Random walk in a quasicontinuum

Charles R. Doering*, Patrick S. Hagan, Philip Rosenau

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

A continuous-time random walk on a spatial lattice described by the Kramers-Moyal expansion has a continuum limit described by a Fokker-Planck equation. It is often desirable to know corrections to quantities computed in the continuum limit, but truncation of the Kramers-Moyal expansion at any level other than the Fokker-Planck either breaks down or yields unphysical results. Here we introduce an alternative approximation to the Kramers-Moyal expansion which circumvents the problems of a naive truncation and correctly incorporates the first-order corrections due to the discrete lattice.

Original languageEnglish
Pages (from-to)985-988
Number of pages4
JournalPhysical Review A
Volume36
Issue number2
DOIs
StatePublished - 1987
Externally publishedYes

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