The mesoscopic reaction-diffusion master equation (RDME) is a popular modeling framework frequently applied to stochastic reaction-diffusion kinetics in systems biology. The RDME is derived from assumptions about the underlying physical properties of the system, and it may produce unphysical results for models where those assumptions fail. In that case, other more comprehensive models are bette...

Fluctuations in diffusion-controlled reactions lack the necessary features for a mesoscopic description. We show how the correlations dominate the dynamics by juxtaposing the macroscopic dynamics of a cellular automaton model for the diffusion-controlled limit to the deterministic diffusion-reaction rate equation for the same reaction. A more detailed N-body master equation is then presented in...

1. Electrocatalysis: This is one of the direct examples of the homogeneous reaction diffusion regime. This involves multiple steps, i.e. diffusion, adsorption and a possible charge transfer at the surface (x = 0). As shown in the schematic of Fig(1), species will adsorb on the catalyst surface, then diffuse along the surface to the right/left surfaces where a charge transfer reaction can occur....

In reaction-diffusion (RD) processors, both the data and the results of the computation are encoded as concentration profiles of the reagents. The computation is performed via the spreading and interaction of wave fronts. Most prototypes of RD computers are specialized to solve certain problems, they can not be, in general, re-programmed. In the paper, we try to show possible means of overcomin...

I have recently worked in the area of partial differential equations (PDE), specifically reaction-diffusion equations, drift-diffusion equations, and fluid dynamics. These equations model physical processes such as combustion, mixing, or turbulence, and my main interest has been in long term dynamics of their solutions as well as in the formation of singularities. I consider myself an applied a...

The tutorial introduces a hot topic of novel and emerging computing paradigms and architectures --computation with travelling waves in reaction-diffusion non-linear media. A reaction-diffusion computer is a massively parallel computing device, where micro-volumes of the chemical medium act as elementary few-bit processors; and chemical species diffuse and react in parallel. In the reaction-diff...

These are rough lecture notes for a course on applied math (Math 350), with an emphasis on chemical kinetics, for advanced undergraduate and beginning graduate students in science and mathematics. There are (Fall 2003) three students enrolled: a second year undergraduate with a major in applied mathematics, a senior with majors in mathematics, chemical engineering, and environmental sciences, a...

Multispecies reaction-diffusion systems, for which the time evolution equations of correlation functions become a closed set, are considered. A formal solution for the average densities is found. Some special interactions and the exact time dependence of the average densities in these cases are also studied. For the general case, the large-time behavior of the average densities has also been ob...