Effects of Simulated Diffusion for Simultaneous Reaction and Diffusion Processes

摘要

A new technique is exploited for dynamic studies of reaction-diffusion equations, where the diffusion coefficient consists of a linear combination of terms of different orders. The analysis results in a set of coupled nonlinear equations for the evolution in time of the amplitude and width of 'bell-shaped' structures with given initial profiles, and covers one, two and three spatial dimensions. These equations can be used to describe a number of interesting cases like: explosive localized solutions (ELS), collapse and anti-collapse solutions, etc., as well as dynamic transitions in between these. A process like collapse may, for example, be affected by the influence of stimulated diffusion, and may be reversed by means of such diffusion. It may subsequently approach another state (singleton), exhibiting a characteristic width and attractor-like behaviour. Such a transition is demonstrated in graphs obtained from the coupled nonlinear equations by computer calculations for a 3-D case. Applications in various contexts of plasma physics may be found e.g. in the areas of Z-pinch and plasma focus experiments. (Atomindex citation 20:038961)