Interfacing at the Stochastic Separatrix

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Abstract

This chapter introduces the concept of the stochastic separatrix and elaborates its application in clarifying the notion of transitions between relatively long-lived states and short-lived transition states. These may be noise-induced transitions over high barriers or the squeezing of Brownian motion through narrow necks connecting relatively large confining compartments. The stochastic separatrix plays a role in determining the dependence of the first nonzero eigenvalue of the Fokker–Planck operator (FPO) on the geometry of the drift field and on the geometry of the domain.

Original languageEnglish
Title of host publicationApplied Mathematical Sciences (Switzerland)
PublisherSpringer
Pages165-197
Number of pages33
DOIs
StatePublished - 2013

Publication series

NameApplied Mathematical Sciences (Switzerland)
Volume186
ISSN (Print)0066-5452
ISSN (Electronic)2196-968X

Keywords

  • Bistable System
  • Planck Equation
  • Principal Eigenvalue
  • Saddle Point
  • Transition State Theory

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