Mathematical Sciences: Pattern Formation Relevant to Turing and Morphological Instabilities: Comparison of Theory with Experiment

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9531797 Wollkind The development of one- and two-dimensional Turing patterns characteristic of the chlorite-iodide-malonic acid/indicator reaction occurring in an open gel continuously fed unstirred reactor is to be investigated by means of various weakly nonlinear stability analyses applied to the appropriately scaled govern- ing chlorine dioxide-iodine-malonic acid/indicator model system. It is then proposed that the resulting theoretical predictions deduced from these pattern formation studies be compared both with the recent experimental evidence rele- vant to the diffusive instabilities under examination which consist of stripes, rhombic arrays of rectangles, and hexagonal arrays of spots or nets, and with similar equilibrium structures characteristic of a diffusion system used to model interfacial morphologies observed during alloy solidification. The ra- tionale for these comparisons is to explain more fully the transition to such stationary symmetry breaking spatial Turing structures when the malonic acid reservoir concentration varies in the first case and to examine the unifying as well as divergent aspects of the model systems in the second. Finally the nonequilibrium Turing and morphological instabilities of chemical turbulence and cellular dendrites, respectively, are to be investigated by application of a numerical bifurcation code to the amplitude equations of nonlinear stability theory in the appropriate parameter ranges for these two phenomena. The antici- pated results of this research have the potential to contribute to the under- standing of pattern formation in a wide variety of application areas. %%% The long-term goal of this project is to develop the simplest reasonable natu- ral science models which preserve the essential features of pattern formation while still being consistent with observation. The candidates for such mathe- matical modeling are those structures generated during chemical reactions in gels and during the solidif ication of two-component mixtures, respectively. Quantification of that sort would allow an experimentalist to obtain a desired outcome without wasting the time and money caused by repeated unsuccessful trials. The relevant application areas for this work range from combustion theory and other energy related interactions to materials processing involving semi-conductor production and steel manufacturing. ***