The Simulation of Chemical Waves in Excitable Reaction-Diffusion-Convection Systems by Finite Difference and Finite Element Methods
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Waves formed by the propagation of gradients in a supporting medium are an ubiquitous phenomenon in the gaseous, liquid and solid phases of matter. The wave motion and shape are maintained by a supply of energy either internal or external to the system. Familiar examples are water waves and acoustic waves coupled to mechanical energy sources. In recent years a new wave phenomenon has become the focus of scientific interest, namely the propagation of concentration gradients in chemical solutions. Here the medium is active rather than passive, with the internal energy source being provided by the participating chemical reactions. The most thoroughly investigated example of this phenomenon occurs during the oxidative bromination of an organic substrate in the presence of a catalyst. This process, the so-called Belousov-Zhabotinskii (BZ) reaction, was discovered in the fifties by the Russian Belousov who observed in a well-stirred reaction mixture the periodic variation of the concentration of the oxidized form of the cerium redox couple Ce /Ce . Later, Zhabotinskii investigated the underlying reaction mechanism and published results of the first experiments on moving waves in a thin layer of the mixture .
KeywordsDispersion Relation Excitable Medium Malonic Acid Marangoni Convection Singular Perturbation Method
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