SINGULAR PERTURBATION APPROACH TO KRAMER'S DIFFUSION PROBLEM.

B. J. Matkowsky; Z. Schuss; E. Ben-Jacobs

doi:10.1137/0142058

SINGULAR PERTURBATION APPROACH TO KRAMER'S DIFFUSION PROBLEM.

B. J. Matkowsky^*, Z. Schuss, E. Ben-Jacobs

^*Corresponding author for this work

Engineering Sciences and Applied Mathematics

Research output: Contribution to journal › Article › peer-review

87 Scopus citations

Abstract

This study considers Kramers' diffusion problem, which seeks to calculate the rate of escape of a particle from one potential well over a barrier, to another presumably deeper and therefore more stable well. A new approach, based on the solution of a singularly perturbed boundary value problem is proposed. The rate of escape is related to the first passage time from the domain of attraction of the stable point corresponding to the first well. The first passage time is then characterized via the Ito calculus, as a solution of an elliptic partial differential equation of singular perturbation type. Finally this equation is solved asymptotically.

Original language	English (US)
Pages (from-to)	835-849
Number of pages	15
Journal	SIAM Journal on Applied Mathematics
Volume	42
Issue number	4
DOIs	https://doi.org/10.1137/0142058
State	Published - Jan 1 1982

ASJC Scopus subject areas

Applied Mathematics

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abstract = "This study considers Kramers' diffusion problem, which seeks to calculate the rate of escape of a particle from one potential well over a barrier, to another presumably deeper and therefore more stable well. A new approach, based on the solution of a singularly perturbed boundary value problem is proposed. The rate of escape is related to the first passage time from the domain of attraction of the stable point corresponding to the first well. The first passage time is then characterized via the Ito calculus, as a solution of an elliptic partial differential equation of singular perturbation type. Finally this equation is solved asymptotically.",

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AB - This study considers Kramers' diffusion problem, which seeks to calculate the rate of escape of a particle from one potential well over a barrier, to another presumably deeper and therefore more stable well. A new approach, based on the solution of a singularly perturbed boundary value problem is proposed. The rate of escape is related to the first passage time from the domain of attraction of the stable point corresponding to the first well. The first passage time is then characterized via the Ito calculus, as a solution of an elliptic partial differential equation of singular perturbation type. Finally this equation is solved asymptotically.

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SINGULAR PERTURBATION APPROACH TO KRAMER'S DIFFUSION PROBLEM.

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