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Related papers: Diffusion with Resetting Inside a Circle

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Recently, a new formalism describing the anomalous diffusion processes, based on the Onsager-Machlup fluctuation theory, has been suggested \cite{Smain, Spub}. We study particles performing this new type of motion, under the action of…

Statistical Mechanics · Physics 2025-08-26 A. S. Bodrova , S. I. Serdyukov

Stochastic processes offer a fundamentally different paradigm of dynamics than deterministic processes, the most prominent example of the latter being Newton's laws of motion. Here, we discuss in a pedagogical manner a simple and…

Statistical Mechanics · Physics 2022-04-15 Shamik Gupta , Arun M. Jayannavar

Diffusion with stochastic resetting has recently emerged as a powerful modeling tool with a myriad of potential applications. Here, we study local time in this model, covering situations of free and biased diffusion with, and without, the…

Statistical Mechanics · Physics 2019-06-06 Arnab Pal , Rakesh Chatterjee , Shlomi Reuveni , Anupam Kundu

We describe a two-dimensional model for active particles whose self-propulsion speed is not fixed, but varies in time, and whose motion is subject to both translational and rotational diffusion. In the conventional treatment of active…

Soft Condensed Matter · Physics 2025-10-01 Tayeb Jamali

We study the Brownian motion of a classical particle in one-dimensional inhomogeneous environments where the transition probabilities follow quasiperiodic or aperiodic distributions. Exploiting an exact correspondence with the…

Statistical Mechanics · Physics 2009-10-31 F. Igloi , L. Turban , H. Rieger

We investigate classic diffusion with the added feature that a diffusing particle is reset to its starting point each time the particle reaches a specified threshold. In an infinite domain, this process is non-stationary and its probability…

Statistical Mechanics · Physics 2021-09-07 B. De Bruyne , J. Randon-Furling , S. Redner

The diffusion of chiral active Brownian particles in three-dimensional space is studied analytically, by consideration of the corresponding Fokker-Planck equation for the probability density of finding a particle at position…

Statistical Mechanics · Physics 2016-12-21 Francisco J. Sevilla

We consider a Brownian particle with diffusion coefficient $D$ in a $d$-dimensional ball of radius $R$ with reflecting boundaries. We study the maximum $M_x(t)$ of the trajectory of the particle along the $x$-direction at time $t$. In the…

Statistical Mechanics · Physics 2022-06-13 Benjamin De Bruyne , Olivier Bénichou , Satya N. Majumdar , Gregory Schehr

We present a formulation of an optimal control problem for a two-dimensional diffusion process governed by a Fokker-Planck equation to achieve a nonequilibrium steady state with a desired circulation while accelerating convergence toward…

Systems and Control · Electrical Eng. & Systems 2026-03-26 Norihisa Namura , Hiroya Nakao

We study the dynamics of overdamped Brownian particles diffusing in conservative force fields and undergoing stochastic resetting to a given location with a generic space-dependent rate of resetting. We present a systematic approach…

Statistical Mechanics · Physics 2017-08-15 Édgar Roldán , Shamik Gupta

We study the relaxation of a diffusive particle confined in an arbitrary external potential and subject to a non-Markovian resetting protocol. With a constant rate $r$, a previous time $\tau$ between the initial time and the present time…

Statistical Mechanics · Physics 2025-02-14 Denis Boyer , Martin R. Evans , Satya N. Majumdar

We consider Brownian motion under resetting in higher dimensions for the case when the return of the particle to the origin occurs at a constant speed. We investigate the behavior of the probability density function (PDF) and of the…

Statistical Mechanics · Physics 2020-09-23 Anna S. Bodrova , Igor M. Sokolov

We analyze the diffusion of a Brownian particle in a fluid under stationary flow. By using the scheme of non-equilibrium thermodynamics in phase space, we obtain the Fokker-Planck equation which is compared with others derived from kinetic…

Statistical Mechanics · Physics 2016-08-16 I. Santamaría-Holek , D. Reguera , J. M. Rubí

Inspired by many examples in nature, stochastic resetting of random processes has been studied extensively in the past decade. In particular, various models of stochastic particle motion were considered where upon resetting the particle is…

Statistical Mechanics · Physics 2022-11-23 Ofir Tal-Friedman , Yael Roichman , Shlomi Reuveni

We consider a particle moving in $d\geq 2$ dimensions, its velocity being a reversible diffusion process, with identity diffusion coefficient, of which the invariant measure behaves, roughly, like $(1+|v|)^{-\beta}$ as $|v|\to \infty$, for…

Probability · Mathematics 2018-12-18 Nicolas Fournier , Camille Tardif

We study the two-dimensional motion of an active Brownian particle of speed $v_0$, with intermittent directional reversals in the presence of a harmonic trap of strength $\mu$. The presence of the trap ensures that the position of the…

Statistical Mechanics · Physics 2022-09-14 Ion Santra , Urna Basu , Sanjib Sabhapandit

We study the dynamics of a Brownian motion with a diffusion coefficient which evolves stochastically. We first study this process in arbitrary dimensions and find the scaling form and the corresponding scaling function of the position…

Statistical Mechanics · Physics 2023-01-30 Ion Santra , Urna Basu , Sanjib Sabhapandit

Diffusion with stochastic resetting, instantaneous returns of a diffusing particle to a reference point, creates a stationary probability distribution. The paradigm is extended here to a doubly stochastic protocol in which the resetting…

Statistical Mechanics · Physics 2025-10-01 Maxence Arutkin , Shlomi Reuveni

We solve a model of sluggish stochastic motion in which a Brownian particle diffuses with a diffusion coefficient that decays algebraically with the distance to the origin, as $|x|^{-\alpha}$. Additionally, the particle resets with a…

Statistical Mechanics · Physics 2026-03-03 Denis Boyer , Satya N. Majumdar

Overdamped Brownian motion of a self-propelled particle is studied by solving the Langevin equation analytically. On top of translational and rotational diffusion, in the context of the presented model, the "active" particle is driven along…

Soft Condensed Matter · Physics 2013-05-15 Borge ten Hagen , Sven van Teeffelen , Hartmut Löwen