139 |
|
average 7\% increase in computation time using the DLM method in |
140 |
|
place of quaternions. This cost is more than justified when |
141 |
|
comparing the energy conservation of the two methods as illustrated |
142 |
< |
in Fig.~\ref{timestep}. |
142 |
> |
in Fig.~\ref{methodFig:timestep}. |
143 |
|
|
144 |
|
\begin{figure} |
145 |
|
\centering |
474 |
|
\end{equation} |
475 |
|
|
476 |
|
Bond constraints are applied at the end of both the {\tt moveA} and |
477 |
< |
{\tt moveB} portions of the algorithm. Details on the constraint |
478 |
< |
algorithms are given in section \ref{oopseSec:rattle}. |
477 |
> |
{\tt moveB} portions of the algorithm. |
478 |
|
|
479 |
|
\subsection{\label{methodSection:NPTf}Constant-pressure integration with a |
480 |
|
flexible box (NPTf)} |
607 |
|
|
608 |
|
\subsection{\label{methodSection:otherSpecialEnsembles}Other Special Ensembles} |
609 |
|
|
610 |
< |
\subsubsection{\label{methodSection:NPAT}NPAT Ensemble} |
610 |
> |
\subsubsection{\label{methodSection:NPAT}\textbf{NPAT Ensemble}} |
611 |
|
|
612 |
|
A comprehensive understanding of structure¨Cfunction relations of |
613 |
|
biological membrane system ultimately relies on structure and |
630 |
|
Note that the iterative schemes for NPAT are identical to those |
631 |
|
described for the NPTi integrator. |
632 |
|
|
633 |
< |
\subsubsection{\label{methodSection:NPrT}NP$\gamma$T Ensemble} |
633 |
> |
\subsubsection{\label{methodSection:NPrT}\textbf{NP$\gamma$T Ensemble}} |
634 |
|
|
635 |
|
Theoretically, the surface tension $\gamma$ of a stress free |
636 |
|
membrane system should be zero since its surface free energy $G$ is |
792 |
|
between the native and denatured states. Because of its stability |
793 |
|
against noise, Langevin dynamics is very suitable for studying |
794 |
|
remagnetization processes in various |
795 |
< |
systems\cite{Garcia-Palacios1998,Berkov2002,Denisov2003}. For |
796 |
< |
instance, the oscillation power spectrum of nanoparticles from |
797 |
< |
Langevin dynamics simulation has the same peak frequencies for |
798 |
< |
different wave vectors,which recovers the property of magnetic |
799 |
< |
excitations in small finite structures\cite{Berkov2005a}. In an |
800 |
< |
attempt to reduce the computational cost of simulation, multiple |
801 |
< |
time stepping (MTS) methods have been introduced and have been of |
802 |
< |
great interest to macromolecule and protein |
803 |
< |
community\cite{Tuckerman1992}. Relying on the observation that |
804 |
< |
forces between distant atoms generally demonstrate slower |
805 |
< |
fluctuations than forces between close atoms, MTS method are |
806 |
< |
generally implemented by evaluating the slowly fluctuating forces |
807 |
< |
less frequently than the fast ones. Unfortunately, nonlinear |
808 |
< |
instability resulting from increasing timestep in MTS simulation |
809 |
< |
have became a critical obstruction preventing the long time |
810 |
< |
simulation. Due to the coupling to the heat bath, Langevin dynamics |
811 |
< |
has been shown to be able to damp out the resonance artifact more |
813 |
< |
efficiently\cite{Sandu1999}. |
795 |
> |
systems\cite{Palacios1998,Berkov2002,Denisov2003}. For instance, the |
796 |
> |
oscillation power spectrum of nanoparticles from Langevin dynamics |
797 |
> |
simulation has the same peak frequencies for different wave |
798 |
> |
vectors,which recovers the property of magnetic excitations in small |
799 |
> |
finite structures\cite{Berkov2005a}. In an attempt to reduce the |
800 |
> |
computational cost of simulation, multiple time stepping (MTS) |
801 |
> |
methods have been introduced and have been of great interest to |
802 |
> |
macromolecule and protein community\cite{Tuckerman1992}. Relying on |
803 |
> |
the observation that forces between distant atoms generally |
804 |
> |
demonstrate slower fluctuations than forces between close atoms, MTS |
805 |
> |
method are generally implemented by evaluating the slowly |
806 |
> |
fluctuating forces less frequently than the fast ones. |
807 |
> |
Unfortunately, nonlinear instability resulting from increasing |
808 |
> |
timestep in MTS simulation have became a critical obstruction |
809 |
> |
preventing the long time simulation. Due to the coupling to the heat |
810 |
> |
bath, Langevin dynamics has been shown to be able to damp out the |
811 |
> |
resonance artifact more efficiently\cite{Sandu1999}. |
812 |
|
|
813 |
|
%review rigid body dynamics |
814 |
|
Rigid bodies are frequently involved in the modeling of different |
896 |
|
average acceleration is not always true for cooperative motion which |
897 |
|
is common in protein motion. An inertial Brownian dynamics (IBD) was |
898 |
|
proposed to address this issue by adding an inertial correction |
899 |
< |
term\cite{Beard2001}. As a complement to IBD which has a lower bound |
899 |
> |
term\cite{Beard2003}. As a complement to IBD which has a lower bound |
900 |
|
in time step because of the inertial relaxation time, long-time-step |
901 |
|
inertial dynamics (LTID) can be used to investigate the inertial |
902 |
|
behavior of the polymer segments in low friction |