From f68adcfe2b7d17b08bdc49f361b5566e29e485c1 Mon Sep 17 00:00:00 2001 From: athomps Date: Mon, 12 Apr 2010 18:00:21 +0000 Subject: [PATCH] fixed error in fix_nh1.tex git-svn-id: svn://svn.icms.temple.edu/lammps-ro/trunk@3981 f3b2605a-c512-4ea7-a41b-209d697bcdaa --- doc/Eqs/fix_nh1.jpg | Bin 43180 -> 54460 bytes doc/Eqs/fix_nh1.tex | 25 +++++++++++-------------- 2 files changed, 11 insertions(+), 14 deletions(-) diff --git a/doc/Eqs/fix_nh1.jpg b/doc/Eqs/fix_nh1.jpg index a100650a57dc7409ca34662dff64884f26e40724..929f97a8c63e6aad36d0f73a3989e412b1f52f58 100644 GIT binary patch literal 54460 zcmeFYbyS;A_b(c(SSb#rxD|pH+Cp)cgkr&i71!WWyu~RVyjZc~P~4%#-JJl%-Q91# z?|Xjd_nx)xxw6*%^X{yfd}f~UJu}aqJPoAB-FvY*7IK0L;$C2_h#+r>z5}!<+}80dN4=02BbFk%_Z|go?^X zWRm|4T}~s@A!&m1pR%+W8ujH_!M2}O%v?iGLOlOBnf@#Kg%h$u004yp89`$4Z!G=~ zHvTtO{|CFfIJh9wSpI`eER9T&*c*vCoYWywNL+x#FD(9z>;J*V|Hi%lU^f$sfAY>E z@f$l+D?0!H6$^YCz>qi>iDh9hdt~{j`$)`c;^2hLi$;RPO#h4v 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zI1|GF!V=myYIMb*YUOztUfWYYmmu0$?UyU9+5Y;$ovv0j-~Pr?)n7SYA?IZ${9{`X z`3NZ9>TULYV`lp0{F3#rb@d{zk_Ybm7H*NuL`oP2l96WZZQINj{+ zseShHa~DGA&IngN^2r}P5yQ;;wdB#SI<}59XrJplkpdDt0oXc0NBE|bbW_5^g%5`O98DeE8cC7 z)9D|-y&=XZAY+Wt%ruf1{A@M04^CereT*Ga@DEKwqnrecT-|$L$(R`UO zLS=!|?|r=g%V|jb*BSMTE%Sh{k%`)0xmJb)6st&E=zWWBs7&54&qz7eBaR~hh0<+O fR1mXejwP%j2bKCWt+o_~=l+j;=>M;ee`o#!K@O^W diff --git a/doc/Eqs/fix_nh1.tex b/doc/Eqs/fix_nh1.tex index 457dfd117f..f6928495ce 100644 --- a/doc/Eqs/fix_nh1.tex +++ b/doc/Eqs/fix_nh1.tex @@ -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}