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Originating from the pioneering study of Alan Turing, the bifurcation analysis predicting spatial pattern formation from a spatially uniform state for diffusing morphogens or chemical species that interact through nonlinear reactions is a…
We prove existence and uniqueness of global solutions for a class of reaction-advection-anisotropic-diffusion systems whose reaction terms have a "triangular structure". We thus extend previous results to the case of time-space dependent…
Generative diffusion models have achieved remarkable success in producing high-quality images. However, these models typically operate in continuous intensity spaces, diffusing independently across pixels and color channels. As a result,…
We investigate the convergence of spatial discretizations for reaction-diffusion systems with mass-action law satisfying a detailed balance condition. Considering systems on the d-dimensional torus, we construct appropriate space-discrete…
Spatial and temporal pattern formation in reaction-diffusion systems is typically studied with two or more equations, as scalar reaction-diffusion equations confined to convex domains do not admit stable inhomogeneous states in time or…
One of the main applications of electromagnetic metasurfaces (MSs) is to tailor spatial field distributions. The radiation pattern of a given source can be desirably modified upon reflection on an MS having proper spatial modulation of its…
Reaction-diffusion equations on infinite graphs can have an infinite number of stationary solutions. These solutions are generally described as roots of a countable system of algebraic equations. As a generalization of periodic stationary…
We study the boundedness and convergence to equilibrium of weak solutions to reaction-diffusion systems with nonlinear diffusion. The nonlinear diffusion is of porous medium type and the nonlinear reaction terms are assumed to grow…
We study instabilities and pattern formation in reaction-diffusion layers that are diffusively coupled. For two-layer systems of identical two-component reactions, we analyze the stability of homogeneous steady states by exploiting the…
We study a large class of 1D reaction diffusion models with quenched disorder using a real space renormalization group method (RSRG) which yields exact results at large time. Particles (e.g. of several species) undergo diffusion with random…
In this paper we obtain the existence of a radial solution for some elliptic nonlocal problem with constraints. The problem arises from some reaction-diffusion equation modelling among others system of self-gravitating particles when one…
Reaction-diffusion systems where transition rates exhibit quenched disorder are common in physical and chemical systems. We study pair reactions on a periodic two-dimensional lattice, including continuous deposition and spontaneous…
We extend ring-polymer molecular dynamics (RPMD) to allow for the direct simulation of general, electronically non-adiabatic chemical processes. The kinetically constrained (KC) RPMD method uses the imaginary-time path-integral…
The Lagrange-mesh $R$-matrix method is generalized to inhomogeneous equations. This method is numerically stable and efficient. It can be directly used for transfer reactions with the formalism discussed by Ascuitto and Glendenning [Phys.…
The global existence and boundedness of solutions to volume-surface reaction diffusion systems with a mass control condition are investigated. Such systems arise typically in e.g. cell biology, ecology or fluid mechanics, when some…
We investigate a broad family of non weakly reversible stochastically modeled reaction networks (CRN), by looking at their steady-state distributions. Most known results on stationary distributions assume weak reversibility and zero…
The convergent reaction-diffusion master equation (CRDME) was recently developed to provide a lattice particle-based stochastic reaction-diffusion model that is a convergent approximation in the lattice spacing to an underlying…
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…
An efficient Monte Carlo simulation method for bosonic reaction-diffusion systems which are mainly used in the renormalization group (RG) study is proposed. Using this method, one dimensional bosonic single species annihilation model is…
We prove that the steady state of a class of multidimensional reaction-diffusion systems is asymptotically stable at the intersection of unweighted space and exponentially weighted Sobolev spaces, and pay particular attention to a special…