| 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)} |
| 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 |
