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 $n^\mu$.