Searching for clusters of targets under stochastic resetting

Calvert, Georgia R.; Evans, Martin R.

doi:10.1140/epjb/s10051-021-00238-0

Cited by 8 publications

(7 citation statements)

References 41 publications

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“…Various generalizations and extensions of this simple model have been studied over the past decade [13][14][15][16][17][18][19]. Examples include resetting of a diffusing particle in a potential [20,21], in the presence of an absorbing target whose position is drawn from a distribution [22], or in the presence of clusters of targets [23]. The role of different resetting protocols has also been explored in the literature, for example the effects of resets with a refractory period [24], and non-instantaneous resets [25,26].…”

Section: J Stat Mech (2023) 053202mentioning

confidence: 99%

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Symmetric exclusion process under stochastic power-law resetting

Seemant¹,

Basu²

2023

J. Stat. Mech.

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We study the behaviour of a symmetric exclusion process in the presence of non-Markovian stochastic resetting, where the configuration of the system is reset to a step-like profile at power-law waiting times with an exponent α. We find that the power-law resetting leads to a rich behaviour for the currents, as well as density profile. We show that, for any finite system, for α < 1, the density profile eventually becomes uniform while for α > 1, an eventual non-trivial stationary profile is reached. We also find that, in the limit of thermodynamic system size, at late times, the average diffusive current grows ∼ t θ with θ = 1 / 2 for α ⩽ 1 / 2 , θ = α for 1 / 2 < α ⩽ 1 and θ = 1 for α > 1. We also analytically characterize the distribution of the diffusive current in the short-time regime using a trajectory-based perturbative approach. Using numerical simulations, we show that in the long-time regime, the diffusive current distribution follows a scaling form with an α − dependent scaling function. We also characterise the behaviour of the total current using renewal approach. We find that the average total current also grows algebraically ∼ t ϕ where ϕ = 1 / 2 for α ⩽ 1 , ϕ = 3 / 2 − α for 1 < α ⩽ 3 / 2 , while for α > 3 / 2 the average total current reaches a stationary value, which we compute exactly. The standard deviation of the total current also shows an algebraic growth with an exponent Δ = 1 2 for α ⩽ 1 , and Δ = 1 − α 2 for 1 < α ⩽ 2 , whereas it approaches a constant value for α > 2. The total current distribution remains non-stationary for α < 1, while, for α > 1, it reaches a non-trivial and strongly non-Gaussian stationary distribution, which we also compute using the renewal approach.

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Section: J Stat Mech (2023) 053202mentioning

confidence: 99%

“…which can be evaluated numerically using the Gaussian form of P 0 (J 0 , t) given in equation (23). Similarly, the contribution from n = 2 trajectories,…”

Section: Probability Distribution Of the Diffusive Currentmentioning

confidence: 99%

Symmetric exclusion process under stochastic power-law resetting

Seemant¹,

Basu²

2023

J. Stat. Mech.

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“…The system is equivalent to a one-dimensional random walk on a segment with absorbing boundaries at −2π and 2π, with the two ends identified by periodic boundary conditions. For an investigation of the mean time to double absorption under resetting by two targets on either side of the origin, see [24].…”

Section: Notations and Quantities Of Interestmentioning

confidence: 99%

Winding number of a Brownian particle on a ring under stochastic resetting

Grange¹

2022

J. Phys. A: Math. Theor.

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We consider a random walker on a ring, subjected to resetting at Poisson-distributed times to the initial position (the walker takes the shortest path along the ring to the initial position at resetting times). In the case of a Brownian random walker the mean first-completion time of a turn is expressed in closed form as a function of the resetting rate. The value is shorter than in the ordinary process if the resetting rate is low enough. Moreover, the mean first-completion time of a turn can be minimised in the resetting rate. At large time the distribution of winding numbers does not reach a steady state, which is in contrast with the non-compact case of a Brownian particle under resetting on the real line. The mean total number of turns and the variance of the net number of turns grow linearly with time, with a proportionality constant equal to the inverse of the mean first-completion time of a turn.

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“…Stochastic resetting induces a renewal structure, which allows to work out (the Laplace transform of) the probability of the configurations in the system undergoing resetting, in terms of the probability of the configurations in the ordinary system. This reasoning has yielded exact results on a variety of stochastic processes and out-of-equlibrium physical systems (including population dynamics, reaction-diffusion systems and active particles) [3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20]. For a review, see [21] and references therein.…”

Section: Introductionmentioning

confidence: 98%

Voter model under stochastic resetting

Grange¹

2022

Preprint

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The voter model is a toy model of consensus formation based on nearest-neighbour interactions. Each voter is endowed with a Boolean variable (a binary opinion) that flips randomly at a rate set according to the opinions of the nearest neighbours. In this paper we subject the system to local resetting by considering stubborn voters. In addition to the usual dynamics, voters revert independently to their initial opinion according to a Poisson process of fixed intensity. The resulting kinetic equations for the average magnetization and two-point function of the model are derived and solved in closed form. They are formally identical to the heat equation coupled to a thermostat, whose temperature profile is induced by the initial conditions. In the case of initial conditions consisting of a single decided voter at the origin in a environment full of undecided voters, the average magnetization evolves as the probability density of a random walker with stochastic resetting to the origin. However, the long-time behaviour of the two-point function contains terms terms that cannot be obtained from a renewal argument. As a result, the steady-state densiity of domain walls can be extremized as a function of the resetting rate.

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Searching for clusters of targets under stochastic resetting

Cited by 8 publications

References 41 publications

Symmetric exclusion process under stochastic power-law resetting

Symmetric exclusion process under stochastic power-law resetting

Winding number of a Brownian particle on a ring under stochastic resetting

Voter model under stochastic resetting

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