Search results for "Reaction–diffusion system"
showing 9 items of 29 documents
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.
Self-organization in the A + B → 0 reaction of charged particles
1992
The formalism of many-particle densities developed earlier by the authors is applied to the study of the self-organization phenomena occuring during the course of the bimolecular A + B → 0 reaction between charged particles, interacting via the Coulomb law. Unlike the Debye-Huckel theory, charge screening has an essentially non-equilibrium character. It is shown that for the asymmetric mobility of reactants (DA = 0, DB ≠ 0) similar immobile reactants A form aggregates characterized by a sharp maximum, observed at short distances, in the joint correlation function XA(r, t). Such an aggregation leads to the accelerated particle recombination n ∝ t-54 (nA = nB = n) instead of the generally acc…
Formation of dislocation patterns: Computer simulations
1996
Dislocations patterns have been extensively studied by means of TEM. In parallel, theoretical approaches have been developed by using two methods; reaction diffusion schemes and computer simulation models. This distinction is not rigid since some computer models include the former approach in their evolution equations. Independently from the difficulties each approach presents in formulating the collective behavior of dislocations, the aim of these studies is to exhibit simple dislocation patterns as persistent slip bands and/or cellular organization. In this context, computer simulations brought a methodology which undoubtedly is a complement to the existing approaches for dislocations. Ne…
Turing instability and traveling fronts for a nonlinear reaction–diffusion system with cross-diffusion
2012
In this work we investigate the phenomena of pattern formation and wave propagation for a reaction–diffusion system with nonlinear diffusion. We show how cross-diffusion destabilizes uniform equilibrium and is responsible for the initiation of spatial patterns. Near marginal stability, through a weakly nonlinear analysis, we are able to predict the shape and the amplitude of the pattern. For the amplitude, in the supercritical and in the subcritical case, we derive the cubic and the quintic Stuart–Landau equation respectively. When the size of the spatial domain is large, and the initial perturbation is localized, the pattern is formed sequentially and invades the whole domain as a travelin…
Propagation failure in discrete bistable reaction-diffusion systems: Theory and experiments
2001
International audience; Wave front propagation failure is investigated in discrete bistable reaction-diffusion systems. We present a theoretical approach including dissipative effects and leading to an analytical expression of the critical coupling beyond which front propagation can occur as a function of the nonlinearity threshold parameter. Our theoretical predictions are confirmed by numerical simulations and experimental results on an equivalent electrical diffusive lattice.
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…
An atlas- and data-driven approach to initializing reaction-diffusion systems in computer cardiac electrophysiology
2016
The cardiac electrophysiology (EP) problem is governed by a nonlinear anisotropic reaction-diffusion system with a very rapidly varying reaction term associated with the transmembrane cell current. The nonlinearity associated with the cell models requires a stabilization process before any simulation is performed. More importantly, when used in a 3-dimensional (3D) anatomy, it is not sufficient to perform this stabilization on the basis of isolated cells only, since the coupling of the different cells through the tissue greatly modulates the dynamics of the system. Therefore, stabilization of the system must be performed on the entire 3D model. This work develops a novel procedure for the i…
Reaction-Diffusion Network For Geometric Multiscale High Speed Image Processing
2010
International audience; In the framework of heavy mid-level processing for high speed imaging, a nonlinear bi-dimensional network is proposed, allowing the implementation of active curve algorithms. Usually this efficient type of algorithm is prohibitive for real-time image processing due to its calculus charge and the inadequate structure for the use of serial or parallel architectures. Another kind of implementation philosophy is proposed here, by considering the active curve generated by a propagation phenomenon inspired from biological modeling. A programmable nonlinear reaction-diffusion system is proposed under front control and technological constraints. Geometric multiscale processin…
On Some Applications of Nonlinear Differential Equations in Image Processing: Concepts and Electronic Implementation
2011
International audience