Anomalous Diffusion in Random-Walks With Memory-Induced Relocations

Masó-Puigdellosas, Axel; Campos, Daniel; Méndez, Vicenç

doi:10.3389/fphy.2019.00112

Cited by 29 publications

(27 citation statements)

References 51 publications

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“…Foremost examples comprise the models that consider diffusion confined in bounded domains [17,18] and in external potentials with a constant [19,20,21] and a space-dependent diffusivity [21], diffusion in arbitrary spacial dimensions [22], under partial absorption [23], and in a presence of interactions [24,25]. Another category of processes studied for stochastic resetting include anomalous diffusion [26,27], Lévy flights [28,29], underdamped and scaled Brownian motions [30,31,32], random walk [33,34,35,36], continuoustime random walk with and without drift [37,38,39], telegraphic processes [40] and many others [41,42,43].…”

Section: Introductionmentioning

confidence: 99%

Non-linear diffusion with stochastic resetting

Chelminiak

2021

Preprint

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Resetting or restart, when applied to a stochastic process, usually brings its dynamics to a timeindependent stationary state. In turn, the optimal resetting rate makes the mean time to reach a target to be the shortest one. These and other problems have been intensively studied in the case of ordinary diffusive processes during the last decade. In this paper we consider the influence of stochastic resetting on a diffusive motion modeled in terms of the non-linear differential equation. The reason for its non-linearity is the power-law dependence of the diffusion coefficient on the probability density function or, in another context, the concentration of particles. We first derive an exact formula for the mean squared displacement and show how it attains the steady-state value under the exponential resetting. Then, we analyse the steady-state properties of the probability density function. We also explore the first-passage properties for the non-linear diffusion affected by the exponential resetting and find the exact expressions for the survival probability, the mean firstpassage time and the optimal resetting rate, which minimizes the mean time needed for a particle to reach a pre-determined target. Finally, we find the universal property that the relative fluctuation in the mean first-passage time of optimally restarted non-linear diffusion is always equal to unity.

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Section: Introductionmentioning

confidence: 99%

Non-linear diffusion with stochastic resetting

Chelminiak

2021

Preprint

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“…For instance, space-dependent reset rates [5] or diffusion in a potential landscape [9] and the telegraphers equation [11] have been analyzed under this perspective. Other works have studied motion with resetting by employing a renewal equation [14][15][16][17][18][19][20][21][22][23][24][25][26][27], which has also been used to study the completion time of search processes with resetting [28][29][30][31][32][33][34].…”

Section: Introductionmentioning

confidence: 99%

Stochastic resetting on comblike structures

Domazetoski

Masó-Puigdellosas

Sandev

et al. 2020

Phys. Rev. Research

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We study a diffusion process on a three-dimensional comb under stochastic resetting. We consider three different types of resetting: global resetting from any point in the comb to the initial position, resetting from a finger to the corresponding backbone and resetting from secondary fingers to the main fingers. The transient dynamics along the backbone in all three cases is different due to the different resetting mechanisms, finding a wide range of dynamics for the mean squared displacement. For the particular geometry studied herein, we compute the stationary solution and the mean square displacement and find that the global resetting breaks the transport in the three directions. Regarding the resetting to the backbone, the transport is broken in two directions but it is enhanced in the main axis. Finally, the resetting to the fingers enhances the transport in the backbone and the main fingers but reaches a steady value for the mean squared displacement in the secondary fingers.

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“…The second problem is related to the fact that it is not always possible to neglect the time cost needed to return to the initial location after the reset. The literature offers models including random refractory times preceding the return [33][34][35], but these do not consider spatiotemporal correlations. For this reason, recent works introduced the idea that the return to the starting location should be performed according to a deterministic law [36][37][38][39][40].…”

Section: Introductionmentioning

confidence: 99%

The one-dimensional telegraphic process with noninstantaneous stochastic resetting

Radice

2021

Preprint

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In this paper we consider the one-dimensional dynamical evolution of a particle traveling at constant speed and performing, at a given rate, random reversals of the velocity direction. The particle is subject to stochastic resetting, meaning that at random times it is forced to return to the starting point. Here we consider a return mechanism governed by a deterministic law of motion, so that the time cost required to return is correlated to the position occupied at the time of the reset. We show that in such conditions the process reaches a stationary state which, for some kinds of deterministic return dynamics, is independent of the return phase. Furthermore, we investigate the first-passage properties of the system and provide explicit formulas for the mean first-hitting time. Our findings are supported by numerical simulations.

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Anomalous Diffusion in Random-Walks With Memory-Induced Relocations

Cited by 29 publications

References 51 publications

Non-linear diffusion with stochastic resetting

Non-linear diffusion with stochastic resetting

Stochastic resetting on comblike structures

The one-dimensional telegraphic process with noninstantaneous stochastic resetting

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