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Residence times of branching diffusion processes.

E Dumonteil1, A Mazzolo2

  • 1IRSN, Nuclear Safety Division, 31 Avenue de la Division Leclerc, 92260 Fontenay-aux-Roses, France.

Physical Review. E
|August 31, 2016
PubMed
Summary

We derived equations for the residence time and its moments for branching diffusion processes. This method helps understand how branching affects particle behavior over time in various environments.

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Area of Science:

  • * Mathematical Physics
  • * Stochastic Processes
  • * Computational Biology

Background:

  • * Branching Brownian motion models particle systems with reproduction.
  • * Residence time quantifies particle presence within a defined space.
  • * Understanding particle behavior is crucial in fields like biology and physics.

Purpose of the Study:

  • * To derive the residence-time equation for branching diffusion processes.
  • * To obtain equations for the moments of residence time.
  • * To analyze the influence of branching mechanisms on particle behavior.

Main Methods:

  • * Application of the Feynman-Kac formalism.
  • * Derivation of general equations for residence time and its moments.
  • * Analysis of branching diffusion with arbitrary numbers of descendants.

Main Results:

  • * Explicit formulas for moments in the long-time limit were obtained.
  • * The influence of the branching mechanism on moments was detailed.
  • * The approach was demonstrated in free space and confined geometries.

Conclusions:

  • * The Feynman-Kac formalism provides a robust method for analyzing branching diffusion.
  • * The study offers insights into the long-time behavior of particle systems.
  • * The methodology can be extended to other additive functionals of branching processes.