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This study analyzes random search efficiency in environments with varying diffusion rates. It reveals that search efficiency depends on diffusion interpretations and spatial distribution, with heterogeneous profiles potentially reducing efficiency.

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Area of Science:

  • Statistical Physics
  • Stochastic Processes
  • Physical Chemistry

Background:

  • Random search is crucial in various scientific fields.
  • Understanding search efficiency in heterogeneous environments is challenging.
  • Diffusion processes are often modeled using stochastic differential equations.

Purpose of the Study:

  • To analyze first-passage-time distributions and search efficiency in environments with space-dependent diffusion coefficients.
  • To investigate the impact of different stochastic process interpretations (Itô, Stratonovich, Hänggi-Klimontovich) on search efficiency.
  • To derive a general expression for search efficiency in power-law diffusion scenarios.

Main Methods:

  • Analysis of first-passage-time distributions for stochastic processes.
  • Computation of search efficiency (E = <1/t>) using derived distributions.
  • Derivation of closed-form expressions for search efficiency under different diffusion interpretations.

Main Results:

  • A general framework for analyzing random search with space-dependent diffusion coefficients is presented.
  • The Stratonovich interpretation yields a closed-form expression for search efficiency, dependent only on diffusivity distribution.
  • Heterogeneous diffusivity profiles generally reduce search efficiency compared to homogeneous ones with the same average.

Conclusions:

  • The interpretation of the stochastic process significantly impacts random search efficiency.
  • Spatial organization of diffusion coefficients plays a role, but its influence varies with interpretation.
  • The study provides insights into optimizing search strategies in complex, heterogeneous environments.