Large-scale emergent properties of an autocatalytic reaction-diffusion model subject to noise

Large-scale emergent properties of an autocatalytic reaction-diffusion model subject to noise.

The nonequilibrium dynamic fluctuations of a stochastic version of the Gray-Scott (GS) model are studied analytically in leading order in perturbation theory by means of the dynamic renormalization group. There is an attracting stable fixed point at one-loop order, and the asymptotic scaling of the correlation functions is predicted for both spatial and temporally correlated noise sources. New ...

Small-scale properties of a stochastic cubic-autocatalytic reaction-diffusion model.

We investigate the small-scale properties of a stochastic cubic-autocatalytic reaction-diffusion (CARD) model using renormalization techniques. We renormalize noise-induced ultraviolet divergences and obtain β functions for the decay rate and coupling at one loop. Assuming colored (power-law) noise, our results show that the behavior of both decay rate and coupling with scale depends crucially ...

Dynamics of a Reaction-diffusion System of Autocatalytic Chemical Reaction

The precise dynamics of a reaction-diffusion model of autocatalytic chemical reaction is described. It is shown that exactly either one, two, or three steady states exists, and the solution of dynamical problem always approaches to one of steady states in the long run. Moreover it is shown that a global codimension one manifold separates the basins of attraction of the two stable steady states....

Autocatalytic reaction-diffusion processes in restricted geometries

We study the dynamics of a system made up of particles of two different species undergoing irreversible quadratic autocatalytic reactions: A + B → 2A. We especially focus on the reaction velocity and on the average time at which the system achieves its inert state. By means of both analytical and numerical methods, we are also able to highlight the role of topology in the temporal evolution of ...

Large scale reaction front dynamics in anisotropic reaction-diffusion systems