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The Diffusion of Passive Tracers in Laminar Shear Flow
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Diffusion of multiple species with excluded-volume effects.

Maria Bruna1, S Jonathan Chapman

  • 1Mathematical Institute, University of Oxford, 24-29 St. Giles', Oxford OX1 3LB, United Kingdom. bruna@maths.ox.ac.uk

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This study models interacting species using stochastic diffusion with excluded-volume effects. It reveals how inter-species competition emerges in population dynamics, distinguishing collective and self-diffusion.

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Area of Science:

  • Statistical Physics
  • Mathematical Biology
  • Physical Chemistry

Background:

  • Stochastic models with excluded-volume effects are crucial for discrete-level modeling in biology and physics.
  • Continuum models using partial differential equations often describe average population properties.

Purpose of the Study:

  • To investigate inter-species competition emergence in multiple interacting subpopulations.
  • To establish a link between discrete stochastic equations of motion and continuum models.

Main Methods:

  • Utilized stochastic models of diffusion with excluded-volume effects.
  • Employed the method of matched asymptotic expansions to connect discrete and continuum models.
  • Simulated discrete systems to validate analytical results.

Main Results:

  • Developed a nonlinear cross-diffusion system for two interacting species.
  • Demonstrated how excluded-volume interactions enhance self-diffusion and diminish collective diffusion.
  • Showed good agreement between discrete simulations and analytical predictions.

Conclusions:

  • The derived cross-diffusion system accurately captures population-level inter-species competition.
  • The model clarifies the distinction between collective and self-diffusion coefficients.
  • Provides a robust framework for understanding diffusion in complex interacting systems.