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Many mathematical models for biological phenomena, such as the spread of diseases, are based on reaction-diffusion equations for densities of interacting cell populations. We present a consistent derivation of reaction-diffusion equations…
In this paper we consider the 2-component reaction-diffusion model that was recently obtained by a systematic reduction of the 3-component Gilad et al. model for dryland ecosystem dynamics. The nonlinear structure of this model is more…
Reaction-diffusion models have been used over decades to study biological systems. In this context, evolution equations for probability distribution functions and the associated stochastic differential equations have nowadays become…
Reaction-diffusion equations are studied on bounded, time-periodic domains with zero Dirichlet boundary conditions. The long-time behaviour is shown to depend on the principal periodic eigenvalue of a transformed periodic-parabolic problem.…
We present a mathematical study for the development of Multiple Sclerosis in which a spatio-temporal kinetic { theory} model describes, at the mesoscopic level, the dynamics of a high number of interacting agents. We consider both…
This study investigates transient wave dynamics in Turing pattern formation, focusing on waves emerging from localised disturbances. While the traditional focus of diffusion-driven instability has primarily centred on stationary solutions,…
A new non-conservative stochastic reaction-diffusion system in which two families of random walks in two adjacent domains interact near the interface is introduced and studied in this paper. Such a system can be used to model the transport…
Detonation propagation in a compressible medium wherein the energy release has been made spatially inhomogeneous is examined via numerical simulation. The inhomogeneity is introduced via step functions in the reaction progress variable,…
We study matrix element fluctuations of the two-body screened Coulomb interaction and of the one-body surface charge potential in ballistic quantum dots. For chaotic dots, we use a normalized random wave model to obtain analytic expansions…
Dynamical systems theory provides powerful methods to extract effective macroscopic dynamics from complex systems with slow modes and fast modes. Here we derive and theoretically support a macroscopic, spatially discrete, model for a class…
Diffusion-mediated surface phenomena are crucial for human life and industry, with examples ranging from oxygen capture by lung alveolar surface to heterogeneous catalysis, gene regulation, membrane permeation and filtration processes.…
Reaction diffusion equations have been used to model a wide range of biological phenomenon related to population spread and proliferation from ecology to cancer. It is commonly assumed that individuals in a population have homogeneous…
A one species time-delay reaction-diffusion system defined on a complex networks is studied. Travelling waves are predicted to occur as follows a symmetry breaking instability of an homogenous stationary stable solution, subject to an…
In a companion paper, we established nonlinear stability with detailed diffusive rates of decay of spectrally stable periodic traveling-wave solutions of reaction diffusion systems under small perturbations consisting of a nonlocalized…
An investigation of the mesoscopic dynamics of chemical systems whose mass action equation gives rise to a deterministic chaotic attractor is carried out. A reactive lattice-gas model for the three-variable autocatalator is used to provide…
We study phase-separating fluid mixtures as they demix in the presence of chemical reactions that maintain them away from thermodynamic equilibrium. We show that in such chemically active emulsions the interplay of chemical reactions, phase…
Stochasticity plays important roles in reaction systems. Vector fields of probability flux and velocity characterize time-varying and steady-state properties of these systems, including high probability paths, barriers, checkpoints among…
Hypothesis:Diffusion in confinement is an important fundamental problem with significant implications for applications of supported liquid phases. However, resolving the spatially dependent diffusion coefficient, parallel and perpendicular…
In absence of advection, reaction-diffusion systems are able to organize into spatiotemporal patterns, in particular spiral and target waves. Whenever advection is present and can be parameterised in terms of effective or turbulent…
Starting from the kinetic approach for a mixture of reacting gases whose particles interact through elastic scattering and a bimolecular reversible chemical reaction, the equations that govern the dynamics of the system are obtained by…