Optimal mean first-passage time of a Brownian searcher with resetting in one and two dimensions: experiments, theory and numerical tests

@article{Faisant2021OptimalMF,
  title={Optimal mean first-passage time of a Brownian searcher with resetting in one and two dimensions: experiments, theory and numerical tests},
  author={F{\'e}lix Faisant and Benjamin Besga and A. N. Petrosyan and Sergio Ciliberto and Satya N. Majumdar},
  journal={Journal of Statistical Mechanics: Theory and Experiment},
  year={2021},
  volume={2021}
}
We experimentally, numerically and theoretically study the optimal mean time needed by a Brownian particle, freely diffusing either in one or two dimensions, to reach, within a tolerance radius R tol, a target at a distance L from an initial position in the presence of resetting. The reset position is Gaussian distributed with width σ. We derived and tested two resetting protocols, one with a periodic and one with random (Poissonian) resetting times. We computed and measured the full first… 

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References

SHOWING 1-10 OF 82 REFERENCES

Optimal mean first-passage time for a Brownian searcher subjected to resetting: Experimental and theoretical results

The optimal mean first-passage time as a function of the resetting period/rate for different values of the ratio b = L/$\sigma$ is studied and an interesting phase transtion at a critical value b = bc is found.

Diffusion with optimal resetting

We consider the mean time to absorption by an absorbing target of a diffusive particle with the addition of a process whereby the particle is reset to its initial position with rate r. We consider

Stochastic Search with Poisson and Deterministic Resetting

Deterministic resetting typically leads to a lower search cost than in stochastic resetting, and several unexpected feature arise for searchers when the resetting is deterministic, including the search time being independent of $T$ for $1/T\to 0$ and the search cost being independentof $N$ over a suitable range of $N$.

Diffusion with resetting in arbitrary spatial dimension

We consider diffusion in arbitrary spatial dimension d with the addition of a resetting process wherein the diffusive particle stochastically resets to a fixed position at a constant rate r. We

Stochastic resetting and applications

In this topical review we consider stochastic processes under resetting, which have attracted a lot of attention in recent years. We begin with the simple example of a diffusive particle whose

Diffusion under time-dependent resetting

We study a Brownian particle diffusing under a time-modulated stochastic resetting mechanism to a fixed position. The rate of resetting r(t) is a function of the time t since the last reset event. We

First Order Transition for the Optimal Search Time of Lévy Flights with Resetting.

An intermittent search process in one dimension where a searcher undergoes a discrete time jump process starting at x_{0}≥0 and the mean first passage time (MFPT) to the origin is studied, which has a global minimum in the (μ,r) plane.

Transport properties and first-arrival statistics of random motion with stochastic reset times.

This work studies the existence of a finite equilibrium mean-square displacement (MSD) when resets are applied to random motion with 〈x^{2}(t)〉_{m}∼t^{p} for 0<p≤2}.

First passage under stochastic resetting in an interval.

A comprehensive study of the first-passage properties of the Brownian particle diffusing in a one-dimensional interval with absorbing end points and shows how this set-up is a manifestation of a success-failure problem.

Diffusion with stochastic resetting.

We study simple diffusion where a particle stochastically resets to its initial position at a constant rate r. A finite resetting rate leads to a nonequilibrium stationary state with non-Gaussian
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