# [Commits] [svn:einsteintoolkit] Paper_EinsteinToolkit_2010/ (Rev. 32)

knarf at cct.lsu.edu knarf at cct.lsu.edu
Mon Feb 28 09:42:55 CST 2011

User: knarf
Date: 2011/02/28 09:42 AM

Modified:
/
ET.tex

Log:
some equations

File Changes:

Directory: /
============

File [modified]: ET.tex
Delta lines: +12 -4
===================================================================
--- ET.tex	2011-02-27 23:06:15 UTC (rev 31)
+++ ET.tex	2011-02-28 15:42:55 UTC (rev 32)
@@ -422,7 +422,6 @@

\subsection{Base Modules}
\label{sec:base_modules}
-\todo{1/3 page Frank}
Modular designs have proven to be essential for distributed development
of complex software systems, and require the use of well defined interfaces.
Low-level interoperability within the Einstein Toolkit is provided by
@@ -463,11 +462,20 @@
In particular, it defines the rest-mass density $\varrho$, the gas
pressure $p$, internal energy density $\epsilon$, the
contravariant gas three velocity defined as
-$v^i = \frac{u^i}{\alpha u^0} + \frac{\beta^i}{\alpha}$, the electron
+\begin{equation}
+ v^i = \frac{u^i}{\alpha u^0} + \frac{\beta^i}{\alpha}
+\end{equation}
+the electron
fraction $Y_e$, the temperature $T$, the specific entropy per
particle $s$ and the contravariant magnetic field vector $B^i$, defined
-as $B^i = \frac{1}{\sqrt{4\pi}} n_{\nu} F^{*\nu i}$, in terms of the dual
-$F^{*\mu\nu} = \frac{1}{2}\varepsilon^{\mu\nu\alpha\beta}F_{\alpha\beta}$
+as
+\begin{equation}
+ B^i = \frac{1}{\sqrt{4\pi}} n_{\nu} F^{*\nu i}
+\end{equation}
+in terms of the dual
+\begin{equation}
+ F^{*\mu\nu} = \frac{1}{2}\varepsilon^{\mu\nu\alpha\beta}F_{\alpha\beta}
+\end{equation}
to the Faraday tensor and the unit normal of the foliation of spacetime
$n^\mu$.