Front propagation dynamics with exponentially-distributed hopping

Elisheva Cohen, David A. Kessler

Research output: Contribution to journalArticlepeer-review

3 Scopus citations

Abstract

We study reaction-diffusion systems where diffusion is by jumps whose sizes are distributed exponentially. We first study the Fisher-like problem of propagation of a front into an unstable state, as typified by the A+B → 2A reaction. We find that the effect of fluctuations is especially pronounced at small hopping rates. Fluctuations are treated heuristically via a density cutoff in the reaction rate. We then consider the case of propagating up a reaction rate gradient. The effect of fluctuations here is pronounced, with the front velocity increasing without limit with increasing bulk particle density. The rate of increase is faster than in the case of a reaction-gradient with nearest-neighbor hopping. We derive analytic expressions for the front velocity dependence on bulk particle density. Computer simulations are performed to confirm the analytical results.

Original languageEnglish
Pages (from-to)925-948
Number of pages24
JournalJournal of Statistical Physics
Volume122
Issue number5
DOIs
StatePublished - Mar 2006

Bibliographical note

Funding Information:
We acknowledge the support of the Israel Science Foundation. We thank Herbert Levine for useful discussions.

Keywords

  • Front propagation
  • Reaction-diffusion

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