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heat_flux_J.tex
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Created
Fri, Apr 4, 05:48
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526 B
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text/x-tex
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Sun, Apr 6, 05:48 (2 d)
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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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