Search results for "reaction-diffusion"

A velocity–diffusion method for a Lotka–Volterra system with nonlinear cross and self-diffusion

2009

The aim of this paper is to introduce a deterministic particle method for the solution of two strongly coupled reaction-diffusion equations. In these equations the diffusion is nonlinear because we consider the cross and self-diffusion effects. The reaction terms on which we focus are of the Lotka-Volterra type. Our treatment of the diffusion terms is a generalization of the idea, introduced in [P. Degond, F.-J. Mustieles, A deterministic approximation of diffusion equations using particles, SIAM J. Sci. Stat. Comput. 11 (1990) 293-310] for the linear diffusion, of interpreting Fick's law in a deterministic way as a prescription on the particle velocity. Time discretization is based on the …

Fully reliable a posteriori error control for evolutionary problems

2015

Pattern formation and bifurcation analysis for some chemotaxis-reaction-diffusion systems

A posteriori error estimates for time-dependent reaction-diffusion problems based on the Payne-Weinberger inequality

2015

We consider evolutionary reaction-diffusion problem with mixed Dirichlet--Robin boundary conditions. For this class of problems, we derive two-sided estimates of the distance between any function in the admissible energy space and exact solution of the problem. The estimates (majorants and minorants) are explicitly computable and do not contain unknown functions or constants. Moreover, it is proved that the estimates are equivalent to the energy norm of the deviation from the exact solution.

Exploiting Reaction-Diffusion Conditions to Trigger Pathway Complexity in the Growth of a MOF.

2021

Coordination polymers (CPs), including metal–organic frameworks (MOFs), are crystalline materials with promising applications in electronics, magnetism, catalysis, and gas storage/separation. However, the mechanisms and pathways underlying their formation remain largely undisclosed. Herein, we demonstrate that diffusion-controlled mixing of reagents at the very early stages of the crystallization process (i.e., within ≈40 ms), achieved by using continuous-flow microfluidic devices, can be used to enable novel crystallization pathways of a prototypical spin-crossover MOF towards its thermodynamic product. In particular, two distinct and unprecedented nucleation-growth pathways were experimen…

Stationary, Oscillatory, Spatio-Temporal Patterns and Existence of Global Solutions in Reaction-Diffusion Models of Three Species

2023

The goal of my Ph.D. research is to analyze three species models in order to describe the behavior of an ecological community. In particular, two reaction-diffusion systems describing different local interactions between three species have been considered to obtain species coexistence, diversity, and distribution patterns. The first analyzed model describes intraguild predation: there are an IG-predator species, an IG-prey species, and a common resource species, which is shared by both of them. The IGP interaction is of Lotka-Volterra type, coupled with nonlinear diffusion, since we assume that the IG-prey moves towards lower density areas of the IG-predator. In this model, the extinction o…

Weakly nonlinear analysis of Turing patterns in a morphochemical model for metal growth

2015

We focus on the morphochemical reaction–diffusion model introduced in Bozzini et al. (2013) and carry out a nonlinear bifurcation analysis with the aim to characterize the shape and the amplitude of the patterns arising as the result of Turing instability of the physically relevant equilibrium. We perform a weakly nonlinear multiple scales analysis, and derive the normal form equations governing the amplitude of the patterns. These amplitude equations allow us to construct relevant solutions of the model equations and reveal the presence of multiple branches of stable solutions arising as the result of subcritical bifurcations. Hysteretic type phenomena are highlighted also through numerica…

On Some Applications of Nonlinear Differential Equations in Image Processing: Concepts and Electronic Implementation

2011

International audience

A particle method for a Lotka-Volterra system with nonlinear cross and self-diffusion

2008

On new ways of group methods for reduction of evolution-type equations

2005

AbstractNew exact solutions of the evolution-type equations are constructed by means of a non-point (contact) symmetries. Also we analyzed the discrete symmetries of Maxwell equations in vacuum and decoupled ones to the four independent equations that can be solved independently.