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...

In this paper, we present the results of a study on the influence of hydrodynamic effects on the surface potentials of the erythrocyte membrane, comparing two different models formulated to simulate the electrophoretic movement of a biological cell: the classical Helmholtz-Smoluchowski model and a model presented by Hsu et al. (1996). This model considers hydrodynamic effects to describe the di...

We solve the Smoluchowski equation for steady state solutions of rigid nematic polymers and suspensions under imposed elongational flow, magnetic or electric fields, respectively. Under the three imposed fields, we show that (1) the Smoluchowski equation can be cast into a generic form, (2) the external field must parallel to one of the eigenvectors of the second moment tensor in steady states,...

Stochastic reaction-diffusion models have become an important tool in studying how both noise in the chemical reaction process and the spatial movement of molecules influences the behavior of biological systems. There are two primary spatially-continuous models that have been used in recent studies: the diffusion limited reaction model of Smoluchowski, and a second approach popularized by Doi. ...

We demonstrate how many classes of Smoluchowski-type coagulation models can be realised as multiplicative Grassmannian flows and are therefore linearisable, thus integrable in this sense. First, we prove that a general equation with constant frequency kernel, encompasses large class such models, is realisable flow. Second, establish several other related kernel also such. These include: the Gal...

We briefly describe a model which seems to be applicable to a variety of coalescence growth systems. Spanning cluster growth, particle growth and hillockformation in thin metal f%ns, this model is based on the Smoluchowski kinetic equations and fractals. We describe how this model has been able to suggest the e$ect of translational to internal energy conversion in coalescing systems in determin...