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This study explores intermittent random walks with stochastic resetting, finding an optimal reset rate for efficient target searching. Initial conditions significantly impact long-term search dynamics, revealing distinct regimes for optimizing search time.

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Area of Science:

  • Statistical Physics
  • Stochastic Processes
  • Complex Systems

Background:

  • Intermittent random walks model various search strategies.
  • Stochastic resetting introduces non-equilibrium dynamics to search processes.
  • Understanding search efficiency is crucial in fields like biophysics and computer science.

Purpose of the Study:

  • To analyze a one-dimensional intermittent random walk with stochastic resetting.
  • To investigate the impact of initial conditions on search dynamics.
  • To determine optimal parameters for efficient target localization.

Main Methods:

  • Mathematical modeling of a one-dimensional intermittent random walk.
  • Incorporation of Poissonian stochastic resetting.
  • Analysis of first arrival time distribution and mean first arrival time.
  • Investigation of different initial conditions (diffusive vs. ballistic).

Main Results:

  • Poissonian resetting establishes a non-equilibrium steady state.
  • An optimal reset rate exists for minimizing mean first arrival time.
  • Initial walker conditions (diffusive or ballistic) critically influence long-time search properties.
  • Distinct parameter regimes emerge for optimizing search when ballistic and diffusive movements compete.

Conclusions:

  • Stochastic resetting can create efficient non-equilibrium search strategies.
  • The interplay between movement types and resetting is key to optimizing search.
  • Initial conditions are a critical factor in the long-term effectiveness of intermittent search processes.