Journal of Statistical Physics

, Volume 34, Issue 1–2, pp 225–238 | Cite as

Localized partial traps in diffusion processes and random walks

  • Attila Szabo
  • Gene Lamm
  • George H. Weiss
Articles

Abstract

Reaction-diffusion equations, in which the reaction is described by a sink term consisting of a sum of delta functions, are studied. It is shown that the Laplace transform of the reactive Green's function can be analytically expressed in terms of the Green's function for diffusion in the absence of reaction. Moreover, a simple relation between the Green's functions satisfying the radiation boundary condition and the reflecting boundary condition is obtained. Several applications are presented and the formalism is used to establish the relationship between the time-dependent geminate recombination yield and the bimolecular reaction rate for diffusion-influenced reactions. Finally, an analogous development for lattice random walks is presented.

Key words

Diffusion-controlled reactions first passage times radiation boundary conditions Green's functions recombination rates rate constants 

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Copyright information

© Plenum Publishing Corporation 1984

Authors and Affiliations

  • Attila Szabo
    • 1
  • Gene Lamm
    • 1
  • George H. Weiss
    • 2
  1. 1.Laboratory of Chemical PhysicsNational Institute of Arthritis, Diabetes, and Digestive and Kidney DiseasesUSA
  2. 2.Physical Sciences Laboratory, Division of Computer Research and TechnologyNational Institutes of HealthBethesda

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