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Kinetic Monte Carlo Algorithms for Active Matter Systems.

Juliane U Klamser1, Olivier Dauchot1, Julien Tailleur2

  • 1Gulliver UMR CNRS 7083, ESPCI Paris, Université PSL, 75005 Paris, France.

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Purely active steps in kinetic Monte Carlo simulations are ill-defined, causing active matter behaviors to vanish. Mixing passive and active steps in kinetic Monte Carlo algorithms creates well-defined limits for active particle dynamics.

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Area of Science:

  • Physics
  • Statistical Mechanics
  • Soft Matter

Background:

  • Kinetic Monte Carlo (KMC) methods are widely used to simulate complex systems.
  • Active matter, composed of self-propelled particles, exhibits unique collective behaviors.
  • Existing KMC models for active particles often struggle with theoretical limitations.

Purpose of the Study:

  • To investigate the continuous-time limit of KMC descriptions for active particles.
  • To identify issues arising from purely persistent active steps in KMC simulations.
  • To develop improved KMC algorithms for accurately capturing active matter dynamics.

Main Methods:

  • Analysis of the continuous-time limit of KMC processes.
  • Mathematical scaling of active and passive steps.
  • Development and proposal of new KMC algorithms.

Main Results:

  • Purely persistent active steps in KMC lead to ill-defined continuous-time limits.
  • This ill-defined limit causes the disappearance of key active matter phenomena like motility-induced phase separation and ratchet effects.
  • A modified approach mixing passive and active steps yields a well-defined, albeit different, continuous-time limit.
  • New KMC algorithms are proposed that correctly reproduce standard active particle dynamics.

Conclusions:

  • Standard KMC approaches with purely persistent active steps are inadequate for describing active matter.
  • A hybrid approach of mixing passive and active steps is crucial for a well-defined KMC continuous-time limit.
  • The proposed KMC algorithms offer a robust framework for simulating diverse active particle models.