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Controlled Synthesis and Fluorescence Tracking of Highly Uniform Poly(N-isopropylacrylamide) Microgels
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Microscopic theory of anomalous diffusion based on particle interactions.

James F Lutsko1, Jean Pierre Boon

  • 1Physics Department, Code Postal 231, Université Libre de Bruxelles, 1050 Bruxelles, Belgium.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|September 17, 2013
PubMed
Summary

This study introduces a new random walk model that unifies subdiffusion, classical diffusion, and superdiffusion. Interactions between walkers generate nonclassical diffusion, explained by attractive and repulsive forces.

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Area of Science:

  • Physics
  • Statistical Mechanics
  • Nonlinear Dynamics

Background:

  • Classical diffusion is described by Brownian motion and linear Fokker-Planck equations.
  • Nonclassical diffusion, including subdiffusion and superdiffusion, deviates from Brownian motion and requires advanced modeling.
  • Understanding the transition between different diffusion regimes is crucial for various scientific fields.

Purpose of the Study:

  • To develop a unified master equation model for subdiffusion, classical diffusion, and superdiffusion.
  • To investigate the role of inter-walker interactions in generating nonclassical diffusion.
  • To establish a connection between microscopic models and macroscopic nonlinear Fokker-Planck equations.

Main Methods:

  • Formulation of a master equation based on a Markovian random walk model.
  • Introduction of inter-walker interactions to generate nonclassical diffusive behavior.
  • Analytical derivation and numerical simulations of the nonlinear Fokker-Planck equation.

Main Results:

  • A single parameter in the master equation controls transitions between subdiffusion, classical diffusion, and superdiffusion.
  • The mean squared displacement exhibits anomalous scaling ~t(γ) with 0<γ≤1.5.
  • Self-similar scaling solutions were found for the nonlinear Fokker-Planck equation, consistent with simulations.

Conclusions:

  • The proposed model successfully unifies different diffusion regimes through inter-walker interactions.
  • Attractive and repulsive interactions provide a physical basis for sub- and superdiffusion.
  • The model offers a robust framework for studying anomalous diffusion phenomena.