forked from lijiext/lammps
25 lines
1.1 KiB
TeX
25 lines
1.1 KiB
TeX
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\documentclass[12pt]{article}
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\begin{document}
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\begin{eqnarray*}
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T_{pq} = T_{ij} & = & \frac{q_j}{r^3} \left[ 1 -
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3\left(\frac{r}{r_c}\right)^{\!2} +
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2\left(\frac{r}{r_c}\right)^{\!3}\right] (\vec{p_i}\times\vec{r}) \\
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T_{qp} = T_{ji} & = & - \frac{q_i}{r^3} \left[ 1 -
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3\left(\frac{r}{r_c}\right)^{\!2} +
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2\left(\frac{r}{r_c}\right)^{\!3} \right] (\vec{p_j}\times\vec{r}) \\
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T_{pp} = T_{ij} & = & -\frac{1}{r^3}\left[1-4\left(\frac{r}{r_c}\right)^{\!3} +
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e3\left(\frac{r}{r_c}\right)^{\!4}\right] (\vec{p_i} \times \vec{p_j}) + \\
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& & \frac{3}{r^5}\left[1-4\left(\frac{r}{r_c}\right)^{\!3} +
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3\left(\frac{r}{r_c}\right)^{\!4}\right] (\vec{p_j}\bullet\vec{r})
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(\vec{p_i} \times \vec{r}) \\
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T_{pp} = T_{ji} & = & -\frac{1}{r^3}\left[1-4\left(\frac{r}{r_c}\right)^{\!3} +
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3\left(\frac{r}{r_c}\right)^{\!4}\right](\vec{p_j} \times \vec{p_i}) + \\
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& & \frac{3}{r^5}\left[1-4\left(\frac{r}{r_c}\right)^{\!3} +
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3\left(\frac{r}{r_c}\right)^{\!4}\right] (\vec{p_i} \bullet \vec{r})
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(\vec{p_j} \times \vec{r}) \\
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\end{eqnarray*}
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\end{document}
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