180 |
|
\begin{eqnarray*} |
181 |
|
\Xi _a^{rr} = \frac{{32\pi }}{3}\eta \frac{{(a^2 - b^2 )b^2 }}{{2a - b^2 S}}, \\ |
182 |
|
\Xi _b^{rr} = \Xi _c^{rr} = \frac{{32\pi }}{3}\eta \frac{{(a^4 - b^4 )}}{{(2a^2 - b^2 )S - 2a}}. |
183 |
< |
\end{eqnarray} |
183 |
> |
\end{eqnarray*} |
184 |
|
|
185 |
|
\subsubsection{\label{introSection:resistanceTensorRegularArbitrary}\textbf{The Resistance Tensor for Arbitrary Shapes}} |
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|
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made of 2266 small identical beads with size of 0.3 \AA on the |
566 |
|
surface. Applying the procedure described in |
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Sec.~\ref{introEquation:ResistanceTensorArbitraryOrigin}, we |
568 |
< |
identified the center of resistance at $(0\AA, 0.7482\AA, |
569 |
< |
-0.1988\AA)$, as well as the resistance tensor, |
568 |
> |
identified the center of resistance at $(0 \AA, 0.7482 \AA, |
569 |
> |
-0.1988 \AA)$, as well as the resistance tensor, |
570 |
|
\[ |
571 |
|
\left( {\begin{array}{*{20}c} |
572 |
|
0.9261 & 0 & 0&0&0.08585&0.2057\\ |
593 |
|
However, because of the stochastic nature, simulation using Langevin |
594 |
|
dynamics was shown to decay slightly faster than MD. In order to |
595 |
|
study the rotational motion of the molecules, we also calculated the |
596 |
< |
auto- correlation function of the principle axis of the second GB |
596 |
> |
auto-correlation function of the principle axis of the second GB |
597 |
|
particle, $u$. The discrepancy shown in Fig.~\ref{langevin:uacf} was |
598 |
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probably due to the reason that the viscosity using in the |
599 |
|
simulations only partially preserved the dynamics of the system. |