The narrow escape problem : a matched asymptotic expansion approach

We consider the motion of a Brownian particle trapped in an arbitrary bounded two or three-dimensional domain, whose boundary is reflecting except for a small absorbing window through which the particle can escape. We use the method of matched asymptotic expansions to calculate the mean first passage time, defined as the time taken for the Brownian particle to escape from the domain through the absorbing window. This is known as the narrow escape problem. Since the mean escape time diverges as the window shrinks, the calculation is a singular perturbation problem. We extend our results to include N absorbing windows of varying length in two dimensions and varying radius in three dimensions. We present findings in two dimensions for the unit disk, unit square and ellipse and in three dimensions for the unit sphere. The narrow escape problem has various applications in many fields including finance, biology, and statistical mechanics.

Name thesis:degree_name

Master of Science - MSc

Level thesis:degree_level

master's

Discipline thesis:degree_discipline

Mathematics

Grantor dc:publisher

University of British Columbia

Year dc:date

2008

Author dc:creator

• Pillay, Samara

Statement dc:rights

• Attribution-NonCommercial-NoDerivatives 4.0 International

Licence

• http://creativecommons.org/licenses/by-nc-nd/4.0/

Language dc:language

eng

Handle dc:identifier

http://hdl.handle.net/2429/1428

OAI identifier oai:identifier

oai:circle.library.ubc.ca:2429/1428