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This study analyzes random searches with position resetting in environments with varying diffusivity. We derived analytical expressions for mean first-passage time, showing how heterogeneity affects search efficiency.

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Area of Science:

  • Statistical Physics
  • Stochastic Processes
  • Physical Chemistry

Background:

  • Random searches are fundamental in various natural and artificial processes.
  • Position resetting can enhance search efficiency but is sensitive to environmental conditions.
  • Space-dependent diffusivity introduces complexity to stochastic dynamics.

Purpose of the Study:

  • To derive analytical expressions for mean first-passage time in bounded 1D environments with space-dependent diffusivity and stochastic resetting.
  • To investigate the impact of different diffusivity profiles and stochastic process prescriptions on search efficiency.
  • To explore the effectiveness of resetting strategies under diffusive heterogeneity.

Main Methods:

  • Derivation of analytical expressions for mean first-passage time (T).
  • Utilizing stochastic simulations for validation.
  • Analysis of Stratonovich, Itô, and anti-Itô stochastic calculus prescriptions.
  • Development of asymptotic approximations for varying resetting rates (r).

Main Results:

  • Exact closed-form expressions for mean first-passage time (T) were obtained for arbitrary diffusivity profiles D(x) under the Stratonovich scenario.
  • Asymptotic approximations for T were derived for Itô and anti-Itô prescriptions for small and large resetting rates (r).
  • Exact results for linear diffusivity D(x) allowed detailed discussion of heterogeneity effects.

Conclusions:

  • Diffusive heterogeneity significantly influences the effectiveness of random searches with resetting.
  • The choice of stochastic calculus prescription impacts the derived analytical results.
  • Resetting strategies can be optimized by considering the specific characteristics of the heterogeneous environment.