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Distribution of randomly diffusing particles in inhomogeneous media.

Yiwei Li1, Osman Kahraman1, Christoph A Haselwandter1

  • 1Department of Physics & Astronomy and Molecular and Computational Biology Program, Department of Biological Sciences, University of Southern California, Los Angeles, California 90089, USA.

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Summary

This study introduces deterministic lattice equations (DLEs) to model particle diffusion in complex, inhomogeneous media. The DLEs accurately predict particle distribution, offering an efficient computational tool for understanding diffusion dynamics.

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Area of Science:

  • Physics
  • Physical Chemistry
  • Materials Science

Background:

  • Diffusion is fundamental to many physical and chemical processes.
  • Understanding diffusion in inhomogeneous media is crucial for predicting system behavior.
  • Existing models may lack computational efficiency or generality for complex systems.

Purpose of the Study:

  • To derive computationally efficient deterministic lattice equations (DLEs) for diffusion in inhomogeneous media.
  • To validate these DLEs against master equations (MEs) and kinetic Monte Carlo simulations.
  • To develop general analytic expressions for steady-state particle distributions.

Main Methods:

  • Derivation of DLEs from master equations (MEs) for diffusion in inhomogeneous media.
  • Consideration of both free (Fickian) diffusion and diffusion with steric constraints.
  • Comparison of DLE predictions with kinetic Monte Carlo simulations of MEs.

Main Results:

  • Excellent agreement was found between DLEs and simulations for both transient and asymptotic regimes.
  • DLEs offer a computationally efficient method, independent of particle number.
  • General analytic expressions for steady-state distributions were derived for free diffusion and specific cases of constrained diffusion.

Conclusions:

  • DLEs provide an efficient and accurate method for predicting particle distributions in inhomogeneous media.
  • Steady-state particle distribution depends on lattice sites, hopping rates, and particle species, not domain arrangement.
  • The study offers insights into how spatially varying hopping rates influence particle distributions.