English
Related papers

Related papers: Stochastic search with space-dependent diffusivity

200 papers

A particle driven by deterministic chaos and moving in a spatially extended environment can exhibit normal diffusion, with its mean square displacement growing proportional to the time. Here we consider the dependence of the diffusion…

Mathematical Physics · Physics 2017-06-29 Georgie Knight , Orestis Georgiou , Carl P. Dettmann , Rainer Klages

We investigate a stochastic search process in one, two, and three dimensions in which $N$ diffusing searchers that all start at $x_0$ seek a target at the origin. Each of the searchers is also reset to its starting point, either with rate…

Statistical Mechanics · Physics 2016-08-11 Uttam Bhat , Caterina De Bacco , S. Redner

Recent massive numerical simulations have shown that the response of a "stochastic resonator" is enhanced as a consequence of spatial coupling. Similar results have been analytically obtained in a reaction-diffusion model, using…

Statistical Mechanics · Physics 2015-11-30 B. von Haeften , R. Deza , H. S. Wio

Mathematically modelling diffusive and advective transport of particles in heterogeneous layered media is important to many applications in computational, biological and medical physics. While deterministic continuum models of such…

Computational Physics · Physics 2024-09-16 Elliot J. Carr

We consider potential type dynamical systems in finite dimensions with two meta-stable states. They are subject to two sources of perturbation: a slow external periodic perturbation of period $T$ and a small Gaussian random perturbation of…

Probability · Mathematics 2007-05-23 Samuel Herrmann , Peter Imkeller , Dierk Peithmann

A considerable number of systems have recently been reported in which Brownian yet non-Gaussian dynamics was observed. These are processes characterised by a linear growth in time of the mean squared displacement, yet the probability…

Statistical Mechanics · Physics 2018-11-26 V. Sposini , A. V. Chechkin , F. Seno , G. Pagnini , R. Metzler

Molecular search phenomena are observed in a variety of chemical and biological systems. During the search the participating particles frequently move in complex inhomogeneous environments with random transitions between different dynamic…

Statistical Mechanics · Physics 2018-11-13 Jaeoh Shin , Anatoly B. Kolomeisky

Cover times quantify the speed of exhaustive search. In this work, we compute exactly the mean cover time associated with a one-dimensional Brownian search under exponentially distributed resetting. We also approximate the moments of cover…

Probability · Mathematics 2025-05-13 Samantha Linn , Sean D Lawley

We consider random search processes alternating stochastically between diffusion and ballistic motion, in which the distribution function of ballistic motion directions varies from point to point in space. The specific space dependence of…

Subcellular Processes · Quantitative Biology 2016-08-29 Karsten Schwarz , Yannick Schröder , Bin Qu , Markus Hoth , Heiko Rieger

In this paper we study the reachability problem for discrete-time nonlinear stochastic systems. Our goal is to present a unified framework for calculating the probabilistic reachable set of discrete-time systems in the presence of both…

Systems and Control · Electrical Eng. & Systems 2024-09-17 Zishun Liu , Saber Jafarpour , Yongxin Chen

The occurrence of stochastic resonance in bistable systems undergoing anomalous diffusions, which arise from density-dependent fluctuations, is investigated with emphasis on the analytical formulation of the problem as well as a possible…

Statistical Mechanics · Physics 2021-03-16 F. Naha Nzoupe , Alain M. Dikande

We study simple diffusion where a particle stochastically resets to its initial position at a constant rate r. A finite resetting rate leads to a nonequilibrium stationary state with non-Gaussian fluctuations for the particle position. We…

Statistical Mechanics · Physics 2015-05-27 Martin R. Evans , Satya N. Majumdar

The friction coefficient of a particle can depend on its position as it does when the particle is near a wall. We formulate the dynamics of particles with such state-dependent friction coefficients in terms of a general Langevin equation…

Soft Condensed Matter · Physics 2009-11-13 A. W. C. Lau , T. C. Lubensky

We study Langevin dynamics with stochastic diffusivity arising from fluctuations of the surrounding medium. The diffusivity is modeled as Ornstein-Uhlenbeck process driven by symmetric dichotomous noise, which confines it to a finite…

Statistical Mechanics · Physics 2026-04-14 Dongho Lee , Jae-Hyung Jeon , Pascal Viot , Gleb Oshanin

In this paper, we propose a stochastic search algorithm for solving general optimization problems with little structure. The algorithm iteratively finds high quality solutions by randomly sampling candidate solutions from a parameterized…

Optimization and Control · Mathematics 2013-01-08 Enlu Zhou , Jiaqiao Hu

Stochastic resonance is a well established phenomenon, which proves relevant for a wide range of applications, of broad trans-disciplinary breath. Consider a one dimensional bistable stochastic system, characterized by a deterministic…

Statistical Mechanics · Physics 2023-10-17 Giuliano Migliorini , Duccio Fanelli

The abrupt changes that are ubiquitous in physical and natural systems are often well characterized by shot noise with a state dependent recurrence frequency and jump amplitude. For such state dependent behavior, we derive the transition…

Statistical Mechanics · Physics 2018-12-05 Mark S. Bartlett , Amilcare Porporato

This paper investigates the well-posedness and small-noise asymptotics of a class of stochastic partial differential equations defined on a bounded domain of $\mathbb{R}^d$, where the diffusion coefficient depends nonlinearly and…

Probability · Mathematics 2025-06-23 Sandra Cerrai , Giuseppina Guatteri , Gianmario Tessitore

Cover times measure the speed of exhaustive searches which require the exploration of an entire spatial region(s). Applications include the immune system hunting pathogens, animals collecting food, robotic demining or cleaning, and computer…

Probability · Mathematics 2024-07-11 Hyunjoong Kim , Sean D Lawley

Probabilistic regression models the entire predictive distribution of a response variable, offering richer insights than classical point estimates and directly allowing for uncertainty quantification. While diffusion-based generative models…

Machine Learning · Computer Science 2025-10-07 Carlo Kneissl , Christopher Bülte , Philipp Scholl , Gitta Kutyniok