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Universal Poisson statistics of a passive tracer diffusing in dilute active suspensions.

Adrian Baule1

  • 1School of Mathematical Sciences, Queen Mary University of London, London E1 4NS, United Kingdom.

Proceedings of the National Academy of Sciences of the United States of America
|December 4, 2023
PubMed
Summary

We derived the statistics of passive tracers in active particle suspensions. The study shows tracer behavior can be modeled by a Poisson process and two-body scattering, revealing universal dynamics independent of swimmer type.

Keywords:
active matternonequilibriumstatistical mechanicsstochastic processes

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Area of Science:

  • Physics
  • Statistical Mechanics
  • Soft Matter Physics

Background:

  • Understanding the behavior of passive tracers in complex fluids is crucial for various scientific disciplines.
  • Active particle suspensions, or 'swimmers,' introduce unique dynamic interactions not found in equilibrium systems.

Purpose of the Study:

  • To derive the statistical properties of a passive tracer within a suspension of active particles from fundamental principles.
  • To develop a theoretical framework that simplifies the complex multiparticle dynamics of tracer-swimmer interactions.

Main Methods:

  • A perturbative expansion of the tracer's interaction with the microscopic swimmer field was employed.
  • The analysis focused on the first-order approximation in swimmer density.
  • The tracer statistics were rigorously reduced to a combination of a spatial Poisson process and independent tracer-swimmer scattering events.

Main Results:

  • The tracer statistics are exactly represented by a spatial Poisson process and two-body scattering events, simplifying multiparticle dynamics.
  • This Poisson representation is valid across different dimensions, interaction forces, and various swimmer dynamics.
  • The study identified universal features in tracer statistics, such as a time-independent velocity distribution, independent of specific swimmer dynamics.

Conclusions:

  • The developed framework provides a systematic method for calculating tracer statistics in diverse dynamical regimes.
  • The findings reveal surprising universal behaviors in active matter systems, simplifying predictions and analysis.
  • This work offers a powerful tool for studying tracer dynamics in complex active suspensions.