Nonlinear dynamics and pattern formation in extended systems

该研究提出了在热力学平衡之外驱动的系统中复杂模式的形成和演化的机制。它是由解决非线性现象的基本问题的原型实验配置和在凝聚态物理和工程中的具体应用驱动的。主要有两种途径：中间相中拓扑缺陷的运动和结构粗化，以及二嵌段共聚物的介观模型来研究剪切作用下层状相的形成、演化和流变学。在第一种情况下，我们的动机是最近关于纳米结构层状相的处理结果，以及拓扑缺陷运动介导的非平衡演化。在第二种情况下，我们考虑了这些原理在嵌段共聚物中的一个具体应用，嵌段共聚物是许多新技术中广泛使用的材料，这些新技术依赖于高性能聚合物材料，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.