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Splitting probabilities and interfacial territory covered by two-dimensional and three-dimensional surface-mediated

T Calandre1, O Bénichou1, D S Grebenkov2

  • 1Laboratoire de Physique Théorique de la Matière Condensée (UMR 7600), CNRS/UPMC, 4 Place Jussieu, 75255 Paris Cedex, France.

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Summary
This summary is machine-generated.

We calculated the mean territory covered by particles undergoing surface-mediated diffusion within spherical domains before they exit. This territory is linked to the particle

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Area of Science:

  • Physics
  • Physical Chemistry

Background:

  • Surface-mediated diffusion is crucial in various physical and biological processes.
  • Understanding particle behavior in confined geometries is essential for nanoscale applications.

Purpose of the Study:

  • To determine the mean territory covered by a particle diffusing on a surface within a spherical domain before exiting.
  • To establish a relationship between covered territory and splitting probabilities.

Main Methods:

  • Derivation of a general formula connecting splitting probability to mean first passage time.
  • Analysis of the formula for pointlike and extended targets.
  • Mathematical modeling of diffusion in 2D and 3D spherical domains.

Main Results:

  • A novel formula relating mean covered territory to splitting probabilities was derived.
  • The formula is exact for point targets and accurate for extended targets.
  • Mean territory was analyzed for varying exit region sizes in spherical domains.

Conclusions:

  • The study provides a theoretical framework for quantifying diffusion-driven territory coverage.
  • The findings are applicable to systems involving surface diffusion in confined spaces.
  • This work advances the understanding of particle dynamics in spherical geometries.