Nonlinear dynamics and pattern formation in extended systems

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The research proposed addresses the mechanisms underlying the formation and evolution of complex patterns in systems that are driven outside of thermodynamic equilibrium. It is motivated by both prototypical experimental configurations in which to address fundamental issues of nonlinear phenomena, and by specific applications in condensed matter physics and engineering. Two main avenues are pursued: the motion of topological defects in mesophases and structure coarsening, and a mesoscopic model of a diblock copolymer to study the formation, evolution, and rheology of lamellar phases under shear. In the first case, we are motivated by recent results about processing nanostructured, layered phases, and their nonequilibrium evolution mediated by topological defect motion. In the second case, we consider one specific application of these principles to block copolymers, a widely used material in many new technologies that rely on high performance polymeric materials that require precise microstructural control and self-assembly.