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First-encounter time of two diffusing particles in two- and three-dimensional confinement.

F Le Vot1, S B Yuste1, E Abad2

  • 1Departamento de Física and Instituto de Computación Científica Avanzada (ICCAEx), Universidad de Extremadura, E-06071 Badajoz, Spain.

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Summary
This summary is machine-generated.

Confinement drastically alters diffusing particle encounter times. Monte Carlo simulations reveal survival probability and first-encounter time dynamics in confined 2D/3D spaces, offering insights into particle interactions.

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Area of Science:

  • Statistical Physics
  • Computational Physics
  • Physical Chemistry

Background:

  • Particle diffusion behavior is significantly altered by confinement effects.
  • Understanding first-encounter time statistics is crucial for various physical and chemical processes.

Purpose of the Study:

  • To investigate the impact of reflecting boundaries on the first-encounter time statistics of a two-particle system.
  • To analyze survival probability S(t) and first-encounter time probability density H(t) in confined domains.

Main Methods:

  • Utilized Monte Carlo simulations to model a two-particle system in 2D and 3D domains with reflecting boundaries.
  • Analyzed survival probability S(t), first-encounter time density H(t), mean first-encounter time , and decay time T.

Main Results:

  • Derived empirical formulas for and T, and an empirical lower bound tB for boundary deviation.
  • Found that for small particles, is dominated by total diffusivity (D=D1+D2), unlike in 1D.
  • Identified weak dependence of subleading contributions to T on diffusivity ratio (D1/D2) in 2D.

Conclusions:

  • Confinement significantly modifies first-encounter time statistics, with boundary effects becoming prominent over time.
  • The dominant contribution to decay time T is linked to total diffusivity, offering a simplified model for confined systems.
  • Provided insights into approximating mean first-encounter time with decay time T under specific conditions.