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Run-and-tumble particle with saturating rates.

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This study models a run-and-tumble particle with space-dependent rates that saturate at large distances. The research reveals unique particle behavior, including non-monotonic mean-squared displacement, differing from previous models.

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Area of Science:

  • Statistical Physics
  • Non-equilibrium Systems
  • Stochastic Processes

Background:

  • Run-and-tumble particle models are crucial for understanding biological and chemical transport.
  • Previous models often assumed unbounded rates, limiting real-world applicability.
  • Space-dependent rates introduce complex dynamics not fully explored.

Purpose of the Study:

  • To investigate the behavior of a run-and-tumble particle with space-dependent, saturating rates.
  • To analyze the steady-state distribution and mean-squared displacement under these conditions.
  • To compare findings with existing models and provide quantitative insights.

Main Methods:

  • Analytical treatment of a one-dimensional run-and-tumble model.
  • Derivation of the steady-state distribution for saturating rate functions.
  • Calculation of the mean-squared displacement.
  • Exact solution for a simplified step-function rate case.

Main Results:

  • Existence of a stationary state with exponentially decaying or faster steady-state distributions.
  • Unimodal or bimodal distribution shapes observed.
  • Non-monotonic or plateauing mean-squared displacement for particles starting far from the origin.
  • Consistency between numerical results and the exact solution of a limiting case.

Conclusions:

  • Saturating rates at large distances lead to distinct particle dynamics compared to unbounded rate models.
  • The boundedness of rates significantly impacts the approach to the stationary state.
  • The study provides a more physically realistic framework for run-and-tumble particle modeling.