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Continuous Measurement of Biological Noise in Escherichia Coli Using Time-lapse Microscopy
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Diffusion with stochastic resetting.

Martin R Evans1, Satya N Majumdar

  • 1SUPA, School of Physics and Astronomy, University of Edinburgh, Edinburgh, United Kingdom.

Physical Review Letters
|May 24, 2011
PubMed
Summary
This summary is machine-generated.

Simple diffusion with resetting creates a nonequilibrium state and non-Gaussian fluctuations. An optimal resetting rate minimizes search time, and resetting alters target survival probability decay in multi-searcher scenarios.

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Area of Science:

  • Statistical Physics
  • Non-equilibrium Systems
  • Stochastic Processes

Background:

  • Simple diffusion is a fundamental process in physics and biology.
  • Nonequilibrium systems exhibit unique statistical properties.
  • Stochastic resetting introduces non-trivial dynamics to diffusive processes.

Purpose of the Study:

  • To investigate the effects of stochastic resetting on particle diffusion.
  • To analyze the emergence of non-Gaussian fluctuations and non-equilibrium steady states.
  • To determine the impact of resetting on target search efficiency and survival probability.

Main Methods:

  • Theoretical analysis of stochastic differential equations.
  • Calculation of probability distributions and statistical moments.
  • Investigation of mean first passage times and survival probabilities.

Main Results:

  • A finite resetting rate induces a non-equilibrium stationary state with non-Gaussian position fluctuations.
  • The mean search time for a stationary target exhibits a minimum at an optimal resetting rate.
  • Resetting fundamentally changes the late-time decay of target survival probability in multi-searcher systems, transitioning from exponential to power-law decay.

Conclusions:

  • Stochastic resetting is a crucial factor in modifying diffusive dynamics.
  • Optimal resetting rates can enhance search efficiency in physical and biological systems.
  • The collective behavior of resetting searchers leads to distinct statistical properties compared to individual searchers.