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Analytical and Numerical Results on Escape of Brownian Particles

Caginalp, Carey (2011) Analytical and Numerical Results on Escape of Brownian Particles. Undergraduate Thesis, University of Pittsburgh. (Unpublished)

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Abstract

A particle moves with Brownian motion in a unit disc with reflection from the boundaries except for a portion (called "window" or "gate") in which it is absorbed. The main problems are to determine the first hitting time and spatial distribution. A closed formula for the mean first hitting time is given for a gate of any size. Also given is the probability density of the location where a particle hits if initially the particle is at the center or uniformly distributed. Numerical simulations of the stochastic process with finite step size and sufficient amount of sample paths are compared with the exact solution to the Brownian motion (the limit of zero stepsize), providing an empirical formula for the divergence. Histograms of first hitting times are also generated.


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Details

Item Type: University of Pittsburgh ETD
Status: Unpublished
Creators/Authors:
CreatorsEmailPitt UsernameORCID
Caginalp, Careycac71@pitt.eduCAC71
ETD Committee:
TitleMemberEmail AddressPitt UsernameORCID
Committee ChairChen, Xinfuxinfu@pitt.eduXINFU
Committee MemberWang, Dehuadhwang@pitt.eduDHWANG
Committee MemberJiang, Huiqianghqjiang@pitt.eduHQJIANG
Committee MemberSlemrod, Marshallslemrod@math.wisc.edu
Date: 29 April 2011
Date Type: Completion
Defense Date: 28 January 2011
Approval Date: 29 April 2011
Submission Date: 17 March 2011
Access Restriction: No restriction; Release the ETD for access worldwide immediately.
Institution: University of Pittsburgh
Schools and Programs: Dietrich School of Arts and Sciences > Mathematics
University Honors College
Degree: BPhil - Bachelor of Philosophy
Thesis Type: Undergraduate Thesis
Refereed: Yes
Uncontrolled Keywords: Brownian motion; stochastics
Other ID: http://etd.library.pitt.edu/ETD/available/etd-03172011-191325/, etd-03172011-191325
Date Deposited: 10 Nov 2011 19:32
Last Modified: 15 Nov 2016 13:37
URI: http://d-scholarship.pitt.edu/id/eprint/6522

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