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Active Brownian particles in a biased periodic potential.

Meng Su1, Benjamin Lindner2,3

  • 1School of Mathematics and Statistics, Northwestern Polytechnical University, 710129, Xi'an, Shaanxi, People's Republic of China. su_mengsm@163.com.

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This study explores the movement of active Brownian particles with Rayleigh-Helmholtz friction in a biased potential. We identified four distinct motion regimes, including locked and running states, and analyzed how noise affects particle velocity.

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Area of Science:

  • Statistical physics
  • Soft matter physics
  • Non-equilibrium systems

Background:

  • Active Brownian particles exhibit complex dynamics influenced by internal driving forces and external potentials.
  • Friction models, such as Rayleigh-Helmholtz, are crucial for understanding particle behavior in various environments.
  • Biased periodic potentials introduce directional forces that can lead to diverse transport phenomena.

Purpose of the Study:

  • To investigate the transport properties of an active Brownian particle with Rayleigh-Helmholtz friction in a biased periodic potential.
  • To map the parameter space of friction and bias force, identifying distinct dynamical regimes.
  • To analyze the influence of noise intensity on particle velocity across these regimes.

Main Methods:

  • Theoretical analysis of particle dynamics in the absence of noise.
  • Numerical simulations to explore behavior in the presence of noise.
  • Analytical estimations for limiting cases of noise intensity.

Main Results:

  • The particle's parameter plane (friction vs. bias force) is divided into four regions: exclusively locked, exclusively running, bistability between locked and running states, or bistability of two running states (left/right motion).
  • In the presence of noise, the mean velocity exhibits distinct dependencies on noise intensity within each identified regime.
  • Both locked and running states, as well as transitions between them, are observed and characterized.

Conclusions:

  • The interplay between Rayleigh-Helmholtz friction, bias force, and noise dictates the complex transport properties of active Brownian particles.
  • Understanding these distinct dynamical regimes is crucial for controlling and predicting particle motion in non-equilibrium systems.
  • The study provides a comprehensive phase diagram of particle behavior, offering insights into directed transport mechanisms.