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Publication 29

Numerical Analysis of Parallel Replica Dynamics

Authors:

MinnesotaGideon Simpson
School of Mathematics, University of Minnesota 206 Church Street SE, Minneapolis, MN 55455, U.S.A.


MinnesotaMitchell Luskin
School of Mathematics, University of Minnesota 206 Church Street SE, Minneapolis, MN 55455, U.S.A.


Abstract:
Parallel replica dynamics is a method for accelerating the computation of processes characterized by a sequence of infrequent events. In this work, the processes are governed by the overdamped Langevin equation. Such processes spend much of their time about the minima of the underlying potential, occasionally transitioning into di erent basins of attraction. The essential idea of parallel replica dynamics is that the exit time distribution from a given well for a single process can be approximated by the minimum of the exit time distributions of N independent identical processes, each run for only 1=N-th the amount of time. While promising, this leads to a series of numerical analysis questions about the accuracy of the exit distributions. Building upon the recent work in [4], we prove a uni ed error estimate on the exit distributions of the algorithm against an unaccelerated process. Furthermore, we study a dephasing mechanism, and prove that it will successfully complete.
Get the paper in its entirety
1204.0819.pdf

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