📄 pcs.tex
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\def\bea{\begin{eqnarray}}\def\eea{ \end{eqnarray}}\def\beq{\begin{equation}}\def\eeq{ \end{equation}}\def\req#1{(\ref{#1})}\def\lp{\left (}\def\rp{\right)}\def\lb{\left [}\def\rb{\right]}\def\pbox#1{ \fbox {$ \displaystyle #1 $}}% ------------------------------------------------------------% trace\def\tr{\texttt{tr}\;}% divergence\def\DIV#1{\nabla \cdot #1}% curl\def\CURL#1{\nabla \times #1}% gradient\def\GRAD#1{\nabla #1}% Laplacian\def\LAPL#1{\nabla^2 #1}% ------------------------------------------------------------% stress tensor\def\ssten{{\bf \sigma}}\def\ssmat{\lp \matrix { \sigma_{11} & \sigma_{12} & \sigma_{13} \cr \sigma_{12} & \sigma_{22} & \sigma_{23} \cr \sigma_{13} & \sigma_{23} & \sigma_{33} \cr} \rp}% strain tensor\def\eeten{{\bf \epsilon}}\def\eemat{\lp \matrix { \epsilon_{11} & \epsilon_{12} & \epsilon_{13} \cr \epsilon_{12} & \epsilon_{22} & \epsilon_{23} \cr \epsilon_{13} & \epsilon_{23} & \epsilon_{33} \cr} \rp}% elastic tensor\def\CC{{\bf C}}% identity tensor\def\I{\;{\bf I}}% particle displacement vector\def\uu{{\bf u}}% particle velocity vector\def\vv{{\bf v}}% force vector\def\ff{{\bf f}}% distance vector\def\xx{{\bf x}}% wavenumber vector\def\kk{{\bf k}}% normal vector\def\nn{{\bf n}}% source vector\def\ss{{\bf s}}% receiver vector\def\rr{{\bf r}}\def\Fop#1{\mathcal{F} \lb #1 \rb}\def\Fin#1{\mathcal{F}^{-1}\lb #1 \rb}\def\dtwo#1#2 {\frac{\partial^2 #1}{\partial #2^2 } }\def\done#1#2 {\frac{\partial #1}{\partial #2 } }
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