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Area of Science:

  • Statistical Physics
  • Nonlinear Dynamics

Background:

  • Diffusive particle transport is fundamental in physics and biology.
  • Stochastic resetting introduces non-equilibrium dynamics, altering search strategies.
  • Rescaling particle positions offers a novel approach to control diffusion.

Purpose of the Study:

  • To investigate a diffusive particle model with stochastic resetting via position rescaling.
  • To analyze the long-time position distribution and mean first-passage time (MFPT).
  • To compare the efficiency of positive and negative rescaling strategies for target search.

Main Methods:

  • Exact computation of the stationary position distribution for |a|<1.
  • Solving a nonlocal second-order differential equation for the MFPT.
  • Analytical solutions for 0≤a<1 and -1
  • Analysis of MFPT as a function of resetting rate r and rescaling factor a.

Main Results:

  • The position distribution is Gaussian near the origin and decays exponentially for large distances.
  • MFPT exhibits a minimum at a specific resetting rate r*(a) for all -1
  • Optimized MFPT increases monotonically with a for -1
  • Negative rescaling (a<0) significantly expedites target search compared to standard resetting (a=0).

Conclusions:

  • Stochastic resetting with position rescaling provides a tunable mechanism to control particle diffusion.
  • Negative rescaling, incorporating a reflection, is a beneficial strategy for accelerating target detection in one dimension.
  • This method offers advantages over standard resetting to the origin for search optimization.