Related papers: Bifurcation Analysis of Reaction Diffusion Systems…
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…
Reaction-diffusion equations are often used in epidemiological models. In this paper we generalize the algorithm of Meerschaert and Tadjeran for fractional advection-dispersion flow equations to a coupled system of fractional…
The reaction-diffusion equation is one of the cornerstones equations in applied science and engineering. In the present study, a deep neural network has been trained in order to predict the solution of the equation with different…
Many astrophysical systems can only be accurately modelled when the behaviour of their baryonic gas components is well understood. The residual distribution (RD) family of partial differential equation (PDE) solvers produce approximate…
Nonlinear phenomena such as optical bistability and spontaneous symmetry breaking play a central role in Kerr resonators, and are increasingly exploited in photonic integrated circuits for all-optical information processing. In this work,…
Model analogies and exchange of ideas between physics or chemistry with biology or epidemiology have often involved inter-sectoral mapping of techniques. Material mechanics has benefitted hugely from such interpolations from mathematical…
In the current work we consider the numerical solutions of equations of stationary states for a general class of the spatial segregation of reaction-diffusion systems with $m\geq 2$ population densities. We introduce a discrete multi-phase…
The aim of this work is to study the effect of diffusion on the stability of the equilibria in a general two-components reaction-diffusion system with Neumann boundary conditions in the space of continuous functions. As by product, we…
We present a new methodology for efficient and high-quality patterning of biological reagents for surface-based biological assays. The method relies on hydrodynamically confined nanoliter volumes of reagents to interact with the substrate…
We survey recent results on reaction-diffusion equations with discontinuous hysteretic nonlinearities. We connect these equations with free boundary problems and introduce a related notion of spatial transversality for initial data and…
There is today a growing need to accurately model the angular scattering response of metasurfaces for optical analog processing applications. However, the current metasurface modeling techniques are not well suited for such a task since…
We propose an adaptive finite element method to approximate the solutions to reaction-diffusion systems on time-dependent domains and surfaces. We derive a computable error estimator that provides an upper bound for the error in the…
Accurately modelling cold and ultracold reactive collisions occuring over deep potential wells, such as \ce{D+ + H2 -> H+ + HD}, requires the development of new theoretical and computational methodologies. One potentially useful framework…
Models of reaction diffusion processes usually employ discrete lattice models with particles interacting at the same site, resulting in localized reactions in the continuum limit. Here, various non-local interactions are considered, and two…
Mass conservation in chemical species appears in a broad class of reaction-diffusion systems (RDs) and is known to bring about coarsening of the pattern in chemical concentration. Recent theoretical studies on RDs with mass conservation…
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.…
Reaction-Diffusion equations can present solutions in the form of traveling waves. Such solutions evolve in different spatial and temporal scales and it is desired to construct numerical methods that can adopt a spatial refinement at…
Derivation of macroscopic models for advection-diffusion processes in the presence of dominant heterogeneous (e.g., surface) reactions using homogenisation theory or volume averaging is often deemed unfeasible due to the strong coupling…
In this article, we systematically explain how to apply the analytical technique called the invariant subspace method to find various types of analytical solutions for a coupled nonlinear time-fractional system of partial differential…
The replication and differentiation of spots in reaction diffusion equations are studied by extending the Gray-Scott model with self-replicating spots to include many degrees of freedom needed to model systems with many chemicals. By…