In systems undergoing chemical reaction and diffusion, a remarkable variety of spatially structured patterns, stationary or moving, local or global, can arise, many of them reminiscent of forms and phenomena seen in living systems. Chemical systems offer the advantage that one can often control the parameters that determine the patterns formed and can thereby probe fundamental issues about patt...

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The spatially distributed reaction networks are indispensable for the understanding of many important phenomena concerning the development of organisms, coordinated cell behavior, and pattern formation. The purpose of this brief discussion paper is to point out some open problems in the theory of PDE and compartmental ODE models of balanced reactiondiffusion networks.

We develop numerical methods for reaction-diffusion systems based on the equations of fluctuating hydrodynamics (FHD). While the FHD formulation is formally described by stochastic partial differential equations (SPDEs), it becomes similar to the reaction-diffusion master equation (RDME) description when those SPDEs are spatially discretized and reactions are modeled as a source term having Poi...

A model of a galactic disk is presented which extends the homogeneous one zone models by incorporating propagation of material and energy in the disk. For reasonable values of the parameters the homogeneous steady state is unstable to the development of inhomogeneities, leading to the development of spatial and temporal structure. At the linearized level a prediction for the length and time sca...

The authors investigate the solution of a nonlinear reaction-diffusion equation connected with nonlinear waves. The equation discussed is more general than the one discussed recently by Manne, Hurd, and Kenkre (2000). The results are presented in a compact and elegant form in terms of Mittag-Leffler functions and generalized Mittag-Leffler functions, which are suitable for numerical computation...

Supplementary data rsta.2012.0179.DC1.html http://rsta.royalsocietypublishing.org/content/suppl/2012/11/23/ "Presentation at Turbulent Mixing and Beyond conference" References 79.full.html#ref-list-1 http://rsta.royalsocietypublishing.org/content/371/1982/201201 This article cites 62 articles Subject collections (52 articles) mathematical physics • collections Articles on similar topics can be...

(1) ut = Auxx + f(u), u ∈ R , x ∈ R, t ∈ [0,∞), where A is a real, positive-definite, N × N matrix and f : R → R is a continuously differentiable nonlinear function. The vector u may represent, for example, the concentrations of chemicals or the population densities of interacting species, the interactions between components of u being modelled by the reaction term f(u) and their diffusion by A...

Reaction-diffusion system The R-D system is a nonequilibrium chemical system consisting of two or more chemicals in which chemical reaction and diffusion coexist under open conditions. It produces orderly spatiotemporal patterns of chemical concentration called the dissipative structure; a simple instance is shown in Fig. 1 (a). Various RD systems exist in nature, and a wide variety of dynamic,...

Reaction-diffusion approach has been used to explain pattern formation arising in neurobiology, chemical physics, population ecology, developmental biology and other fields. Despite its simple structure, a class of reaction-diffusion systems exhibit a lot of spatial and spatio-temporal patterns. Some of these patterns in a reacting and diffusing medium can be often observed by internal layers o...