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In this paper we consider the mathematical relationship between nonlocal interactions of convolution type and multiple diffusive substances in high dimensions. Motivated by that the nonlocal evolution equations reproduce similar patterns to…

Analysis of PDEs · Mathematics 2025-11-07 Hiroshi Ishii , Yoshitaro Tanaka

We investigate Turing instability and pattern formation in two-dimensional domains for two reaction-diffusion models, obtained as diffusive limits of kinetic equations for mixtures of monatomic and polyatomic gases. The first model is of…

Mathematical Physics · Physics 2026-02-23 Stefano Boccelli , Giorgio Martalò , Romina Travaglini

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

Pattern formation has been extensively studied in the context of evolving (time-dependent) domains in recent years, with domain growth implicated in ameliorating problems of pattern robustness and selection, in addition to more realistic…

Pattern Formation and Solitons · Physics 2023-01-18 Andrew L. Krause , Eamonn A. Gaffney , Benjamin J. Walker

Realistic examples of reaction-diffusion phenomena governing spatial and spatiotemporal pattern formation are rarely isolated systems, either chemically or thermodynamically. However, even formulations of `open' reaction-diffusion systems…

Pattern Formation and Solitons · Physics 2021-05-14 Andrew L. Krause , Václav Klika , Philip K. Maini , Denis Headon , Eamonn A. Gaffney

A class of systems is considered, where immobile species associated to distinct patches, the nodes of a network, interact both locally and at a long-range, as specified by an (interaction) adjacency matrix. Non local interactions are…

Pattern Formation and Solitons · Physics 2020-06-30 Giulia Cencetti , Federico Battiston , Timoteo Carletti , Duccio Fanelli

We study the behaviour of catalytically active droplets in multi-component conserved mixtures affected by noise. Working in the thin interface limit, we analytically determine the state diagram of the system, characterized by multiple…

Soft Condensed Matter · Physics 2025-12-01 Jacopo Romano , Martin Kjøllesdal Johnsrud , Benoît Mahault , Ramin Golestanian

Logistic growth process with nonlocal interactions is considered in one dimension. Spontaneous breakdown of translational invariance is shown to take place at some parameter region, and the bifurcation regime is identified for short and…

Soft Condensed Matter · Physics 2009-11-10 Nadav M. Shnerb

We report new chemoconvective pattern formation phenomena observed in a two-layer system of miscible fluids filling a vertical Hele-Shaw cell. We show both experimentally and theoretically that the concentration-dependent diffusion coupled…

Fluid Dynamics · Physics 2015-06-26 Dmitry Bratsun , Konstantin Kostarev , Alexey Mizev , Elena Mosheva

We propose an open-boundary molecular dynamics method in which an atomistic system is in contact with an infinite particle reservoir at constant temperature, volume and chemical potential. In practice, following the Hamiltonian adaptive…

Statistical Mechanics · Physics 2020-06-24 Maziar Heidari , Kurt Kremer , Ramin Golestanian , Raffaello Potestio , Robinson Cortes-Huerto

We investigate dynamics of large scale and slow deformations of layered structures. Starting from the respective model equations for a non-conserved system, a conserved system and a binary fluid, we derive the interface equations which are…

Soft Condensed Matter · Physics 2009-10-30 Takao Ohta , David Jasnow

The dynamics and internal structure of doping fronts in organic semiconductors are investigated theoretically using an extended drift-diffusion model for ions, electrons and holes. The model also involves the injection barriers for…

Materials Science · Physics 2012-09-14 M. Modestov , V. Bychkov , D. Valiev , M. Marklund

Two front instabilities in a reaction-diffusion system are shown to lead to the formation of complex patterns. The first is an instability to transverse modulations that drives the formation of labyrinthine patterns. The second is a…

patt-sol · Physics 2009-10-28 Aric Hagberg , Ehud Meron

We study the pattern dynamics in a reaction diffusion model of the activator--inhibitor type in the oscillatory regime. We consider finite systems with partially absorptive boundary conditions analizing examples in different geometries in…

Statistical Mechanics · Physics 2007-05-23 S. Bouzat , H. S. Wio

By analytically solving some simple models of phase-ordering kinetics, we suggest a mechanism for the onset of non-equilibrium behaviour in colloid-polymer mixtures. These mixtures can function as models of atomic systems; their physics…

Soft Condensed Matter · Physics 2016-08-31 R. M. L. Evans , W. C. K. Poon

This work deals with a parabolic chemotaxis model with nonlinear diffusion and nonlocal reaction source. The problem is formulated on the whole space and, depending on a specific interplay between the coefficients associated to such…

Analysis of PDEs · Mathematics 2020-04-24 Tongxing Li , Giuseppe Viglialoro

We propose and study a one-dimensional model which consists of two cross-diffusion systems coupled via a moving interface. The motivation stems from the modelling of complex diffusion processes in the context of the vapor deposition of thin…

Analysis of PDEs · Mathematics 2024-07-23 Clément Cancès , Jean Cauvin-Vila , Claire Chainais-Hillairet , Virginie Ehrlacher

The quantitative convergence to equilibrium for reaction-diffusion systems arising from complex balanced chemical reaction networks with mass action kinetics is studied by using the so-called entropy method. In the first part of the paper,…

Analysis of PDEs · Mathematics 2016-11-11 Laurent Desvillettes , Klemens Fellner , Bao Quoc Tang

We consider a nonlinear damped hyperbolic reaction-diffusion system in a bounded interval of the real line with homogeneous Neumann boundary conditions and we study the metastable dynamics of the solutions. Using an "energy approach"…

Analysis of PDEs · Mathematics 2019-11-06 Raffaele Folino

Phase separation in passive systems leads to uncontrolled droplet growth, limiting structural control in soft materials and cells. We identify a generic mechanism to arrest coarsening based on chemical interconversion between molecular…

Soft Condensed Matter · Physics 2026-03-19 Florian Raßhofer , Erwin Frey