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Stochastic chemical systems with diffusion are modeled with a reaction-diffusion master equation. On a macroscopic level, the governing equation is a reaction-diffusion equation for the averages of the chemical species. On a mesoscopic…

Numerical Analysis · Mathematics 2009-03-06 Stefan Engblom , Lars Ferm , Andreas Hellander , Per Lötstedt

We briefly review some aspects of the anomalous diffusion, and its relevance in reactive systems. In particular we consider {\it strong anomalous} diffusion characterized by the moment behaviour $\langle x(t)^q \rangle \sim t^{q \nu(q)}$,…

Statistical Mechanics · Physics 2016-09-06 Fabio Cecconi , Davide Vergni , Angelo Vulpiani

We analyze numerically a forward-backward diffusion equation with a cubic-like diffusion function, -emerging in the framework of phase transitions modeling- and its "entropy" formulation determined by considering it as the singular limit of…

Analysis of PDEs · Mathematics 2010-08-31 Pauline Lafitte , Corrado Mascia

We explore chaos in the Kuramoto model with multimodal distributions of the natural frequencies of oscillators and provide a comprehensive description under what conditions chaos occurs. For a natural frequency distribution with $M$ peaks…

Adaptation and Self-Organizing Systems · Physics 2019-10-07 Lachlan D. Smith , Georg A. Gottwald

We generalize the reaction-diffusion model A + B -> 0 in order to study the impact of an excess of A (or B) at the reaction front. We provide an exact solution of the model, which shows that linear response breaks down: the average…

Statistical Mechanics · Physics 2015-01-07 Iacopo Mastromatteo , Bence Toth , Jean-Philippe Bouchaud

This paper investigates the dynamics of a reaction-diffusion system with two free boundaries, modeling the invasion of two cooperative species, where the free boundaries represent expanding fronts. We first analyze the long-term behavior of…

Analysis of PDEs · Mathematics 2025-11-21 Qian Qin , JinJing Jiao , Zhiguo Wang , Hua Nie

This paper is concerned with the propagation phenomenon of the combustion reaction-diffusion equations in domains with multiple cylindrical branches. We first show that there is an entire solution emanating from planar traveling fronts in…

Analysis of PDEs · Mathematics 2026-03-25 Yang-Yang Yan , Wei-Jie Sheng , Zhi-Cheng Wang

This work addresses the propagation of chaos properties in a class of moderately interacting particle systems for the approximation of singular kinetic McKean-Vlasov SDEs driven by alpha-stable processes.

Analysis of PDEs · Mathematics 2026-02-16 Zimo Hao , Jean-Francois Jabir , Stéphane Menozzi , Michael Röckner , Xicheng Zhang

Multifractality of charged particle pseudorapidity distributions is analyzed in central collisions of carbon and copper nuclei at 4.5 GeV/c per nucleon. Within the method of normalized factorial moments, modified to remove the bias of…

High Energy Physics - Phenomenology · Physics 2007-05-23 L. K. Gelovani , G. L. Gogiberidze , E. K. G. Sarkisyan

The current paper is a corrected version of our previous paper arXiv:adap-org/9608001. Similarly to previous version we investigate the problem of flame propagation. This problem is studied as an example of unstable fronts that wrinkle on…

Chaotic Dynamics · Physics 2013-04-23 Oleg Kupervasser , Zeev Olami

Propagation failure (pinning) of traveling waves is studied in a discrete scalar reaction-diffusion equation with a piecewise linear, bistable reaction function. The critical points of the pinning transition, and the wavefront profile at…

patt-sol · Physics 2009-10-30 Gabor Fath

This paper is concerned with the interaction between a planar traveling front and a compact obstacle for monotone bistable reaction-diffusion systems in exterior domains. By constructing appropriate sub- and supersolutions, we first…

Analysis of PDEs · Mathematics 2026-03-25 Yang-Yang Yan , Wei-Jie Sheng

Reaction-diffusion systems are ubiquitous in nature and in engineering applications, and are often modeled using a non-linear system of governing equations. While robust numerical methods exist to solve them, deep learning-based reduced…

Computational Engineering, Finance, and Science · Computer Science 2020-06-11 Kaushik Balakrishnan , Devesh Upadhyay

The master equation of one-dimensional three-species reaction-diffusion processes is mapped onto an imaginary-time Schr\"odinger equation. In many cases the Hamiltonian obtained is that of an integrable quantum chain. Within this approach…

Condensed Matter · Physics 2009-10-22 Silvio R. Dahmen

Two important classes of spatio-temporal patterns, namely, spatio-temporal chaos and self-replicating patterns, for a representative three variable autocatalytic reaction mechanism coupled with diffusion has been studied. The…

chao-dyn · Physics 2015-06-24 Nita Parekh , V. Ravi Kumar , B. D. Kulkarni

In this paper, we study the diffusion approximation for singularly perturbed stochastic reaction-diffusion equation with a fast oscillating term. The asymptotic limit for the original system is obtained, where an extra Gaussian term…

Probability · Mathematics 2021-06-08 Longjie Xie , Li Yang

Reaction-diffusion systems with cross-diffusion terms in addition to, or instead of, the usual self-diffusion demonstrate interesting features which motivate their further study. The present work is aimed at designing a toy…

Pattern Formation and Solitons · Physics 2020-09-18 Abdullah Aldurayhim , Vadim N. Biktashev

We consider reaction-diffusion fronts in spatially periodic bistable media with large periods. Whereas the homogenization regime associated with small periods had been well studied for bistable or Fisher-KPP reactions and, in the latter…

Analysis of PDEs · Mathematics 2024-12-24 Weiwei Ding , François Hamel , Xing Liang

The sensitivity to perturbations of the Fisher and Kolmogorov, Petrovskii, Piskunov front is used to find a quantity revealing perturbations of diffusion in a concentrated solution of two chemical species with different diffusivities. The…

Pattern Formation and Solitons · Physics 2019-02-20 Gabriel Morgado , Bogdan Nowakowski , Annie Lemarchand

The self-diffusion process of a hard sphere fluid confined by two parallel plates separated by a distance on the order of the particle diameter is studied. The starting point is a closed kinetic equation for the distribution function that…

Statistical Mechanics · Physics 2025-10-24 Manuel Mayo , María Isabel García de Soria , Pablo Maynar , José Javier Brey