Reduced dynamics of stochastically perturbed gradient flows

Ibrahim Fatkullin, Gregor Kovačič, Eric Vanden Eijnden

Research output: Contribution to journalArticle

Abstract

We consider stochastically perturbed gradient flows in the limit when the amplitude of random fluctuations is small relative to the typical energy scale in the system and the minima of the energy are not isolated but form submanifolds of the phase space. In this case the limiting dynamics may be described in terms of a diffusion process on these manifolds. We derive explicit equations for this limiting dynamics and illustrate them on a few finite-dimensional examples. Finally, we formally extrapolate the reduction technique to several infinite-dimensional examples and derive equations of the stochastic kink motion in Allen-Cahn-type systems.

Original languageEnglish (US)
Pages (from-to)439-461
Number of pages23
JournalCommunications in Mathematical Sciences
Volume8
Issue number2
StatePublished - Jun 2010

Fingerprint

Gradient Flow
Limiting
Extrapolate
Kink
Energy
Type Systems
Diffusion Process
Submanifolds
Phase Space
Fluctuations
Motion
Form

Keywords

  • Kinks
  • Reduced dynamics
  • Stochastic Allen-Cahn
  • Stochastic gradient flows

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

Cite this

Reduced dynamics of stochastically perturbed gradient flows. / Fatkullin, Ibrahim; Kovačič, Gregor; Eijnden, Eric Vanden.

In: Communications in Mathematical Sciences, Vol. 8, No. 2, 06.2010, p. 439-461.

Research output: Contribution to journalArticle

Fatkullin, Ibrahim ; Kovačič, Gregor ; Eijnden, Eric Vanden. / Reduced dynamics of stochastically perturbed gradient flows. In: Communications in Mathematical Sciences. 2010 ; Vol. 8, No. 2. pp. 439-461.
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