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rate. Furthermore, various scaling frequencies can be tested for one |
302 |
|
single swapping rate. To compare the performance between swapping and |
303 |
|
scaling method, temperatures of different dimensions in all the slabs |
304 |
< |
were observed. |
304 |
> |
were observed. Most of the simulations include $10^5$ steps of |
305 |
> |
equilibration without imposing momentum flux, $10^5$ steps of |
306 |
> |
stablization with imposing momentum transfer, and $10^6$ steps of data |
307 |
> |
collection under RNEMD. For relatively high momentum flux simulations, |
308 |
> |
${5\times10^5}$ step data collection is sufficient. For some low momentum |
309 |
> |
flux simulations, ${2\times10^6}$ steps were necessary. |
310 |
|
|
311 |
|
After each simulation, the shear viscosity was calculated in reduced |
312 |
|
unit. The momentum flux was calculated with total unphysical |
348 |
|
|
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|
\section{Results And Discussion} |
350 |
|
\subsection{Shear Viscosity} |
351 |
+ |
Our calculations (Table \ref{shearRate}) shows that scale RNEMD method |
352 |
+ |
produced comparable shear viscosity to swap RNEMD method. In Table |
353 |
+ |
\ref{shearRate}, the names of the calculated samples are devided into |
354 |
+ |
two parts. The first number refers to total slabs in one simulation |
355 |
+ |
box. The second number refers to the swapping interval in swap method, or |
356 |
+ |
in scale method the equilvalent swapping interval that the same |
357 |
+ |
momentum flux would theoretically result in swap method. All the scale |
358 |
+ |
method results were from simulations that had 10 time steps of scaling |
359 |
+ |
interval. The average molecular momentum gradients of these samples |
360 |
+ |
are shown in Figures \ref{shearGradSwap} and \ref{shearGradScale} |
361 |
+ |
respectively. |
362 |
+ |
|
363 |
+ |
\begin{table*} |
364 |
+ |
\begin{minipage}{\linewidth} |
365 |
+ |
\begin{center} |
366 |
+ |
|
367 |
+ |
\caption{Calculation results for shear viscosity of Lennard-Jones |
368 |
+ |
fluid at ${T^* = 0.72}$ and ${\rho^* = 0.85}$, with swap and scale |
369 |
+ |
methods at various momentum exchange rates. Results in reduced |
370 |
+ |
unit. Errors of calculations in parentheses. } |
371 |
+ |
|
372 |
+ |
\begin{tabular} |
373 |
+ |
\hline |
374 |
+ |
Name & $\eta^*_{swap}$ & $\eta^*_{scale}$\\ |
375 |
+ |
\hline |
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+ |
20-500 & 3.64(0.05) & 3.76(0.09)\\ |
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+ |
20-1000 & 3.52(0.16) & -\\ |
378 |
+ |
20-2000 & - & 3.32(0.18)\\ |
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+ |
20-2500 & - & 3.43(0.08)\\ |
380 |
+ |
\end{tabular} |
381 |
+ |
\label{shearRate} |
382 |
+ |
\end{center} |
383 |
+ |
\end{minipage} |
384 |
+ |
\end{table*} |
385 |
+ |
|
386 |
+ |
\begin{figure} |
387 |
+ |
\includegraphics[width=\linewidth]{shearGradSwap.eps} |
388 |
+ |
\caption{Average momentum gradients of simulations using swap method.} |
389 |
+ |
\label{shearGradSwap} |
390 |
+ |
\end{figure} |
391 |
|
|
392 |
+ |
\begin{figure} |
393 |
+ |
\includegraphics[width=\linewidth]{shearGradScale.eps} |
394 |
+ |
\caption{Average momentum gradients of simulations using scale |
395 |
+ |
method.} |
396 |
+ |
\label{shearGradScale} |
397 |
+ |
\end{figure} |
398 |
+ |
|
399 |
+ |
\begin{figure} |
400 |
+ |
\includegraphics[width=\linewidth]{shearTempScale.eps} |
401 |
+ |
\caption{Temperature profile for scaling RNEMD simulation.} |
402 |
+ |
\label{shearTempScale} |
403 |
+ |
\end{figure} |
404 |
+ |
However, observations of temperatures along three dimensions show that |
405 |
+ |
inhomogeneity occurs in scaling RNEMD simulations, particularly in the |
406 |
+ |
two slabs which were scaled. Figure \ref{shearTempScale} indicate that with |
407 |
+ |
increased imposed momentum flux, the temperature difference among $x$ |
408 |
+ |
and the other two dimensions were larger. This would result from the |
409 |
+ |
scaling method. From Eq. \ref{eq:fluxPlane}, after momentum gradient |
410 |
+ |
is set up, $P_c^x$ would be roughly stable ($<0$). Consequently, scaling |
411 |
+ |
factor $x$ would most probably larger than 1. Therefore, the kinetic |
412 |
+ |
energy in $x$-dimension $K_c^x$ would keep increase after most scaling |
413 |
+ |
step. And if there is not enough time for the kinetic energy to |
414 |
+ |
exchange among different dimensions and different slabs, the system would finally build up temperature (kinetic energy) difference among the three dimensions. |
415 |
+ |
Also, between $y$ and $z$ dimensions in the scaled slabs, temperatures of |
416 |
+ |
$z$-axis are closer to neighbor slabs. This is due to momentum |
417 |
+ |
transfer along $z$ dimension between slabs. |
418 |
+ |
|
419 |
+ |
Although results between scaling and swapping methods are comparable, |
420 |
+ |
the inherent temperature inhomogeneity makes scaling RNEMD method less |
421 |
+ |
attractive than swapping RNEMD in shear viscosity calculation. |
422 |
+ |
|
423 |
+ |
\subsection{Thermal Conductivity} |
424 |
+ |
|
425 |
+ |
|
426 |
+ |
|
427 |
|
\section{Acknowledgments} |
428 |
|
Support for this project was provided by the National Science |
429 |
|
Foundation under grant CHE-0848243. Computational time was provided by |