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...

Herein, a diffusion model for the dissolution of oxide particles in multicomponent slag systems is developed. It assumed this that sharp-interface separates solid particle from liquid slag. Minimization Gibbs energy provides conditions at interface. The differential equations are solved numerically via finite-difference scheme. indicated parameter studies controlled kinetics may result strongly...

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. ...

The rate of CO binding to myoglobin increases 4-fold, from 5 X 10(5) M-1 s-1 to 2 X 10(6) M-1 s-1, in going from 0 to 80% glycerol in phosphate buffer at pH 7, 20 degrees C. Under the same conditions, the rate of CO binding to protoheme decreases monotonically from about 1 X 10(8) M-1 s-1 to 2 X 10(7) M-1 s-1. The kinetic behavior of protoheme at neutral pH is that expected for a diffusion-cont...

In the presented work CaCO3 powders were produced by controlled fast precipitation through gaseous carbon dioxide absorption in calcium hydroxide slurry. This multiphase reaction was conducted in a modified prototypical rotating disk reactor (RDR). The concept is based on continuous formation of thin liquid films at a surface of rotating discs where the mass transfer proceeds in diffusion-conve...

A stochastic theory of diffusion-controlled reaction is developed with the emphasis on the many-body aspects which rigorous stochastic theories inevitably encounter. The field operator method developed in our previous paper is extensively used in the analysis. The classical Smoluchowski theory is shown to be strictly valid in the long-time scale, and its relation to the Boltzmann equation is di...

The controlled synthesis of terpolymer structures is often limited by the intrinsic reactivities monomers. For a statistical from cyclohexene oxide (CHO) and propylene (PO) with CO2, an instrumental solution demanded. Implementing setup where one monomer can be added to reaction mixture over whole course reaction, random distribution epoxides chain realized. successful terpolymerization determi...