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...

This Letter proposes generalized reaction–diffusion equations for treating noisy magnetic resonance images. An edge-enhancing functional is introduced for image enhancement. A number of super-diffusion operators are introduced for fast and effective smoothing. Statistical information is utilized for robust edge-stopping and diffusion-rate estimation. A quasi-interpolating wavelet algorithm is u...

Reaction-diffusion systems produce a variety of patterns such as spots, labyrinths, and rotating spirals. Circular spots may be stationary or unstable to oscillating motion. The oscillations are sometimes steady but may lead to collapsing or infinitely expanding spots. Using a singular perturbation technique we derive a set of ordinary differential equations for the dynamics of circular spots. ...

<p style='text-indent:20px;'>In this paper we analyse the asymptotic behaviour of some nonlocal diffusion problems with local reaction term in general metric measure spaces. We find certain classes nonlinear terms, including logistic type for which solutions are globally defined initial data Lebesgue prove satisfy maximum and comparison principles give sign conditions to ensure global bou...

the kinetic of the heterogeneous chemical reaction of aluminum hydroxide and fluosilicic acid was studied. it was found that the diffusion of the reactants through the porous silica coating to the aluminum hydroxide surface and the interfacial chemical reaction between the diffusing reactant and aluminum hydroxide platelets control the overall reaction rate. these two phenomena were studied and...