Nonlinear dynamics and pattern formation in extended systems

这项研究提出了在热力学平衡之外的系统中形成和演化复杂图案的潜在机制。它的动机既有解决非线性现象基本问题的典型实验配置，也有在凝聚态物理和工程中的具体应用。主要通过两条途径来研究剪切作用下片层相的形成、演化和流变性：一是通过两相拓扑缺陷的运动和结构粗化；二是通过两嵌段共聚物的介观模型研究剪切作用下片层相的形成、演化和流变性。在第一种情况下，我们的动机是最近关于处理纳米结构的层状相的结果，以及它们由拓扑缺陷运动所介导的非平衡演化。在第二种情况下，我们考虑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，这些新技术依赖于需要精确的微结构控制和自组装的高性能聚合物材料。

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.