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Exploring run-and-tumble movement in confined settings through simulation.

Dario Javier Zamora1,2, Roberto Artuso1,3

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Area of Science:

  • Physics
  • Mathematical Biology
  • Statistical Mechanics

Background:

  • Motion in bounded domains is key in fields like billiard dynamics and random walks.
  • The Mean Path Length Theorem (MPLT) describes universal properties of particle return times to boundaries.

Purpose of the Study:

  • Investigate deviations from the MPLT in confined systems.
  • Analyze run-and-tumble particle dynamics in a 2D circular domain.
  • Understand the impact of boundary interactions and angular dynamics.

Main Methods:

  • Theoretical modeling of particle motion.
  • Numerical simulations of particle trajectories.
  • Validation of the Mean Path Length Theorem (MPLT).

Main Results:

  • MPLT is validated for uniform, isotropic particle inflow.
  • Deviations from MPLT observed with non-uniform angular distributions.
  • Non-elastic boundary conditions and memory processes also cause deviations.

Conclusions:

  • Boundary interactions and angular dynamics significantly influence confined particle motion.
  • MPLT is broadly applicable but sensitive to specific conditions.
  • Insights applicable to diverse phenomena from bacterial motion to neutron transport.