Search results for "reaction-diffusion"
showing 10 items of 15 documents
Fully reliable a posteriori error control for evolutionary problems
2015
From classical to operatorial models
2023
Mathematical models for the collective dynamics of interacting and spatially distributed populations find applications in several contexts (biology, ecology, social sciences). Their formulation depends primarily on the (continuous or discrete) description of the space. Reaction-diffusion equations have been widely used in bioecology (morphogenesis, migration of biological species, tumor growth, neuro-degenerative diseases) and in the social sciences (diffusion of opinions or decisionmaking processes), and exhibit complex behaviors (propagation of oscillatory phenomena, pattern formation caused by instability). A reaction–diffusion system exhibits diffusion-driven instability, sometimes call…
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.
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…
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 …
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
A particle method for a Lotka-Volterra system with nonlinear cross and self-diffusion
2008
ANALYTICAL DETERMINATION OF INITIAL CONDITIONS LEADING TO FIRING IN NERVE FIBERS
2007
International audience; An analytical solution characterizing initial conditions leading to action potential firing in smooth nerve fibers is determined, using the bistable equation. In the first place, we present a nontrivial stationary solution wave, then, using the perturbative method, we analyze the stability of this stationary wave. We show that it corresponds to a frontier between the initiation of the travelling waves and a decay to the resting state. Eventually, this analytical approach is extended to FitzHugh-Nagumo model.