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On the reaction-diffusion type modelling of the self-propelled object motion.

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Area of Science:

  • Mathematical Physics
  • Soft Matter Physics
  • Fluid Dynamics

Background:

  • Self-propelled objects exhibit complex behaviors in various physical systems.
  • Existing models often struggle to unify deformable and solid object dynamics.
  • Phase-field models offer a versatile framework for describing evolving interfaces.

Purpose of the Study:

  • To develop a unified mathematical model for self-propelled objects capable of shape change.
  • To integrate phase-field dynamics with surfactant concentration for controlled motion.
  • To establish a connection between the phase-field model and established free boundary models.

Main Methods:

  • Utilizing an Allen-Cahn type phase-field equation.
  • Incorporating an equation for surfactant concentration.
  • Analyzing the singular limit to derive a free boundary model.

Main Results:

  • A novel phase-field model capable of simulating both deformable (droplets) and solid (camphor disks) self-propelled objects.
  • Demonstration of shape change capabilities by controlling a single model parameter.
  • Equivalence shown between the phase-field model and a variational free boundary model.

Conclusions:

  • The proposed phase-field model provides a unified framework for studying diverse self-propelled objects.
  • The model offers a physically interpretable approach to self-propulsion and shape dynamics.
  • This work bridges phase-field methods and free boundary dynamics in active matter research.