| 2 |
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| 3 |
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\subsection{Static Property Analysis} |
| 4 |
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The static properties of the trajectories are analyzed with the |
| 5 |
< |
program staticProps. The code is capable of calculating the following |
| 5 |
> |
program \texttt{staticProps}. The code is capable of calculating the following |
| 6 |
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pair correlations between species A and B: |
| 7 |
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\begin{itemize} |
| 8 |
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\item $g_{\text{AB}}(r)$: Eq.~\ref{eq:gofr} |
| 90 |
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correlation that gives the average correlation of two directional |
| 91 |
|
entities as a function of their distance from each other. |
| 92 |
|
|
| 93 |
+ |
All static properties are calculated on a frame by frame basis. The |
| 94 |
+ |
trajectory is read a single frame at a time, and the appropriate |
| 95 |
+ |
calculations are done on each frame. Once one frame is finished, the |
| 96 |
+ |
next frame is read in, and a running average of the property being |
| 97 |
+ |
calculated is accumulated in each frame. The program allows for the |
| 98 |
+ |
user to specify more than one property be calculated in single run, |
| 99 |
+ |
preventing the need to read a file multiple times. |
| 100 |
+ |
|
| 101 |
|
\subsection{Dynamic Property Analysis} |
| 102 |
|
The dynamic properties of a trajectory are calculated with the program |
| 103 |
< |
dynamicProps. |
| 103 |
> |
\texttt{dynamicProps}. The program will calculate the following properties: |
| 104 |
> |
\begin{gather} |
| 105 |
> |
\langle | \mathbf{r}(t) - \mathbf{r}(0) |^2 \rangle \label{eq:rms}\\ |
| 106 |
> |
\langle \mathbf{v}(t) \cdot \mathbf{v}(0) \rangle \label{eq:velCorr} \\ |
| 107 |
> |
\langle \mathbf{j}(t) \cdot \mathbf{j}(0) \rangle \label{eq:angularVelCorr} |
| 108 |
> |
\end{gather} |
| 109 |
> |
|
| 110 |
> |
Eq.~\ref{eq:rms} is the root mean square displacement |
| 111 |
> |
function. Eq.~\ref{eq:velCorr} and Eq.~\ref{eq:angularVelCorr} are the |
| 112 |
> |
velocity and angular velocity correlation functions respectively. The |
| 113 |
> |
latter is only applicable to directional species in the simulation. |
| 114 |
> |
|
| 115 |
> |
The \texttt{dynamicProps} program handles he file in a manner different from |
| 116 |
> |
\texttt{staticProps}. As the properties calculated by this program are time |
| 117 |
> |
dependent, multiple frames must be read in simultaneously by the |
| 118 |
> |
program. For small trajectories this is no problem, and the entire |
| 119 |
> |
trajectory is read into memory. However, for long trajectories of |
| 120 |
> |
large systems, the files can be quite large. In order to accommodate |
| 121 |
> |
large files, \texttt{dynamicProps} adopts a scheme whereby two blocks of memory |
| 122 |
> |
are allocated to read in several frames each. |
| 123 |
> |
|
| 124 |
> |
In this two block scheme, the correlation functions are first |
| 125 |
> |
calculated within each memory block, then the cross correlations |
| 126 |
> |
between the frames contained within the two blocks are |
| 127 |
> |
calculated. Once completed, the memory blocks are incremented, and the |
| 128 |
> |
process is repeated. A diagram illustrating the process is shown in |
| 129 |
> |
Fig.~\ref{fig:dynamicPropsMemory}. As was the case with \texttt{staticProps}, |
| 130 |
> |
multiple properties may be calculated in a single run to avoid |
| 131 |
> |
multiple reads on the same file. |
| 132 |
> |
|
| 133 |
> |
\begin{figure} |
| 134 |
> |
\includegraphics[angle=-90,width=80mm]{dynamicPropsMem.eps} |
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> |
\caption{This diagram illustrates the dynamic memory allocation used by \texttt{dynamicProps}, which follows the scheme: $\sum^{N_{\text{memory blocks}}}_{i=1}[ \operatorname{self}(i) + \sum^{N_{\text{memory blocks}}}_{j>i} \operatorname{cross}(i,j)]$. The shaded region represents the self correlation of the memory block, and the open blocks are read one at a time and the cross correlations between blocks are calculated.} |
| 136 |
> |
\label{fig:dynamicPropsMemory} |
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> |
\end{figure} |
