Search results for " Reaction-diffusion"

Global stability of coupled Markovian switching reaction–diffusion systems on networks

2014

Abstract In this paper, we investigate the stability problem for some Markovian switching reaction–diffusion coupled systems on networks (MSRDCSNs). By using the Lyapunov function, we establish some novel stability principles for stochastic stability, asymptotically stochastic stability, globally asymptotically stochastic stability and almost surely exponential stability of the MSRDCSNs. These stability principles have a close relation to the topology property of the network. We also provide a systematic method for constructing global Lyapunov function for these MSRDCSNs by using graph theory. The new method can help analyze the dynamics of complex networks.

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…

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

Dynamiques de populations en milieu hétérogène : modèles et estimation de paramètres

2017

Prod 2017-344i SPE équipe EA GESTAD INRA; National audience; Cet exposé traite de (i) la modélisation de dynamiques de populations dans des paysages hétérogènes, (ii) la modélisation des paysages eux-mêmes, (iii) l'estimation des paramètres de ces modèles à partir de données d'abondance ou de données génétiques. Nous nous concentrerons sur deux grandes classes de modèles de dynamique des populations : les modèles individu-centrés basés sur des équations différentielles stochastiques, et les modèles de réaction-diffusion. Après une introduction du lien entre ces approches, 5 illustrations issues des projets sont présentées: - modélisation de paysages hétérogènes fragmentés, via l’outil MULTI…

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.