</math>
  </td>
</tr>

<tr>
  <td align="right">
<math>
\frac{m_\mathrm{cgs}}{m_\mathrm{code}}
</math>
  </td>
  <td align="center">
<math>
=
</math>
  </td>
  <td align="left">
<math>
\frac{\Lambda}{ G \bar{\mu}^2} \biggl( \frac{\tilde{g}^3 \tilde{a} }{\tilde{r}^4} \biggr)^{1/2}
</math>
  </td>
  <td align="center">
<math>
=
</math>
  </td>
  <td align="left">
<math>
4.609\times 10^{33}~\mathrm{g} \biggl( \frac{\tilde{g}^3 \tilde{a} }{\tilde{r}^4 \bar{\mu}^4} \biggr)^{1/2}
</math>
  </td>
</tr>

</table></td></tr>
</table>


Hence, for Dominic's first simulation ('''Case A'''), the following conversions apply.

<table border="1" align="center" cellpadding="8">
<tr>
  <td colspan="1" align="center">
<b>Case A</b>:<br />
<math>\tilde{g} = 1</math>; <math>\tilde{c} = 198</math>; <math>\tilde{r} = 0.44</math>; <math>\tilde{a} = 0.044</math>; <math>\bar\mu = 4/3</math>
  </td>
</tr>

<tr><td align="center"><table border="0" cellpadding="3" cellspacing="10">

<tr>
  <td align="right">
<math>
\frac{T_\mathrm{cgs}}{T_\mathrm{code}}
</math>
  </td>
  <td align="center">
<math>
=
</math>
  </td>
  <td align="left">
<math>
1.083\times 10^{13}~\mathrm{K} \biggl[ \frac{0.44 (4/3)}{198^2} \biggr]
</math>
  </td>
  <td align="left">
<math>= 1.621\times 10^8~\mathrm{K}</math>
  </td>
</tr>

<tr>
  <td align="right">
<math>
\frac{\ell_\mathrm{cgs}}{\ell_\mathrm{code}}
</math>
  </td>
  <td align="center">
<math>
=
</math>
  </td>
  <td align="left">
<math>
3.418\times 10^{5}~\mathrm{cm} \biggl[ \frac{198^4 (0.044) }{(0.44)^4 (4/3)^4} \biggr]^{1/2}
</math>
  </td>
  <td align="left">
<math>= 8.167\times 10^9~\mathrm{cm}</math>
  </td>
</tr>

<tr>
  <td align="right">
<math>
\frac{t_\mathrm{cgs}}{t_\mathrm{code}}
</math>
  </td>
  <td align="center">
<math>
=
</math>
  </td>
  <td align="left">
<math>
1.139\times 10^{-5}~\mathrm{s} \biggl[ \frac{198^6 (0.044) }{(0.44)^4 (4/3)^4} \biggr]^{1/2}
</math>
  </td>
  <td align="left">
<math>= 5.334\times 10^1~\mathrm{s}</math>
  </td>
</tr>

<tr>
  <td align="right">
<math>
\frac{m_\mathrm{cgs}}{m_\mathrm{code}}
</math>
  </td>
  <td align="center">
<math>
=
</math>
  </td>
  <td align="left">
<math>
4.609\times 10^{33}~\mathrm{g} \biggl[ \frac{ 0.044 }{(0.44)^4 (4/3)^4} \biggr]^{1/2}
</math>
  </td>
  <td align="left">
<math>= 2.809\times 10^{33}~\mathrm{g}</math>
  </td>
</tr>

</table></td></tr>


<tr><td align="center"><table border="0" cellpadding="3" cellspacing="10">

<tr>
  <td align="right">
<math>
\frac{\rho_\mathrm{cgs}}{\rho_\mathrm{code}}
</math>
  </td>
  <td align="center">
<math>
=
</math>
  </td>
  <td align="left">
<math>
\biggl( \frac{m_\mathrm{cgs}}{m_\mathrm{code}} \biggr)
\biggl( \frac{\ell_\mathrm{cgs}}{\ell_\mathrm{code}} \biggr)^{-3}
</math>
  </td>
  <td align="left">
<math>= 5.157\times 10^{3}~\mathrm{g}~\mathrm{cm}^{-3}</math>
  </td>
</tr>

<tr>
  <td align="right">
<math>
\frac{\kappa_\mathrm{cgs}}{\kappa_\mathrm{code}}
</math>
  </td>
  <td align="center">
<math>
=
</math>
  </td>
  <td align="left">
<math>
\biggl( \frac{\ell_\mathrm{cgs}}{\ell_\mathrm{code}} \biggr)^{2}
\biggl( \frac{m_\mathrm{cgs}}{m_\mathrm{code}} \biggr)^{-1}
</math>
  </td>
  <td align="left">
<math>= 2.375\times 10^{-14}~\mathrm{cm}^2~\mathrm{g}^{-1}</math>
  </td>
</tr>

</table></td></tr>

</table>

When using the above tabulated '''Case A''' conversion units, it must be understood that the "code unit" values refer to units used in Dominic's rad-hydro code.  But it should also be appreciated, as discussed above, that the initial model provided to Dominic by Wes &#8212; which had been generated by the SCF code &#8212; used a different unit of length from Dominic.  The conversion factor from SCF-code lengths to the length's used in Dominic's code is:

<div align="center">
<math>
\frac{\ell_\mathrm{code}}{\ell_\mathrm{SCF}} =  \biggl[ \frac{\pi (128-3)}{128} \biggr] = 3.068 .
</math>
</div>

<span id="Q0.7properties">Hence, beginning with the values of various binary system parameters [http://www.phys.lsu.edu/~tohline/clayton/q07.pdf as generated by the SCF code], we conclude that the initial model used by Dominic in his '''Case A''' rad-hydro simulations has the following properties:</span>

<table align="center" border="1" cellpadding="5">
<tr>
  <td align="center" colspan="5">
'''Properties of Initial Q0.7 Polytropic Binary'''
  </td>
</tr>

<tr>
  <td align="center">
Quantity
  </td>
  <td align="center">
SCF-code<br/>
Value
  </td>
  <td align="center">
Conversion<br/>
Factor
  </td>
  <td align="center">
RadHydro-code<br/>
Value
  </td>
  <td align="center">
'''Case A'''<br/>
physical units
  </td>
</tr>

<tr>
  <td align="center">
<math>M_\mathrm{Accretor}</math>
  </td>
  <td align="center">
<math>0.01394</math>
  </td>
  <td align="center">
<math>\biggl( \frac{\ell_\mathrm{code}}{\ell_\mathrm{SCF}} \biggr)^{3}</math>
  </td>
  <td align="center">
<math>0.4025</math>
  </td>
  <td align="center">
<math>0.565~M_\odot</math>
  </td>
</tr>

<tr>
  <td align="center">
<math>M_\mathrm{Donor}</math>
  </td>
  <td align="center">
<math>0.009761</math>
  </td>
  <td align="center">
<math>\biggl( \frac{\ell_\mathrm{code}}{\ell_\mathrm{SCF}} \biggr)^{3}</math>
  </td>
  <td align="center">
<math>0.2819</math>
  </td>
  <td align="center">
<math>0.396~M_\odot</math>
  </td>
</tr>

<tr>
  <td align="center">
<math>\rho_\mathrm{Accretor}</math>
  </td>
  <td align="center">
<math>1.000</math>
  </td>
  <td align="center">
<math>1</math>
  </td>
  <td align="center">
<math>1.000</math>
  </td>
  <td align="center">
<math>5.16\times 10^{3}~\mathrm{g}~\mathrm{cm}^{-3}</math>
  </td>
</tr>

<tr>
  <td align="center">
<math>a_\mathrm{separation}</math>
  </td>
  <td align="center">
<math>0.8394</math>
  </td>
  <td align="center">
<math>\biggl( \frac{\ell_\mathrm{code}}{\ell_\mathrm{SCF}} \biggr)</math>
  </td>
  <td align="center">
<math>2.575</math>
  </td>
  <td align="center">
<math>0.300~R_\odot</math>
  </td>
</tr>

<tr>
  <td align="center">
<math>P_\mathrm{orbit}</math>
  </td>
  <td align="center">
<math>31.19</math>
  </td>
  <td align="center">
<math>1</math>
  </td>
  <td align="center">
<math>31.19</math>
  </td>
  <td align="center">
<math>27.7~\mathrm{min}</math>
  </td>
</tr>
</table>