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Parallel random target searches in a confined space.

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  • 1Graduate School of Nanoscience and Technology, Korea Advanced Institute of Science and Technology, Deajeon 34141, Korea.

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This study analyzes random target searching by N independent searchers. Uniformly distributed searchers show a universal power-law search time, while point-distributed searchers exhibit logarithmic dependence on N.

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Area of Science:

  • Physics
  • Mathematics
  • Statistical Mechanics

Background:

  • Random search processes are fundamental in various scientific fields.
  • Understanding searcher distribution and its impact on search time is crucial.
  • Previous studies often focused on single searchers or specific distributions.

Purpose of the Study:

  • To investigate the mean first arrival time (searching time) for N independent random searchers.
  • To compare searching times for uniform and point initial searcher distributions.
  • To analyze the influence of dimensionality, domain size, and initial distance on search efficiency.

Main Methods:

  • Analytical estimation of mean searching time.
  • Mathematical modeling of searcher dynamics in a d-dimensional domain.
  • Numerical simulations to validate theoretical predictions.
  • Phase diagram construction in the (r0, N) parameter space.

Main Results:

  • Uniformly distributed searchers exhibit a universal power-law dependence of searching time on N.
  • Point-distributed searchers show logarithmic dependence on N for large N.
  • Small N for point-distributed searchers reveals behavior dependent on initial distance (r0).
  • A phase diagram illustrates distinct regions based on initial distribution and parameters.

Conclusions:

  • Searcher distribution significantly impacts search efficiency and time.
  • The study provides a comprehensive understanding of random search dynamics.
  • The findings are applicable to diverse fields involving search and exploration processes.