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git-svn-id: svn://svn.icms.temple.edu/lammps-ro/trunk@3933 f3b2605a-c512-4ea7-a41b-209d697bcdaa

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sjplimp
2010-03-29 23:48:03 +00:00
parent 367c73f9d0
commit ecd35ece89
2 changed files with 11 additions and 14 deletions
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doc/Eqs/heat_flux_J.jpg
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doc/Eqs/heat_flux_J.tex
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@ -2,13 +2,10 @@
\begin{document} \begin{document}
$$ \begin{eqnarray*}
\mathbf{J} \mathbf{J} & = & \frac{1}{V} \left[ \sum_i e_i \mathbf{v}_i - \sum_{i} \mathbf{S}_{i} \mathbf{v}_i \right] \\
= \sum_i e_i \mathbf{v}_i & = & \frac{1}{V} \left[ \sum_i e_i \mathbf{v}_i + \sum_{i<j} \left( \mathbf{f}_{ij} \cdot \mathbf{v}_j \right) \mathbf{x}_{ij} \right] \\
+ \sum_{i<j} \left( \mathbf{f}_{ij} \cdot \mathbf{v}_j \right) \mathbf{x}_{ij} & = & \frac{1}{V} \left[ \sum_i e_i \mathbf{v}_i + \frac{1}{2} \sum_{i<j} \left( \mathbf{f}_{ij} \cdot \left(\mathbf{v}_i + \mathbf{v}_j \right) \right) \mathbf{x}_{ij} \right]
= \sum_i e_i \mathbf{v}_i \end{eqnarray*}
+ \frac{1}{2} \sum_{i<j} \left( \mathbf{f}_{ij} \cdot \left(\mathbf{v}_i + \mathbf{v}_j \right) \right) \mathbf{x}_{ij}
$$
\end{document} \end{document}