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Two-dimensional active motion.

Francisco J Sevilla1

  • 1Instituto de Física, Universidad Nacional Autónoma de México, Apdo. Postal 20-364, 01000, Ciudad de México, México.

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Summary
This summary is machine-generated.

This study analyzes the 2D diffusion of active particles with arbitrary motility patterns. We derive analytical expressions for particle position probability, revealing a connection to generalized diffusion equations.

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Area of Science:

  • Physics
  • Statistical Mechanics
  • Soft Matter Physics

Background:

  • Active particles exhibit complex motion beyond simple diffusion.
  • Understanding their collective behavior is crucial in fields like biophysics and materials science.
  • Existing models often simplify particle motility patterns.

Purpose of the Study:

  • To develop a generalized Fokker-Planck equation for active particle diffusion in 2D.
  • To derive exact analytical expressions for particle position probability density.
  • To investigate the influence of arbitrary motility patterns on diffusion dynamics.

Main Methods:

  • Generalization of the Fokker-Planck equation to include arbitrary scattering angle distributions.
  • Derivation of analytical expressions for marginal probability density.
  • Calculation of time-dependent mean-square displacement and kurtosis.
  • Focus on the intermediate-time regime to highlight motility pattern effects.

Main Results:

  • An exact analytical expression for the marginal probability density was obtained.
  • A connection between active particle diffusion and a generalized diffusion equation was established.
  • Analytical expressions for the time evolution of mean-square displacement and kurtosis were derived.
  • It was shown that only the first two harmonics of the scattering angle distribution are necessary for analysis.

Conclusions:

  • The study provides a comprehensive analytical framework for 2D active particle diffusion.
  • The derived expressions offer insights into how motility patterns influence particle spreading.
  • The findings are applicable to systems with persistent or circular motion, enhancing understanding of active matter dynamics.