Effect of partial absorption on diffusion with resetting

Whitehouse, Justin; Evans, Martin R.; Majumdar, Satya N.

doi:10.1103/physreve.87.022118

Cited by 81 publications

(105 citation statements)

References 14 publications

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“…In all these problems the mean first-passage time plays a crucial role in characterising the efficiency of the search strategy. Recently, another interesting search model, where the searcher diffuses and stochastically resets to its initial position, was introduced for which the mean first-passage time is exactly computable [108,[391][392][393].…”

Section: Discussionmentioning

confidence: 99%

Persistence and first-passage properties in nonequilibrium systems

Bray

Majumdar

Schehr

2013

Advances in Physics

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531

669

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In this review we discuss the persistence and the related first-passage properties in extended many-body nonequilibrium systems. Starting with simple systems with one or few degrees of freedom, such as random walk and random acceleration problems, we progressively discuss the persistence properties in systems with many degrees of freedom. These systems include spins models undergoing phase ordering dynamics, diffusion equation, fluctuating interfaces etc. Persistence properties are nontrivial in these systems as the effective underlying stochastic process is non-Markovian. Several exact and approximate methods have been developed to compute the persistence of such non-Markov processes over the last two decades, as reviewed in this article. We also discuss various generalisations of the local site persistence probability. Persistence in systems with quenched disorder is discussed briefly. Although the main emphasis of this review is on the theoretical developments on persistence, we briefly touch upon various experimental systems as well.

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Section: Discussionmentioning

confidence: 99%

Persistence and first-passage properties in nonequilibrium systems

Bray

Majumdar

Schehr

2013

Advances in Physics

Self Cite

531

669

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“…'Stochastic resetting' is a mechanism where a Brownian particle is stochastically reset to its initial position at a constant rate thus driving the system away from any equilibrium state [10][11][12][13]. It is thus a simple mechanism to generate a non equilibrium stationary state.…”

Section: Introductionmentioning

confidence: 99%

Diffusion in a potential landscape with stochastic resetting

2015

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The steady state of a Brownian particle diffusing in an arbitrary potential under the stochastic resetting mechanism has been studied. We show that there are different classes of nonequilibrium steady states depending on the nature of the potential. In the stable potential landscape, the system attains a well defined steady state however existence of the steady state for the unstable landscape is constrained. We have also investigated the transient properties of the propagator towards the steady state under the stochastic resetting mechanism. Finally, we have done numerical simulations to verify our analytical results.

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“…The generalization from the one-dimensional case to higher dimensions has been considered in [26]. In the context of a target search process, the effect of partial absorption has been considered in [27]. Properties of non-equilibrium steady state for diffusion with resetting have been studied in the presence of a potential [28] or in a bounded domain [29].…”

Section: Introductionmentioning

confidence: 99%

Diffusion under time-dependent resetting

Pal

Kundu

Evans

2016

J. Phys. A: Math. Theor.

271

319

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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 derive a sufficient condition on r(t) for a steady-state probability distribution of the position of the particle to exist. We derive the form of the steady-state distributions under some particular choices of r(t) and also consider the late time relaxation behavior of the probability distribution. We consider first passage time properties for the Brownian particle to reach the origin and derive a formula for the mean first passage time. Finally, we study optimal properties of the mean first passage time and show that a threshold function is at least locally optimal for the problem of minimizing the mean first passage time.

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Effect of partial absorption on diffusion with resetting

Cited by 81 publications

References 14 publications

Persistence and first-passage properties in nonequilibrium systems

Persistence and first-passage properties in nonequilibrium systems

Diffusion in a potential landscape with stochastic resetting

Diffusion under time-dependent resetting

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