Non-equilibrium dynamics of reaction-diffusion systems

Thesis



Fluctuations are known to radically alter the behaviour of reaction-diffusion systems. Below a certain upper critical dimension d_c , this effect results in the breakdown of traditional approaches, such as mean field rate equations. In this thesis we tackle this fluctuation problem by employing systematic field theoretic/renormalisation group methods, which enable perturbative calculations to be made below d_c.

We first consider a steady state reaction front formed in the two species irreversible reaction A + B → Ø. In one dimension we demonstrate that there are two components to the front - one an intrinsic width, and one caused by the ability of the centre of the front to wander. We make theoretical predictions for the shapes of these components, which are found to be in good agreement with our one dimensional simulations. In higher dimensions, where the intrinsic component dominates, we also make calculations for its asymptotic profile. Furthermore, fluctuation effects lead to a prediction of asymptotic power law tails in the intrinsic front in all dimensions. This effect causes high enough order spatial moments of a time dependent reaction front to exhibit multiscaling.

The second system we consider is a time dependent multispecies reaction-diffusion system with three competing reactions A+A → Ø, B + B → Ø, and A + B → Ø, starting with homogeneous initial conditions. Using our field theoretic formalism we calculate the asymptotic density decay rates for the two species for d ≤ d_c. These calculations are compared with other approximate methods, such as the Smoluchowski approach, and also with previous simulations and exact results.

Authors: Howard, M; Howard, Martin

• Publication date: 1996
• DOI: 10.5287/ora-2a8nn1yad
• Type of award: DPhil
• Level of award: Doctoral
• Awarding institution: University of Oxford
• Language: English
• Subjects: Reaction-diffusion equations