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Theory and Simulation of Rare Events in Stochastic Systems

Zhang, Bin W (2009) Theory and Simulation of Rare Events in Stochastic Systems. Doctoral Dissertation, University of Pittsburgh. (Unpublished)

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Abstract

Activated processes driven by rare fluctuations are discussed in this thesis. Understanding the dynamics of these activated processes is important for understanding chemical and biological reactions, drug design and many other important applications. First, theoretical tools including the Langevin equation, the Fokker-Planck equation and the path integral technique are reviewed. Based on these theories, simulation methods have been developed to sample the activated processes by a number of investigators. Several of the most important path sampling and path generating approaches are introduced. A combination of analytic and numerical techniques are applied to study the distribution of the durations of transition events over a barrier in a one-dimensional system undergoing over-damped Langevin dynamics. Then we employ the ``weighted ensemble' path sampling method to generate an unbiased ensemble of paths for a conformational transition in a 210-dimensional model of the protein calmodulin, and also find the reaction rate. The results show that the weighted ensemble approach is a remarkably straightforward and successful method. At last, systems with multiple channels are studied by the weighted ensemble approach and the more common transition path sampling approach. The weighted ensemble method is distinguished by its ability to perform complete path sampling for systems with multiplechannels at reasonable cost.

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Details

Item Type: University of Pittsburgh ETD
Status: Unpublished
Creators/Authors:
CreatorsEmailPitt UsernameORCID
Zhang, Bin Wbiz6@pitt.eduBIZ6
ETD Committee:
TitleMemberEmail AddressPitt UsernameORCID
Committee CoChairZuckerman, Daniel Mdmz@ccbb.pitt.eduDDMMZZ
Committee CoChairJasnow, Davidjasnow@pitt.eduJASNOW
Committee MemberDuncan, Anthony Htony@dectony.phyast.pitt.eduHAD
Committee MemberBoyanovsky, Danielboyan@pitt.eduBOYAN
Committee MemberCoalson, Robertrob@ringo.chem.pitt.eduCOALSON
Committee MemberGoldburg, Walter Igoldburg@pitt.eduGOLDBURG
Date: 29 January 2009
Date Type: Completion
Defense Date: 7 August 2008
Approval Date: 29 January 2009
Submission Date: 17 November 2008
Access Restriction: No restriction; Release the ETD for access worldwide immediately.
Institution: University of Pittsburgh
Schools and Programs: Dietrich School of Arts and Sciences > Physics
Degree: PhD - Doctor of Philosophy
Thesis Type: Doctoral Dissertation
Refereed: Yes
Uncontrolled Keywords: Brownian Motion; Path Sampling; Rare Events; Stochastic Systems
Other ID: http://etd.library.pitt.edu/ETD/available/etd-11172008-215923/, etd-11172008-215923
Date Deposited: 10 Nov 2011 20:05
Last Modified: 15 Nov 2016 13:51
URI: http://d-scholarship.pitt.edu/id/eprint/9705

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