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Generalized model for dynamic percolation

Benichou1, Klafter, Moreau

  • 1Laboratoire de Physique Theorique et Modeles Statistiques, Universite Paris-Sud, 91405 Orsay Cedex, France and Laboratoire de Physique Theorique des Liquides, Universite Paris 6, 4, Place Jussieu, 75252 Paris, France.

Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics
|November 23, 2000
PubMed
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This study investigates carrier motion in a dynamic, percolating environment. The carrier

Area of Science:

  • Statistical Physics
  • Complex Systems
  • Condensed Matter Physics

Background:

  • Understanding particle dynamics in complex environments is crucial for various scientific fields.
  • Dynamic percolation models offer a framework to study systems with evolving connectivity.
  • Carrier motion in disordered media presents unique challenges in predicting transport properties.

Purpose of the Study:

  • To investigate the biased motion of a carrier within a dynamic percolation environment.
  • To determine the terminal velocity and density profiles of environment particles relative to the carrier.
  • To derive an analog Stokes formula and friction coefficient for this system.

Main Methods:

  • Simulating a carrier's biased motion under an external field.

Related Experiment Videos

  • Modeling the environment using dynamic percolation with hard-core particles.
  • Analyzing particle density profiles and calculating terminal velocity.
  • Deriving theoretical relationships for viscous-like behavior and friction.

    • Main Results:

    • The carrier's terminal velocity V(c) was calculated as a function of the applied field and system parameters.
    • For small driving forces, the environment exerts a viscous-like force on the carrier.
    • An analog Stokes formula and friction coefficient were derived for dynamic percolative environments.
    • A significant inhomogeneity in environment particle density was observed: higher density ahead of the carrier and lower density behind it.

    Conclusions:

    • The study provides insights into carrier transport in dynamic, disordered environments.
    • The derived Stokes-like formula offers a new tool for analyzing friction in such systems.
    • The inhomogeneous density profile highlights the complex interactions between the carrier and its environment.