EXIT PROBLEM

A NEW APPROACH TO DIFFUSION ACROSS POTENTIAL BARRIERS.

Zeev Schuss*, Bernard J. Matkowsky

*Corresponding author for this work

Research output: Contribution to journalArticle

79 Citations (Scopus)

Abstract

The problem is considered of a Brownian particle confined in a potential well of forces, which escapes the potential barrier as the result of white noise forces acting on it. The problem is characterized by a diffusion process in a force field and is described by Langevin's stochastic differential equation. Potential wells with many transition states are considered and the expected exit time of the particle from the well as well as the probability distribution of the exit points are computed. The method relates these quantities to the solutions of certain singularly perturbed elliptic boundary value problems which are solved asymptotically. The results are then applied to the calculation of chemical reaction rates by considering the breaking of chemical bonds caused by random molecular collisions, and to the calculation of the diffusion matrix in crystals by considering random atomic migration in the periodic force field of the crystal lattice, caused by thermal vibrations of the lattice.

Original languageEnglish (US)
Pages (from-to)604-623
Number of pages20
JournalSIAM J Appl Math
Volume36
Issue number3
DOIs
StatePublished - Jan 1 1979

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Exit Problem
Potential Well
Force Field
Crystal lattices
Crystal
Exit Time
Singularly Perturbed Boundary Value Problem
Transition State
Chemical bonds
Elliptic Boundary Value Problems
Reaction Rate
White noise
Chemical Reaction
Diffusion Process
Probability distributions
Boundary value problems
Reaction rates
Migration
Stochastic Equations
Chemical reactions

ASJC Scopus subject areas

  • Applied Mathematics

Cite this

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abstract = "The problem is considered of a Brownian particle confined in a potential well of forces, which escapes the potential barrier as the result of white noise forces acting on it. The problem is characterized by a diffusion process in a force field and is described by Langevin's stochastic differential equation. Potential wells with many transition states are considered and the expected exit time of the particle from the well as well as the probability distribution of the exit points are computed. The method relates these quantities to the solutions of certain singularly perturbed elliptic boundary value problems which are solved asymptotically. The results are then applied to the calculation of chemical reaction rates by considering the breaking of chemical bonds caused by random molecular collisions, and to the calculation of the diffusion matrix in crystals by considering random atomic migration in the periodic force field of the crystal lattice, caused by thermal vibrations of the lattice.",
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EXIT PROBLEM : A NEW APPROACH TO DIFFUSION ACROSS POTENTIAL BARRIERS. / Schuss, Zeev; Matkowsky, Bernard J.

In: SIAM J Appl Math, Vol. 36, No. 3, 01.01.1979, p. 604-623.

Research output: Contribution to journalArticle

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