Local accumulation times for source, diffusion, and degradation models in two and three dimensions

Peter V. Gordon, Cyrill B. Muratov, Stanislav Y. Shvartsman

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16 Scopus citations

Abstract

We analyze the transient dynamics leading to the establishment of a steady state in reaction-diffusion problems that model several important processes in cell and developmental biology and account for the diffusion and degradation of locally produced chemical species. We derive expressions for the local accumulation time, a convenient characterization of the time scale of the transient at a given location, in two- and three-dimensional systems with first-order degradation kinetics, and analyze their dependence on the model parameters. We also study the relevance of the local accumulation time as a single measure of timing for the transient and demonstrate that, while it may be sufficient for describing the local concentration dynamics far from the source, a more delicate multi-scale description of the transient is needed near a tightly localized source in two and three dimensions.

Original languageEnglish (US)
Article number104121
JournalJournal of Chemical Physics
Volume138
Issue number10
DOIs
StatePublished - Mar 14 2013

All Science Journal Classification (ASJC) codes

  • Physics and Astronomy(all)
  • Physical and Theoretical Chemistry

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