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\chapter{\label{chapt:methodology}LANGEVIN DYNAMICS for RIGID BODIES of ARBITRARY SHAPE} |
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\chapter{\label{chapt:methodology}LANGEVIN DYNAMICS FOR RIGID BODIES OF ARBITRARY SHAPE} |
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\section{Introduction} |
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estimation of friction tensor from hydrodynamics theory into the |
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sophisticated rigid body dynamics. |
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\section{Method{\label{methodSec}}} |
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\section{Computational methods{\label{methodSec}}} |
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\subsection{\label{introSection:frictionTensor}Friction Tensor} |
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Theoretically, the friction kernel can be determined using velocity |
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where $x_OR$, $y_OR$, $z_OR$ are the components of the vector |
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joining center of resistance $R$ and origin $O$. |
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\subsection{Langevin dynamics for rigid particles of arbitrary shape} |
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\subsection{Langevin dynamics for rigid particles of arbitrary shape\label{LDRB}} |
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Consider a Langevin equation of motions in generalized coordinates |
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\begin{equation} |
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\end{equation} |
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where $M_i$ is a $6\times6$ generalized diagonal mass (include mass |
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and moment of inertial) matrix and $V_i$ is a generalized velocity, |
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$V_i = V_i(v_i,\omega _i)$. The right side of Eq. |
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$V_i = V_i(v_i,\omega _i)$. The right side of Eq.~ |
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(\ref{LDGeneralizedForm}) consists of three generalized forces in |
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lab-fixed frame, systematic force $F_{s,i}$, dissipative force |
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$F_{f,i}$ and stochastic force $F_{r,i}$. While the evolution of the |
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\end{align*} |
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\section{Results and discussion} |
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The Langevin algorithm described in Sec.~\ref{LDRB} has been |
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implemented in {\sc oopse}\cite{Meineke2005} and applied to several |
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test systems. |
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\subsection{Langevin dynamics of} |
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\begin{figure} |
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\centering |
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\includegraphics[width=\linewidth]{temperature.eps} |
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\caption[]{.} \label{langevin:temperature} |
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\end{figure} |
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\subsection{LD of banana-shaped molecule} |
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\begin{figure} |
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\centering |
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\includegraphics[width=\linewidth]{one_banana.eps} |
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\caption[]{.} \label{langevin:banana} |
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\end{figure} |
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\section{Conclusions} |