Nonlinear dynamics and pattern formation in extended systems

提出的研究解决了在热力学平衡之外驱动的系统中复杂模式的形成和演变的机制。它的动机是解决非线性现象的基本问题的原型实验配置，以及凝聚态物理和工程中的具体应用。采取了两个主要途径：拓扑缺陷在中间相和结构粗化的运动，和一个介观模型的二嵌段共聚物研究剪切下的层状相的形成，演变和流变学。在第一种情况下，我们的动机是最近的结果有关处理纳米结构，层状相，和它们的非平衡演化介导的拓扑缺陷运动。在第二种情况下，我们考虑这些原则的一个具体应用，嵌段共聚物，广泛使用的材料在许多新技术，依赖于高性能的聚合物材料，需要精确的微观结构控制和自组装。

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.