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Stochastic resetting of a population of random walks with resetting-rate-dependent diffusivity

Abstract : Abstract We consider the problem of diffusion with stochastic resetting in a population of random walks where the diffusion coefficient is not constant, but behaves as a power-law of the average resetting rate of the population. Resetting occurs only beyond a threshold distance from the origin. This problem is motivated by physical realizations like soft matter under shear, where diffusion of a walk is induced by resetting events of other walks. We first reformulate in the broader context of diffusion with stochastic resetting the so-called Hébraud–Lequeux model for plasticity in dense soft matter, in which diffusivity is proportional to the average resetting rate. Depending on parameter values, the response to a weak external field may be either linear, or non-linear with a non-zero average position for a vanishing applied field, and the transition between these two regimes may be interpreted as a continuous phase transition. Extending the model by considering a general power-law relation between diffusivity and average resetting rate, we notably find a discontinuous phase transition between a finite diffusivity and a vanishing diffusivity in the small field limit.
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https://hal-cnrs.archives-ouvertes.fr/hal-03851558
Contributor : Eric Bertin Connect in order to contact the contributor
Submitted on : Monday, November 14, 2022 - 3:14:29 PM
Last modification on : Wednesday, November 16, 2022 - 3:07:33 AM

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Eric Bertin. Stochastic resetting of a population of random walks with resetting-rate-dependent diffusivity. Journal of Physics A: Mathematical and Theoretical, 2022, 55 (38), pp.384007. ⟨10.1088/1751-8121/ac8845⟩. ⟨hal-03851558⟩

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