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In order to describe excitable reaction-diffusion systems, we derive a two-dimensional model with a Hopf and a semilocal saddle-node homoclinic bifurcation. This model gives the theoretical framework for the analysis of the saddle-node…

Mathematical Physics · Physics 2007-05-23 Rui Dilao , Andras Volford

Mathematical models describing the spatial spreading and invasion of populations of biological cells are often developed in a continuum modelling framework using reaction-diffusion equations. While continuum models based on linear diffusion…

Cellular Automata and Lattice Gases · Physics 2024-01-23 Matthew J Simpson , Keeley M Murphy , Scott W McCue , Pascal R Buenzli

We expand on a recent study of a lattice model of interacting particles [Phys. Rev. Lett. 111, 110601 (2013)]. The adsorption isotherm and equilibrium fluctuations in particle number are discussed as a function of the interaction. Their…

Statistical Mechanics · Physics 2014-11-20 T. Becker , K. Nelissen , B. Cleuren , B. Partoens , C. Van den Broeck

Back-diffusion is the phenomenon by which random walkers revisit binding sites on a lattice. This phenomenon must occur on interstellar dust particles, slowing down dust-grain reactions, but it is not accounted for by standard rate-equation…

Astrophysics of Galaxies · Physics 2018-09-12 Eric R. Willis , Robin T. Garrod

We consider a finite region of a lattice of weakly interacting geodesic flows on manifolds of negative curvature and we show that, when rescaling the interactions and the time appropriately, the energies of the flows evolve according to a…

Mathematical Physics · Physics 2015-05-20 Dmitry Dolgopyat , Carlangelo Liverani

We study a lattice-gas model of penetrable particles on a square-lattice substrate with same-site and nearest-neighbor interactions. Penetrability implies that the number of particles occupying a single lattice site is unlimited and the…

Soft Condensed Matter · Physics 2020-08-21 Derek Frydel , Yan Levin

We investigate reversible diffusion-influenced reactions of an isolated pair in two dimensions. To this end, we employ convolution relations that permit deriving the survival probability of the reversible reaction directly in terms of the…

Quantitative Methods · Quantitative Biology 2015-06-16 Thorsten Prüstel , M. Tachiya

The paper deals with reaction-diffusion equations involving a hysteretic discontinuity in the source term, which is defined at each spatial point. In particular, such problems describe chemical reactions and biological processes in which…

Analysis of PDEs · Mathematics 2014-04-17 Pavel Gurevich , Roman Shamin , Sergey Tikhomirov

Quantum dissipation arises when a large system can be split in a quantum system and an environment where the energy of the former flows to. Understanding the effect of dissipation on quantum many-body systems is of particular importance due…

Strongly Correlated Electrons · Physics 2024-06-11 Zheng Yan , L. Pollet , Jie Lou , Xiaoqun Wang , Yan Chen , Zi Cai

We study reaction-diffusion processes with concentration-dependent diffusivity. First, we determine the decay of the concentration in the single-species and two-species diffusion-controlled annihilation processes. We then consider two…

Statistical Mechanics · Physics 2013-05-30 P. L. Krapivsky

Binary magnetic square lattice Ising system with nearest neighbour interactions were simulated using the Monte Carlo technique. Two types of ions were randomly distributed on the lattice sites, one type interacting ferromagnetic and the…

Statistical Mechanics · Physics 2013-01-23 Ike Q. Sikakana

In this paper we present computational techniques to investigate the solutions of two-component, nonlinear reaction-diffusion (RD) systems on arbitrary surfaces. We build on standard techniques for linear and nonlinear analysis of RD…

Computational Engineering, Finance, and Science · Computer Science 2016-05-06 Daljit Singh J. Dhillon , Michel C. Milinkovitch , Matthias Zwicker

We study diffusion-limited pair annihilation $A+A\to 0$ on one-dimensional lattices with inhomogeneous nearest neighbour hopping in the limit of infinite reaction rate. We obtain a simple exact expression for the particle concentration…

Statistical Mechanics · Physics 2009-10-31 G. M. Schütz , K. Mussawisade

Considering a two-dimensional Bose-Hubbard spinor lattice with weak nearest neighbour interactions and no particle transfer between sites, we theoretically study the transport of energy from one initially excited dimer, to the rest of the…

Quantum Gases · Physics 2017-04-05 Amit Dey , Amichay Vardi

It is shown, concerning equivalent classes, that on a one-dimensional lattice with nearest neighbor interaction, there are only four independent models possessing double-shocks. Evolution of the width of the double-shocks in different…

Statistical Mechanics · Physics 2007-05-23 Maryam Arabsalmani , Amir Aghamohammadi

Direct interactions between the flow field and the chemical reaction in premixed flames occur when the reaction zone thickness is comparable to, or greater than flow length scales. To study such interactions, a laminar model is considered…

Fluid Dynamics · Physics 2024-07-02 Prabakaran Rajamanickam , Joel Daou

The kinetics of geminate subdiffusion-assisted reactions (SDARs) of interacting particles is analyzed in detail with the use of the non-Markovian fractional Smoluchowki equation (FSE). It is suggested that the interparticle interaction…

Statistical Mechanics · Physics 2008-08-22 A. I. Shushin

The trend to equilibrium for reaction-diffusion systems modelling chemical reaction networks is investigated, in the case when reaction processes happen on subsets of the domain. We prove the convergence to equilibrium by directly showing…

Analysis of PDEs · Mathematics 2024-12-17 Laurent Desvillettes , Kim Dang Phung , Bao Quoc Tang

On a two-dimensional circular domain, we analyze the formation of spatio-temporal patterns for a class of coupled bulk-surface reaction-diffusion models for which a passive diffusion process occurring in the interior bulk domain is linearly…

Pattern Formation and Solitons · Physics 2020-08-11 Frédéric Paquin-Lefebvre , Wayne Nagata , Michael J. Ward

We study the evolution of fronts in a bistable reaction-diffusion system when the nonlinear reaction term is spatially non-homogeneous. This equation has been used to model wave propagation in various biological systems. Extending previous…

Pattern Formation and Solitons · Physics 2009-10-31 Horacio G. Rotstein , Anatol M. Zhabotinsky , Irving R. Epstein