The Experts below are selected from a list of 698337 Experts worldwide ranked by ideXlab platform
Irving R. Epstein - One of the best experts on this subject based on the ideXlab platform.
-
breathing spiral waves in the chlorine dioxide iodine malonic acid reaction diffusion System
Physical Review E, 2008Co-Authors: Igal Berenstein, Lingfa Yang, Milos Dolnik, Anatol M. Zhabotinsky, Alberto P Munuzuri, Irving R. EpsteinAbstract:Breathing spiral waves are observed in the oscillatory chlorine dioxide-iodine-malonic acid Reaction-Diffusion System. The breathing develops within established patterns of multiple spiral waves after the concentration of polyvinyl alcohol in the feeding chamber of a continuously fed, unstirred reactor is increased. The breathing period is determined by the period of bulk oscillations in the feeding chamber. Similar behavior is obtained in the Lengyel-Epstein model of this System, where small amplitude parametric forcing of spiral waves near the spiral wave frequency leads to the formation of breathing spiral waves in which the period of breathing is equal to the period of forcing.
-
segmented spiral waves in a reaction diffusion System
Proceedings of the National Academy of Sciences of the United States of America, 2003Co-Authors: Vladimir K Vanag, Irving R. EpsteinAbstract:Pattern formation in Reaction-Diffusion Systems is often invoked as a mechanism for biological morphogenesis. Patterns in chemical Systems typically occur either as propagating waves or as stationary, spatially periodic, Turing structures. The spiral and concentric (target) waves found to date in spatially extended chemical or physical Systems are smooth and continuous; only living Systems, such as seashells, lichens, pine cones, or flowers, have been shown to demonstrate segmentation of these patterns. Here, we report observations of segmented spiral and target waves in the Belousov–Zhabotinsky reaction dispersed in water nanodroplets of a water-in-oil microemulsion. These highly ordered chemical patterns, consisting of short wave segments regularly separated by gaps, form a link between Turing and trigger wave patterns and narrow the disparity between chemistry and biology. They exhibit aspects of such fundamental biological behavior as self-replication of structural elements and preservation of morphology during evolutionary development from a simpler precursor to a more complex structure.
-
Superlattice Turing structures in a photosensitive Reaction-Diffusion System.
Physical review letters, 2003Co-Authors: Igal Berenstein, Lingfa Yang, Milos Dolnik, Anatol M. Zhabotinsky, Irving R. EpsteinAbstract:Families of complex superlattice structures, consisting of combinations of basic hexagonal or square patterns, are found in a photosensitive Reaction-Diffusion System. The structures are induced by simple illumination patterns whose wavelengths are appropriately related to that of the System's intrinsic Turing pattern. Computer simulations agree with the structures and their stability. The technique offers a general approach to generating superlattices for use in information storage and other applications.
-
packet waves in a reaction diffusion System
Physical Review Letters, 2002Co-Authors: Vladimir K Vanag, Irving R. EpsteinAbstract:The finite-wavelength instability gives rise to a new type of wave in Reaction-Diffusion Systems: packet waves, which propagate only within a wave packet, are found in experiments on the Belousov-Zhabotinsky reaction dispersed in water-in-oil AOT microemulsion (BZ-AOT) as well as in model simulations. Inwardly moving packet waves with negative curvature occur in experiments and in a model of the BZ-AOT System when the dispersion d omega(k)/dk is negative at the characteristic wave number k(0). This result sheds light on the origin of anti-spirals.
Salem Abdelmalek - One of the best experts on this subject based on the ideXlab platform.
-
invariant regions and existence of global solutions to a generalized m component reaction diffusion System with tridiagonal symmetric toeplitz diffusion matrix
Advances in Pure and Applied Mathematics, 2021Co-Authors: Karima Abdelmalek, Belgacem Rebiai, Salem AbdelmalekAbstract:The aim of this paper is to construct invariant regions of a generalized m-component Reaction-Diffusion System with tridiagonal symmetric Toeplitz diffusion matrix and nonhomogeneous boundary conditions and polynomial growth for the nonlinear reaction terms. Using the eigenvalues and eigenvectors of the diffusion matrix and the parabolicity conditions. So we prove the global existence of solutions using Lyapunov functional.
-
Extended Global Asymptotic Stability Conditions for a Generalized Reaction–Diffusion System
Acta Applicandae Mathematicae, 2019Co-Authors: Salem Abdelmalek, Samir Bendoukha, Belgacem Rebiai, Mokhtar KiraneAbstract:In this paper, we consider the general reaction–diffusion System proposed in Abdelmalek and Bendoukha (Nonlinear Anal., Real World Appl. 35:397–413, 2017 ) as a generalization of the original Lengyel–Epstein model developed for the revolutionary Turing-type CIMA reaction. We establish sufficient conditions for the global existence of solutions. We also follow the footsteps of Lisena (Appl. Math. Comput. 249:67–75, 2014 ) and other similar studies to extend previous results regarding the local and global asymptotic stability of the System. In the local PDE sense, more relaxed conditions are achieved compared to Abdelmalek and Bendoukha (Nonlinear Anal., Real World Appl. 35:397–413, 2017 ). Also, new extended results are achieved for the global existence, which when applied to the Lengyel–Epstein System, provide weaker conditions than those of Lisena (Appl. Math. Comput. 249:67–75, 2014 ). Numerical examples are used to affirm the findings and benchmark them against previous results.
-
global existence of solutions for an m component reaction diffusion System with a tridiagonal 2 toeplitz diffusion matrix and polynomially growing reaction terms
arXiv: Analysis of PDEs, 2016Co-Authors: Salem Abdelmalek, Samir BendoukhaAbstract:This paper is concerned with the local and global existence of solutions for a generalized $m$-component reaction--diffusion System with a tridiagonal $2$--Toeplitz diffusion matrix and polynomial growth. We derive the eigenvalues and eigenvectors and determine the parabolicity conditions in order to diagonalize the proposed System. We, then,determine the invariant regions and utilize a Lyapunov functional to establish the global existence of solutions for the proposed System. A numerical example is used to illustrate and confirm the findings of the study.
-
Global existence of solutions for an $m$-component reaction--diffusion System with a tridiagonal 2-Toeplitz diffusion matrix and polynomially growing reaction terms
arXiv: Analysis of PDEs, 2016Co-Authors: Salem Abdelmalek, Samir BendoukhaAbstract:This paper is concerned with the local and global existence of solutions for a generalized $m$-component reaction--diffusion System with a tridiagonal $2$--Toeplitz diffusion matrix and polynomial growth. We derive the eigenvalues and eigenvectors and determine the parabolicity conditions in order to diagonalize the proposed System. We, then,determine the invariant regions and utilize a Lyapunov functional to establish the global existence of solutions for the proposed System. A numerical example is used to illustrate and confirm the findings of the study.
Danielle Hilhorst - One of the best experts on this subject based on the ideXlab platform.
-
a fast precipitation and dissolution reaction for a reaction diffusion System arising in a porous medium
Nonlinear Analysis-real World Applications, 2009Co-Authors: Nicolas Bouillard, Robert Eymard, Marie Henry, Raphaele Herbin, Danielle HilhorstAbstract:Abstract This paper is devoted to the study of a fast reaction–diffusion System arising in reactive transport. It extends the articles [R. Eymard, T. Gallouet, R. Herbin, D. Hilhorst, M. Mainguy, Instantaneous and noninstantaneous dissolution: Approximation by the finite volume method, ESAIM Proc. (1998); J. Pousin, Infinitely fast kinetics for dissolution and diffusion in open reactive Systems, Nonlinear Anal. 39 (2000) 261–279] since a precipitation and dissolution reaction is considered so that the reaction term is not sign-definite and is moreover discontinuous. Energy type methods allow us to prove uniform estimates and then to study the limiting behavior of the solution as the kinetic rate tends to infinity in the special situation of one aqueous species and one solid species.
-
A fast precipitation and dissolution reaction for a reaction–diffusion System arising in a porous medium☆
Nonlinear Analysis: Real World Applications, 2009Co-Authors: Nicolas Bouillard, Robert Eymard, Marie Henry, Raphaele Herbin, Danielle HilhorstAbstract:Abstract This paper is devoted to the study of a fast reaction–diffusion System arising in reactive transport. It extends the articles [R. Eymard, T. Gallouet, R. Herbin, D. Hilhorst, M. Mainguy, Instantaneous and noninstantaneous dissolution: Approximation by the finite volume method, ESAIM Proc. (1998); J. Pousin, Infinitely fast kinetics for dissolution and diffusion in open reactive Systems, Nonlinear Anal. 39 (2000) 261–279] since a precipitation and dissolution reaction is considered so that the reaction term is not sign-definite and is moreover discontinuous. Energy type methods allow us to prove uniform estimates and then to study the limiting behavior of the solution as the kinetic rate tends to infinity in the special situation of one aqueous species and one solid species.
-
A fast precipitation and dissolution reaction for a reaction diffusion System arising in a porous medium
ESAIM: Mathematical Modelling and Numerical Analysis, 2007Co-Authors: Nicolas Bouillard, Robert Eymard, Marie Henry, Raphaele Herbin, Danielle HilhorstAbstract:This paper is devoted to the study of a fast reaction diffusion System arising in reactive transport. It extends previous articles since a precipitation and dissolution reaction is considered so that the reaction term is not sign-definite and is moreover discontinuous. %Therefore the reaction term is discontinuous and of unknown sign. %Monotonicity methods allow to prove uniform estimates and then to Energy type methods allow us to prove uniform estimates and then to study the limiting behavior of the solution as the kinetic rate tends to infinity in the special situation of one aqueous species and one solid species.
Michel Pierre - One of the best experts on this subject based on the ideXlab platform.
-
Cross-Diffusion Limit for a Reaction-Diffusion System with Fast Reversible Reaction
Communications in Partial Differential Equations, 2012Co-Authors: Dieter Bothe, Michel Pierre, Guillaume RollandAbstract:We consider a Reaction-Diffusion System which models a fast reversible reaction of type $C_1 + C_2 = C_3$ between mobile reactants inside an isolated vessel. Assuming mass action kinetics, we study the limit when the reaction speed tends to infinity in case of unequal diffusion coefficients and prove convergence of a subsequence of solutions to a weak solution of an appropriate limiting pde-System, where the limiting problem turns out to be of cross-diffusion type. The proof combines the $L^2$-approach to Reaction-Diffusion Systems having at most quadratic reaction terms with a thorough exploitation of the entropy functional for mass action Systems. The limiting cross-diffusion System has unique local strong solutions for sufficiently regular initial data, while uniqueness of weak solutions is in general open but is shown to be valid under restrictions on the diffusivities.
-
quasi steady state approximation for a reaction diffusion System with fast intermediate
Journal of Mathematical Analysis and Applications, 2010Co-Authors: Dieter Bothe, Michel PierreAbstract:Abstract We consider a prototype reaction–diffusion System which models a network of two consecutive reactions in which chemical components A and B form an intermediate C which decays into two products P and Q. Such a situation often occurs in applications and in the typical case when the intermediate is highly reactive, the species C is eliminated from the System by means of a quasi-steady-state approximation. In this paper, we prove the convergence of the solutions in L 2 , as the decay rate of the intermediate tends to infinity, for all bounded initial data, even in the case of initial boundary layers. The limiting System is indeed the one which results from formal application of the QSSA. The proof combines the recent L 2 -approach to reaction–diffusion Systems having at most quadratic reaction terms, with local L ∞ -bounds which are independent of the decay rate of the intermediate. We also prove existence of global classical solutions to the initial System.
-
Quasi-steady-state approximation for a reaction–diffusion System with fast intermediate
Journal of Mathematical Analysis and Applications, 2010Co-Authors: Dieter Bothe, Michel PierreAbstract:Abstract We consider a prototype reaction–diffusion System which models a network of two consecutive reactions in which chemical components A and B form an intermediate C which decays into two products P and Q. Such a situation often occurs in applications and in the typical case when the intermediate is highly reactive, the species C is eliminated from the System by means of a quasi-steady-state approximation. In this paper, we prove the convergence of the solutions in L 2 , as the decay rate of the intermediate tends to infinity, for all bounded initial data, even in the case of initial boundary layers. The limiting System is indeed the one which results from formal application of the QSSA. The proof combines the recent L 2 -approach to reaction–diffusion Systems having at most quadratic reaction terms, with local L ∞ -bounds which are independent of the decay rate of the intermediate. We also prove existence of global classical solutions to the initial System.
Igal Berenstein - One of the best experts on this subject based on the ideXlab platform.
-
breathing spiral waves in the chlorine dioxide iodine malonic acid reaction diffusion System
Physical Review E, 2008Co-Authors: Igal Berenstein, Lingfa Yang, Milos Dolnik, Anatol M. Zhabotinsky, Alberto P Munuzuri, Irving R. EpsteinAbstract:Breathing spiral waves are observed in the oscillatory chlorine dioxide-iodine-malonic acid Reaction-Diffusion System. The breathing develops within established patterns of multiple spiral waves after the concentration of polyvinyl alcohol in the feeding chamber of a continuously fed, unstirred reactor is increased. The breathing period is determined by the period of bulk oscillations in the feeding chamber. Similar behavior is obtained in the Lengyel-Epstein model of this System, where small amplitude parametric forcing of spiral waves near the spiral wave frequency leads to the formation of breathing spiral waves in which the period of breathing is equal to the period of forcing.
-
Superlattice Turing structures in a photosensitive Reaction-Diffusion System.
Physical review letters, 2003Co-Authors: Igal Berenstein, Lingfa Yang, Milos Dolnik, Anatol M. Zhabotinsky, Irving R. EpsteinAbstract:Families of complex superlattice structures, consisting of combinations of basic hexagonal or square patterns, are found in a photosensitive Reaction-Diffusion System. The structures are induced by simple illumination patterns whose wavelengths are appropriately related to that of the System's intrinsic Turing pattern. Computer simulations agree with the structures and their stability. The technique offers a general approach to generating superlattices for use in information storage and other applications.
