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This study introduces a random search model with stochastic resetting and a partially accessible target. The research analytically derives the nonequilibrium stationary state and mean first passage time statistics for various configurations.

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Area of Science:

  • Physical Chemistry
  • Statistical Physics
  • Stochastic Processes

Background:

  • Standard search processes assume immediate target access upon contact.
  • This study considers a more realistic scenario with a partially accessible target.
  • Searchers require sequential diffusion and surface interaction periods before target entry.

Purpose of the Study:

  • To analyze a random search process with stochastic resetting and a partially accessible target.
  • To investigate the impact of a random waiting time on target access.
  • To derive analytical results for nonequilibrium stationary states and mean first passage times.

Main Methods:

  • Renewal theory is employed for analytical derivations.
  • The study considers configurations including the half-line and higher-dimensional geometries.
  • Non-Markovian absorption models are incorporated.

Main Results:

  • Analytical derivation of the nonequilibrium stationary state.
  • Calculation of mean first passage time statistics.
  • The model accounts for attachment, detachment, and target entry dynamics.

Conclusions:

  • The findings provide insights into search dynamics with delayed target access.
  • The analytical framework is applicable to various geometric configurations.
  • This work extends understanding of stochastic processes in partially reactive environments.