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Derek Frydel1

  • 1Department of Chemistry, Universidad Técnica Federico Santa María, Campus San Joaquin, Santiago, Chile.

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Summary
This summary is machine-generated.

This study extends the Kuramoto model to include run-and-tumble dynamics, allowing particle angular velocity to change. This provides a framework for understanding phase transitions in self-propelled particle systems.

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Area of Science:

  • Statistical Physics
  • Complex Systems
  • Nonlinear Dynamics

Background:

  • The Kuramoto model is a foundational model for studying synchronization in coupled oscillator systems.
  • Self-propelled particles exhibit unique collective behaviors not captured by traditional models.
  • Understanding phase transitions in active matter is crucial for diverse fields.

Purpose of the Study:

  • To introduce and analyze an extended Kuramoto model incorporating run-and-tumble dynamics.
  • To investigate how variable angular velocity affects collective behavior and phase transitions.
  • To establish a simplified model for studying phase transitions in self-propelled particle systems.

Main Methods:

  • Modification of the standard Kuramoto model to include stochastic changes in angular velocity.
  • Analysis of the system's dynamics, focusing on phase transitions.
  • Mathematical modeling and simulation of self-propelled particles with run-and-tumble motion.

Main Results:

  • The extended model demonstrates rich collective dynamics due to intermittent velocity changes.
  • Phase transition phenomena are observed and characterized within this extended framework.
  • The model provides insights into the role of motility in emergent order.

Conclusions:

  • The extended Kuramoto model with run-and-tumble dynamics offers a valuable platform for studying active matter.
  • Variable particle velocity significantly influences collective synchronization and phase transition properties.
  • This work bridges concepts from synchronization theory and self-propelled particle dynamics.