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A continuous-time persistent random walk model for flocking.

Daniel Escaff1, Raúl Toral2, Christian Van den Broeck3

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This summary is machine-generated.

This study models active particles using persistent random walkers. Introducing interactions reveals transitions to flocking, clustering, and complex spatial structures, confirmed by simulations.

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Area of Science:

  • Physics
  • Complex Systems
  • Statistical Mechanics

Background:

  • Classical random walkers, like those modeling Brownian motion, describe inanimate particles influenced by environmental fluctuations.
  • Persistent random walkers, characterized by constant speed and random direction changes, model self-propelled entities such as living organisms and synthetic materials.

Purpose of the Study:

  • To model active particles using persistent random walkers.
  • To investigate the effects of particle interactions on collective behavior.
  • To analyze transitions to flocking and complex spatial structures.

Main Methods:

  • Developed a model for interacting persistent random walkers.
  • Employed mean-field strategies, including all-to-all interaction and advection-reaction equations.
  • Validated model predictions through direct numerical simulations of particle ensembles.

Main Results:

  • Identified a transition to flocking, where particles exhibit collective directional motion.
  • Observed secondary transitions leading to clustering and more complex spatially structured states.
  • Analyzed these transitions using bifurcation theory.

Conclusions:

  • Interacting persistent random walkers can exhibit rich collective behaviors, including flocking and complex spatial organization.
  • Mean-field theories and numerical simulations provide effective tools for analyzing these active matter systems.
  • The model offers insights into the emergence of order in systems of self-propelled particles.