diff --git a/doc/Eqs/fix_nh1.jpg b/doc/Eqs/fix_nh1.jpg new file mode 100644 index 0000000000..a100650a57 Binary files /dev/null and b/doc/Eqs/fix_nh1.jpg differ diff --git a/doc/Eqs/fix_nh1.tex b/doc/Eqs/fix_nh1.tex new file mode 100644 index 0000000000..457dfd117f --- /dev/null +++ b/doc/Eqs/fix_nh1.tex @@ -0,0 +1,38 @@ +\documentclass[24pt]{article} + +\pagestyle{empty} +\Huge + +\begin{document} + +\mathchardef\mhyphen="2D + +% The imaginary unit +\providecommand*{\iu}% + {\ensuremath{{\rm i}}} + + +$$ +\exp \left(\iu{} L \Delta t \right) = +\exp \left(\iu{} L_{\rm T\mhyphen baro} \frac{\Delta t}{2} \right) +\exp \left(\iu{} L_{\rm T\mhyphen part} \frac{\Delta t}{2} \right) +\exp \left(\iu{} L_{\epsilon , 2} \frac{\Delta t}{2} \right) +\exp \left(\iu{} L_{2}^{(2)} \frac{\Delta t}{2} \right) +$$ +$$ +\times \left[ +\exp \left(\iu{} L_{2}^{(1)} \frac{\Delta t}{2n} \right) +\exp \left(\iu{} L_{\epsilon , 1} \frac{\Delta t}{n} \right) +\exp \left(\iu{} L_1 \frac{\Delta t}{n} \right) +\exp \left(\iu{} L_{2}^{(1)} \frac{\Delta t}{2n} \right) +\right]^n +$$ +$$ +\exp \left(\iu{} L_{2}^{(2)} \frac{\Delta t}{2} \right) +\exp \left(\iu{} L_{\epsilon , 2} \frac{\Delta t}{2} \right) +\exp \left(\iu{} L_{\rm T\mhyphen part} \frac{\Delta t}{2} \right) +\exp \left(\iu{} L_{\rm T\mhyphen baro} \frac{\Delta t}{2} \right) ++ \mathcal{O} \left(\Delta t^3 \right) +$$ + +\end{document} diff --git a/doc/fix_nh.html b/doc/fix_nh.html index 1fa07e3c14..6bc2b61591 100644 --- a/doc/fix_nh.html +++ b/doc/fix_nh.html @@ -73,13 +73,13 @@ When used correctly, the time-averaged temperature and stress tensor of the particles will match the target values specified by Tstart/Tstop and Pstart/Pstop.

-

The equations of motion used are those of Shinoda et al in +

The equations of motion used are those of Shinoda et al. in (Shinoda), which combine the hydrostatic equations of Martyna, Tobias and Klein in (Martyna) with the strain energy proposed by Parrinello and Rahman in -(Parrinello). The time integration schemes follow the -time-reversible measure-preserving integrators derived by Tuckerman et -al in (Tuckerman). +(Parrinello). The time integration schemes closely +follow the time-reversible measure-preserving Verlet and +rRESPA integrators derived by Tuckerman et al. in (Tuckerman).

@@ -386,19 +386,19 @@ simulation, otherwise its value is 3. follows. The notation means there are tchain values for eta, followed by tchain for eta_dot, followed by ndof for omega, etc:

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