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fixed error in fix_nh1.tex 

git-svn-id: svn://svn.icms.temple.edu/lammps-ro/trunk@3981 f3b2605a-c512-4ea7-a41b-209d697bcdaa
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athomps 2010-04-12 18:00:21 +00:00
parent 6bd79b1c2e
commit f68adcfe2b
2 changed files with 11 additions and 14 deletions
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25
doc/Eqs/fix_nh1.tex
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@ -12,27 +12,24 @@
{\ensuremath{{\rm i}}}
$$
\exp \left(\iu{} L \Delta t \right) =
\begin{eqnarray*}
\exp \left(\iu{} L \Delta t \right) &=&Ê
\exp \left(\iu{} L_{\rm T\mhyphen baro} \frac{\Delta t}{2} \right)
\exp \left(\iu{} L_{\rm T\mhyphen part} \frac{\Delta t}{2} \right)
\exp \left(\iu{} L_{\epsilon , 2} \frac{\Delta t}{2} \right)
\exp \left(\iu{} L_{2}^{(2)} \frac{\Delta t}{2} \right)
$$
$$
\times \left[
\exp \left(\iu{} L_{2}^{(2)} \frac{\Delta t}{2} \right) \\
&&\times \left[
\exp \left(\iu{} L_{2}^{(1)} \frac{\Delta t}{2n} \right)
\exp \left(\iu{} L_{\epsilon , 1} \frac{\Delta t}{n} \right)
\exp \left(\iu{} L_1 \frac{\Delta t}{n} \right)
\exp \left(\iu{} L_{2}^{(1)} \frac{\Delta t}{2n} \right)
\right]^n
$$
$$
\right]^n \\
&&\times
\exp \left(\iu{} L_{2}^{(2)} \frac{\Delta t}{2} \right)
\exp \left(\iu{} L_{\epsilon , 2} \frac{\Delta t}{2} \right)
\exp \left(\iu{} L_{\rm T\mhyphen part} \frac{\Delta t}{2} \right)
\exp \left(\iu{} L_{\rm T\mhyphen baro} \frac{\Delta t}{2} \right)
+ \mathcal{O} \left(\Delta t^3 \right)
$$
\exp \left(\iu{} L_{\epsilon , 2} \frac{\Delta t}{2} \right)
\exp \left(\iu{} L_{\rm T\mhyphen part} \frac{\Delta t}{2} \right)
\exp \left(\iu{} L_{\rm T\mhyphen baro} \frac{\Delta t}{2} \right) \\
&&+ \mathcal{O} \left(\Delta t^3 \right)
\end{eqnarray*}
\end{document}