Date of Graduation

1996

Document Type

Dissertation/Thesis

Abstract

Competition and convection effects in reaction-diffusion fronts and controlling chaos are studied. In Chapter 3 we report theoretical studies of competition in which two self-replicating organic molecules compete for a common reactant. We found that the self-replicating organic molecule can give sustained reaction-diffusion fronts. This phenomenon is investigated by numerical solutions of partial differential equations that couple local nonlinear kinetics and diffusion. Reaction-diffusion fronts involving competing species are then initiated and the concentration profiles of the autocatalysts monitored. The results show that the more reactive species totally predominates over the less reactive species as its front moves ahead into the fresh reactant solution and consuming all of the common resource. Observations of steady nonaxisymmetric chemical reaction-reaction diffusion fronts in an upward propagation in iodate-arsenous acid solutions within vertical tubes are reported in Chapter 4. These observations confirm theoretical predictions of hydrodynamic stability theory that the onset of convection in such fronts should be nonaxisymmetrical. The nonaxisymmetric waveform reflects the presence of a single convective roll in the vicinity of the moving front. The Belousov-Zhabotinsky reaction exhibits deterministic chaos which is characterized by long term unpredictability arising from extreme sensitivity to initial conditions. Feedback algorithms have been used to stabilize periodic oscillations in chaotic systems like laser, diodes and myocardial tissue. In chapter 5 we report the stabilization of periodic behavior in the BZ reaction, the first example of controlling chaos in a chemical system. Unstable periodic orbits are stabilized by supplying small, controlled perturbations to a system constraint according to a map-based, proportional-feedback algorithm.

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