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Related Concept Videos

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Related Experiment Video

Updated: Nov 5, 2025

Methods for Measuring the Orientation and Rotation Rate of 3D-printed Particles in Turbulence
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Local time for run and tumble particle.

Prashant Singh1, Anupam Kundu1

  • 1International Centre for Theoretical Sciences, Tata Institute of Fundamental Research, Bengaluru 560089, India.

Physical Review. E
|May 19, 2021
PubMed
Summary

We analyzed the local time statistics for a run and tumble particle (RTP) model, crucial for understanding bacterial motion. Our findings reveal how position-dependent rates affect particle revisit probabilities and temporal fluctuations.

Area of Science:

  • Statistical Physics
  • Biophysics
  • Stochastic Processes

Background:

  • The run and tumble particle (RTP) model is a fundamental representation of bacterial motion.
  • Existing research often treats RTP dynamics as persistent Brownian motion.
  • This study explores an inhomogeneous version of the RTP model with position-dependent rates.

Purpose of the Study:

  • To investigate the local time statistics of a one-dimensional run and tumble particle (RTP).
  • To analyze the impact of position-dependent rates on RTP dynamics.
  • To determine the probability distribution and scaling behavior of local time.

Main Methods:

  • Analytical derivation of the probability distribution for local time (Tloc) when the rate parameter α=0.
  • Mathematical analysis to determine the scaling behavior of Tloc fluctuations for general α.

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  • Numerical simulations to validate analytical findings for both exact and scaled distributions.

    • Main Results:

    • For α=0, the exact probability distribution of Tloc was derived, revealing insights into particle revisits to the origin.
    • For general α, typical Tloc fluctuations scale as Tloc∼t^{1+α/2+α} for large times.
    • The probability distribution of Tloc exhibits a universal scaling behavior, analytically computed.

    Conclusions:

    • The study provides a comprehensive analytical framework for understanding local time statistics in inhomogeneous RTP models.
    • The derived scaling laws and probability distributions offer valuable insights into bacterial motility and stochastic processes.
    • Analytical results are robustly supported by numerical simulations, confirming the model's predictive power.