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Propagation of traveling fronts in three-dimensional reaction-diffusion media with spatially modulated cross-section is studied using the Schl\"ogl model as a representative example. Applying appropriate perturbation techniques leads first…

Pattern Formation and Solitons · Physics 2015-02-26 S. Martens , J. Löber , H. Engel

We investigate the fractional diffusion approximation of a kinetic equation in the upper-half plane with diffusive reflection conditions at the boundary. In an appropriate singular limit corresponding to small Knudsen number and long time…

Analysis of PDEs · Mathematics 2019-09-04 Ludovic Cesbron , Antoine Mellet , Marjolaine Puel

Reactio-nonlocal diffusion equations model nonlocal transport and anomalous diffusion by replacing the Laplacian with a fractional power, capturing diffusion mechanisms beyond Brownian motion. We primarily study the semilinear problem \[…

Analysis of PDEs · Mathematics 2026-01-30 Pu Yuan , Paul A. Zegeling

We consider the inverse problem of determining different type of information about a diffusion process, described by ordinary or fractional diffusion equations stated on a bounded domain, like the density of the medium or the velocity field…

Analysis of PDEs · Mathematics 2019-07-05 Yavar Kian , Zhiyuan Li , Yikan Liu , Masahiro Yamamoto

The calculation of the diffusion-controlled reaction rate for partially absorbing, non-spherical boundaries presents a formidable problem of broad relevance. In this paper we take the reference case of a spherical boundary and work out a…

Statistical Mechanics · Physics 2019-11-11 Francesco Piazza , Denis Grebenkov

We study the asymptotic speed of traveling fronts of the scalar reaction diffusion for positive reaction terms and with a diffusion coefficient depending nonlinearly on the concentration and on its gradient. We restrict our study to…

Analysis of PDEs · Mathematics 2018-07-06 R. D. Benguria , M. C. Depassier

We consider a simple mean reverting diffusion process, with piecewise constant drift and diffusion coefficients, discontinuous at a fixed threshold. We discuss estimation of drift and diffusion parameters from discrete observations of the…

Statistics Theory · Mathematics 2024-03-12 Sara Mazzonetto , Paolo Pigato

We consider a particle diffusing outside a compact planar set and investigate its boundary local time $\ell_t$, i.e., the rescaled number of encounters between the particle and the boundary up to time $t$. In the case of a disk, this is…

Statistical Mechanics · Physics 2020-12-30 Denis S. Grebenkov

We develop an immersed-boundary approach to modeling reaction-diffusion processes in dispersions of reactive spherical particles, from the diffusion-limited to the reaction-limited setting. We represent each reactive particle with a…

Numerical Analysis · Mathematics 2015-06-16 A. Pal Singh Bhalla , B. E. Griffith , N. A. Patankar , A. Donev

The reversible A <-> B reaction-diffusion process, when species A and B are initially mixed and diffuse with different diffusion coefficients, is investigated using the boundary layer function method. It is assumed that the ratio of the…

Statistical Mechanics · Physics 2008-10-22 M. Sinder , V. Sokolovsky , J. Pelleg

In this paper we consider one-dimensional diffusions with constant coefficients in a finite interval with jump boundary and a certain deterministic jump distribution. We use coupling methods in order to identify the spectral gap in the case…

Probability · Mathematics 2011-01-17 Martin Kolb , Achim Wübker

The charging of insulating samples degrades the quality and complicates the interpretation of images in scanning electron microscopy and is important in other applications, such as particle detectors. In this paper we analyze this…

Classical Physics · Physics 2020-06-19 Behrouz Raftari , Neil Budko , Kees Vuik

In this review, we present the encounter-based approach to target search problems, in which the diffusive dynamics is described by the joint probability of the position of the particle and the number of its encounters with a given target…

Statistical Mechanics · Physics 2025-07-16 Denis S. Grebenkov

We investigate the fractional diffusion approximation of a kinetic equation set in a bounded interval with diffusive reflection conditions at the boundary. In an appropriate singular limit corresponding to small Knudsen number and long time…

Analysis of PDEs · Mathematics 2021-07-05 Ludovic Cesbron , Antoine Mellet , Marjolaine Puel

This paper addresses the nonparametric estimation of the drift function over a compact domain for a time-homogeneous diffusion process, based on high-frequency discrete observations from $N$ independent trajectories. We propose a neural…

Machine Learning · Statistics 2026-04-01 Yuzhen Zhao , Yating Liu , Marc Hoffmann

Diffusion-coagulation can be simply described by a dynamic where particles perform a random walk on a lattice and coalesce with probability unity when meeting on the same site. Such processes display non-equilibrium properties with strong…

Statistical Mechanics · Physics 2018-03-13 L. Turban , J. -Y. Fortin

In this paper, we establish a relationship between the asymptotic form of conditional boundary crossing probabilities and first passage time densities for diffusion processes. Namely, we show that, under broad assumptions, the first…

Probability · Mathematics 2008-11-18 Konstantin A. Borovkov , Andrew N. Downes

This paper aims at an efficient strategy to solve drift-diffusion problems with non-linear boundary conditions as they appear, e.g., in heterogeneous catalysis. Since the non-linearity only involves the degrees of freedom along (a part of)…

Numerical Analysis · Mathematics 2025-10-29 Sebastian Matera , Christian Merdon , Daniel Runge

Motivated by a novel method for granular segregation, we analyze the one dimensional drift-diffusion between two absorbing boundaries. The time evolution of the probability distribution and the rate of absorption are given by explicit…

Statistical Mechanics · Physics 2009-10-31 Zeno Farkas , Tamas Fulop

We investigate the statistical correlation between the first-reaction time of a diffusing particle and its boundary local time accumulated until the reaction event. Since the reaction event occurs after multiple encounters of the particle…

Statistical Mechanics · Physics 2026-02-04 Yilin Ye , Denis S. Grebenkov