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42222-AC6
Localized Structures in Reaction-Diffusion Systems
During the past year, we have made significant progress in developing the theory of localized structures in reaction-diffusion systems while continuing our efforts to realize in the laboratory some of the structures predicted by our analysis and simulations. Our primary experimental system has been the oscillatory Belousov-Zhabotinsky (BZ) reaction in an aerosol OT water-in-oil reverse microemulsion. By varying the relative amounts of oil, water and surfactant, we can control the size and spacing of the water nanodroplets, while setting the concentrations of the BZ reactants gives us control over the chemistry as well. By using a photosensitive ruthenium complex as the catalyst, we obtain the ability to manipulate the system with light. Since these experiments are done in a thin (0.1 mm) layer, they are effectively two-dimensional. Recently we have developed the ability, using microfluidic techniques, to study larger (ca. 100 micron) aqueous droplets of BZ solution separated by droplets of oil in a one-dimensional (capillary tube) geometry. We are able to vary the sizes of the water droplets and their separation over a considerable range. We have obtained both stationary and oscillatory localized structures in the 2D system and are have begun initial experiments to search for localized structures in the 1D geometry.
In an analytical/numerical study of a nonlinear wave equation, we were able to obtain the equation of motion for fronts in one and two dimensions in systems with global inhibitory feedback. These fronts separate localized regions of one state from regions of a second stationary state. The motion of interfaces is found to be qualitatively different from, and much richer than that of its counterpart with no global coupling.
Our simulations of reaction-diffusion models have revealed a number of novel localized phenomena. In a numerical study of a three-variable model due to Purwins, we find jumping solitary waves, which propagate in such a manner that the pulse periodically disappears from its original position and reemerges at a fixed distance. These waves, which have not previously been reported, combine features of both solitons and oscillons: constant motion and sustained oscillation. It appears that it may be possible, in the photosensitive version of the BZ-AOT system, to realize experimentally the conditions that the simulations suggest are required for the existence of such waves.
In another numerical study using the Brusselator model, we examined wave propagation, interaction, and transmission across the boundary between two chemical media in an oscillatory reaction-diffusion medium subjected to local periodic forcing. Inwardly and outwardly propagating waves behave quite differently from one another, particularly with respect to the competition between low frequency and high frequency wave trains. The most significant behavior found in this system is that under appropriate conditions, a phenomenon analogous to refraction of light in a medium with negative refractive index may occur. Negative refraction has been observed in certain “metamaterials,” but has not yet been reported in a reaction-diffusion system. Again, we have begun efforts to create conditions conducive to experimental observation of this behavior in a photosensitive BZ-AOT system subject to periodic forcing with light.
