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Particle-environment interactions in arbitrary dimensions: A unifying analytic framework to model diffusion with

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We developed a general analytic theory to model particle movement in disordered environments. Our framework captures complex interactions and reveals a surprising "disorder indifference" phenomenon in certain systems.

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Area of Science:

  • Physics
  • Biophysics
  • Computational Science

Background:

  • Particle movement in disordered systems is crucial across disciplines.
  • Existing models lack a general framework for spatial heterogeneities.
  • Modeling inert interactions requires accounting for environmental complexity.

Purpose of the Study:

  • Develop a general analytic theory for inert particle-environment interactions.
  • Model movement in arbitrary domains with spatial disorder.
  • Provide exact expressions for transport quantities.

Main Methods:

  • Discrete space formulation for agent-environment interactions.
  • Modeling spatial disorder (obstacles, diffusivity variations).
  • Deriving generating functions for occupation probability and transport metrics.

Main Results:

  • Exact expressions for first-passage, return, and exit probabilities.
  • Discovery of "disorder indifference" in mean first-passage time with permeable barriers in quasi-1D systems.
  • Demonstrated applicability across drug delivery, animal behavior, and gene transcription.

Conclusions:

  • The developed theory offers a unified approach to modeling diffusion in heterogeneous environments.
  • The "disorder indifference" phenomenon presents novel insights into transport dynamics.
  • The framework has broad applications in diverse scientific fields.