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Swarming Transition in Super-Diffusive Self-Propelled Particles.

Morteza Nattagh Najafi1, Rafe Md Abu Zayed1, Seyed Amin Nabavizadeh1

  • 1Department of Mechanical Engineering, University of Akron, Akron, OH 44325, USA.

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Summary

This study introduces a super-diffusive Vicsek model with Levy flights, enhancing disorder and altering phase transitions. Critical exponents remain constant, but fractal dimensions and critical exponents vary with Levy flight behavior.

Keywords:
Levy flightscritical exponentssecond-order phase transitionsuper-diffusive Vicsek model

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Area of Science:

  • Statistical Physics
  • Complex Systems
  • Non-equilibrium Dynamics

Background:

  • The Vicsek model is a fundamental framework for studying self-propelled particles and emergent order.
  • Understanding the impact of anomalous diffusion on collective behavior is crucial in complex systems.

Purpose of the Study:

  • To investigate the effects of Levy flights on the Vicsek model's phase transitions and critical phenomena.
  • To analyze how anomalous diffusion influences order parameter fluctuations and cluster formation.

Main Methods:

  • Introduction of Levy flights with exponent α into the Vicsek model.
  • Formulation of a mean-field theory based on swarmed cluster growth.
  • Conducting simulations to analyze critical exponents and fractal dimensions.

Main Results:

  • Levy flights increase order parameter fluctuations, favoring the disorder phase as α increases.
  • The order-disorder transition shifts from first-order (α near 2) to second-order-like (small α).
  • Critical exponents (β, ν, γ) and fractal dimensions remain constant under certain conditions, but vary with α.

Conclusions:

  • The super-diffusive Vicsek model with Levy flights exhibits rich phase transition behavior.
  • The study connects the model's fractal properties to the 2D Potts (Ising) model.
  • Anomalous diffusion significantly alters critical phenomena and scaling in active matter systems.