Doctor of Philosophy (PhD)
Physics and Astronomy
A study of the effects of system boundaries on bistable front propagation in nonequilibrium reaction-diffusion systems is presented. Two model partial differential equations displaying bistable fronts, with distinct experimental motivations and mathematical structure, are examined in detail utilizing simulations and perturbation techniques. We see that propagating fronts in both models bounce, trap, pin, or oscillate at the boundary, contingent on the imposed boundary condition, initial front speed and distance from the boundary. The similarities in front boundary interactions in these two models is traced to the fact that they display the same front instability (Ising-Bloch bifurcation) that controls the speed of propagation. A simplified dynamical picture based on ordinary differential equations that captures the essential features of front motion described by the original partial differential equations, is derived and analyzed for both models. In addition to addressing experimentally important boundary effects, we establish the universality of the Ising-Bloch bifurcation. Useful analytical insights into perturbative analysis of reaction diffusion systems are also presented.
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Yadav, Aniruddha, "Boundary effects on non-equilibrium localized structures in spatially extended systems" (2005). LSU Doctoral Dissertations. 2828.