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Motivated by the diffusion-reaction kinetics on interstellar dust grains, we study a first-passage problem of mortal random walkers in a confined two-dimensional geometry. We provide an exact expression for the encounter probability of two…

Statistical Mechanics · Physics 2009-10-02 Ingo Lohmar , Joachim Krug

We consider a reaction-diffusion system where some components react and diffuse on the boundary of a region, while other components diffuse in the interior and react with those on the boundary through mass transport. We establish local…

Analysis of PDEs · Mathematics 2015-11-20 Vandana Sharma , Jeff Morgan

We consider a nonlinear reaction--diffusion equation in a domain consisting of two bulk regions connected via small channels periodically distributed within a thin layer. The height and the thickness of the channels are of order $\epsilon$,…

Analysis of PDEs · Mathematics 2021-12-02 Markus Gahn , Maria Neuss-Radu

We expand on a previous study of fronts in finite particle number reaction-diffusion systems in the presence of a reaction rate gradient in the direction of the front motion. We study the system via reaction-diffusion equations, using the…

Statistical Mechanics · Physics 2009-11-11 Elisheva Cohen , David A. Kessler , Herbert Levine

This paper establishes existence, uniqueness, and an L^1-comparison principle for weak solutions of a PDE system modeling phase transition reaction-diffusion in congested crowd motion. We consider a general reaction term and mixed…

Analysis of PDEs · Mathematics 2025-09-17 Noureddine Igbida , Fahd Karami , Driss Meskine

We study reaction-diffusion processes on graphs through an extension of the standard reaction-diffusion equation starting from first principles. We focus on reaction spreading, i.e. on the time evolution of the reaction product, M(t). At…

Statistical Mechanics · Physics 2015-06-12 R. Burioni , S. Chibbaro , D. Vergni , A. Vulpiani

We study a reaction-diffusion process that involves two species of atoms, immobile and diffusing. We assume that initially only immobile atoms, uniformly distributed throughout the entire space, are present. Diffusing atoms are injected at…

Statistical Mechanics · Physics 2014-07-18 P. L. Krapivsky

Morphogenesis is central to biology but remains largely unexplored in chemistry. Reaction-diffusion (RD) mechanisms are, however, essential to understand how shape emerges in the living world. While numerical methods confirm the incredible…

Pattern Formation and Solitons · Physics 2014-07-17 Anton S. Zadorin , Yannick Rondelez , Jean-Christophe Galas , André Estevez-Torres

We consider a reaction-diffusion system for two densities lying in adjacent domains of $\mathbb{R}^N$. We treat two configurations: either a cylinder and its complement, or two half-spaces. Diffusion and reaction heterogeneities for the two…

Analysis of PDEs · Mathematics 2025-06-06 Henri Berestycki , Luca Rossi , Andrea Tellini

We confront, quantitatively, the theoretical description of the reaction-diffusion of a second order reaction to experiment. The reaction at work is \ca/CaGreen, and the reactor is a T-shaped microchannel, 10 $\mu$m deep, 200 $\mu$m wide,…

Fluid Dynamics · Physics 2009-11-07 Charles N. Baroud , Fridolin Okkels , Laure Menetrier , Patrick Tabeling

Problems involving the capture of a moving entity by a trap occur in a variety of physical situations, the moving entity being an electron, an excitation, an atom, a molecule, a biological object such as a receptor cluster, a cell, or even…

Statistical Mechanics · Physics 2015-06-17 K. Spendier , S. Sugaya , V. M. Kenkre

In this paper, we consider a reaction-diffusion system describing the propagation of flames under the assumption of ignition-temperature kinetics and fractional reaction order. It was shown in [3] that this system admits a traveling front…

Analysis of PDEs · Mathematics 2024-02-29 Amanda Matson , Claude-Michel Brauner , Peter V. Gordon

A model for diffusion on a cubic lattice with a random distribution of traps is developed. The traps are redistributed at certain time intervals. Such models are useful for describing systems showing dynamic disorder, such as ion-conducting…

Condensed Matter · Physics 2009-10-31 S. Mandal , R. Dasgupta

We develop an efficient method to calculate probabilities of large deviations from the typical behavior (rare events) in reaction--diffusion systems. The method is based on a semiclassical treatment of underlying "quantum" Hamiltonian,…

Statistical Mechanics · Physics 2009-11-10 Vlad Elgart , Alex Kamenev

Reaction-diffusion equations are one of the most common mathematical models in the natural sciences and are used to model systems that combine reactions with diffusive motion. However, rather than normal diffusion, anomalous subdiffusion is…

Statistical Mechanics · Physics 2021-04-23 Amanda M Alexander , Sean D Lawley

We undertake a detailed analysis of a reaction-advection-diffusion (RAD) equation from the viewpoint of pulse-response studies, with particular attention to effects due to the advection velocity. Our boundary-value problem is a mathematical…

Analysis of PDEs · Mathematics 2026-03-05 Jiasong Zhu , Renato Feres , Donsub Rim , Gregory Yablonsky

This work discusses the homogenization analysis for diffusion processes on scale-free metric graphs, using weak variational formulations. The oscillations of the diffusion coefficient along the edges of a metric graph induce internal…

Analysis of PDEs · Mathematics 2016-05-31 Fernando A. Morales , Daniel E. Restrepo

The fractional diffusion equation is rigorously derived as a scaling limit from a deterministic Rayleigh gas, where particles interact via short range potentials with support of size $\varepsilon$ and the background is distributed in space…

Analysis of PDEs · Mathematics 2025-11-04 Karsten Matthies , Theodora Syntaka

To analyze possible generalizations of reaction-diffusion schemes for the case of subdiffusion we discuss a simple monomolecular conversion A --> B. We derive the corresponding kinetic equations for local A and B concentrations. Their form…

Statistical Mechanics · Physics 2009-11-11 I. M. Sokolov , M. G. W. Schmidt , F. Sagues

We consider a single-species diffusion-limited annihilation reaction with reactants confined to a two-dimensional surface with one arbitrarily large dimension and the other comparable in size to interparticle distances. This situation could…

Biomolecules · Quantitative Biology 2015-03-20 Aleksandr Kivenson , Michael F. Hagan