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heat_flux_J.tex
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Mon, Aug 26, 11:35
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rLAMMPS lammps
heat_flux_J.tex
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\documentclass[12pt]{article}
\begin{document}
\begin{eqnarray*}
\mathbf{J} & = & \frac{1}{V} \left[ \sum_i e_i \mathbf{v}_i - \sum_{i} \mathbf{S}_{i} \mathbf{v}_i \right] \\
& = & \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] \\
& = & \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]
\end{eqnarray*}
\end{document}
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