Fluctuation effects in steric reaction-diffusion systems

Fluctuation effects in steric reaction-diffusion systems

We propose a simple model for reaction-diffusion systems with orientational constraints on the reactivity of particles, and map it onto a field theory with upper critical dimension dc52. To the two-loop level, long-time particle density N(t) is given by the same universal expression as for a nonsteric system, with N(t);t for d<2. For slow rotations of the particles we find an intermediate regim...

Fluctuation-regularized front propagation dynamics in reaction-diffusion systems.

We introduce and study a new class of fronts in finite particle-number reaction-diffusion systems, corresponding to propagating up a reaction-rate gradient. We show that these systems have no traditional mean-field limit, as the nature of the long-time front solution in the stochastic process differs essentially from that obtained by solving the mean-field deterministic reaction-diffusion equat...

Fluctuation Kinetics in a Multispecies Reaction-Diffusion System

We study fluctuation effects in a two species reaction-diffusion system, with three competing reactions A + A → ∅, B + B → ∅, and A + B → ∅. Asymptotic density decay rates are calculated for d ≤ 2 using two separate methods the Smoluchowski approximation, and also field theoretic/renormalisation group (RG) techniques. Both approaches predict power law decays, with exponents which asymptotically...

Pattern formation in reaction-diffusion and reaction-diffusion-convection systems

Diffusion-Driven Instability in Reaction Diffusion Systems

For a stable matrix A with real entries, sufficient and necessary conditions for A D to be stable for all non-negative diagonal matrices D are obtained. Implications of these conditions for the stability and instability of constant steadystate solutions to reaction diffusion systems are discussed and an example is given to show applications. 2001 Academic Press