Narrow escape and leakage of Brownian particles

A. Singer, Z. Schuss, D. Holcman

Research output: Contribution to journalArticle

41 Scopus citations

Abstract

Questions of flux regulation in biological cells raise a renewed interest in the narrow escape problem. The determination of a higher order asymptotic expansion of the narrow escape time depends on determining the singularity behavior of the Neumann Green's function for the Laplacian in a three-dimensional (3D) domain with a Dirac mass on the boundary. In addition to the usual 3D Coulomb singularity, this Green's function also has an additional weaker logarithmic singularity. By calculating the coefficient of this logarithmic singularity, we calculate the second term in the asymptotic expansion of the narrow escape time and in the expansion of the principal eigenvalue of the Laplace equation with mixed Dirichlet-Neumann boundary conditions, with small Dirichlet and large Neumann parts. We also determine the leakage flux of Brownian particles that diffuse from a source to an absorbing target on a reflecting boundary of a domain, if a small perforation is made in the reflecting boundary.

Original languageEnglish (US)
Article number051111
JournalPhysical Review E - Statistical, Nonlinear, and Soft Matter Physics
Volume78
Issue number5
DOIs
StatePublished - Nov 14 2008

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Statistics and Probability
  • Condensed Matter Physics

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