Nonequilibrium and metastable structures

我的兴趣是理解和预测非平衡和亚稳态结构的性质。这些包括玻璃、相分离合金和流体、外延生长膜、固化晶体、聚合物塑料，以及微观和宏观尺度的生物系统。作为一个具体的例子，材料的结构和机械性能，例如，它们有多脆，以及它们如何自组装，是由非平衡处理历史决定的。这产生了纳米到微米尺度的复杂结构。应用程序通过动态调整形态来利用这种复杂的结构，例如，最大限度地减少材料在应力下的故障率。通过非平衡处理在相边界处捕获晶格缺陷来强化合金，例如，通过对合金进行热处理（一些升高和降低温度的处方）和冷加工。剩下的不是平衡相，而是具有调谐微观结构的非平衡材料。通常这些复杂的结构涉及尺度不变性在一个内在的和深的方式，其中占主导地位的长度尺度渐近地控制所有尺度上的结构的演变。因此，物理学中的一个基本问题是：这些复杂的结构从何而来，如何理解它们？我和我的小组正在通过非线性分析和大规模计算机模拟来研究这些和其他系统。我们利用在其他背景下开发的思想和类比，特别是那些在临界现象理论中开发的思想和类比-即对波动，相关性，尺度不变性，界面动力学的深刻理解，以及对通过建模和大规模模拟表现出来的普遍问题的关注-来理解复杂结构的起源。在过去的几年里，在继续研究复杂材料中的相变和非线性弹性问题的同时，我已经将我的小组转移到研究软材料，活性物质和生物系统的弹性问题。 这项工作的大部分涉及开发模型和方法，并分析这些模型的分析，特别是数字。 在接下来的五年里，我的团队将概括我们在此类系统上所做的工作，并且我们将扩展我们对软系统的相场处理，以纳入我们的相场晶体形式主义的一些有用特征。

My interests are in understanding and predicting the properties of nonequilibrium and metastable structures. These include glasses, phase separating alloys and fluids, epitaxially-grown films, solidifying crystals, polymeric plastics, and, indeed, biological systems at the microscopic and macroscopic scales. As a specific example, the structural and mechanical properties of materials, e.g, how brittle they are, and how they self-assemble, are determined by a nonequilibrium processing history. This gives rise to a complex structure on the scale of nanometers to microns. Applications make use of this complex structure by dynamically tuning the morphology to, for example, minimize failure rates of materials under stress. Alloys are strengthened by trapping lattice defects at phase boundaries through nonequilibrium processing, e.g., by subjecting the alloy to heat treatments (some prescription for raising and lowering the temperature), and cold working. What is left is not an equilibrium phase, it is a nonequilibrium material with a tuned microstructure. Often these complex structures involve scale invariance in an intrinsic and deep way, where a dominant length scale asymptotically controls the evolution of the structure on all scales. Hence, a fundamental issue in physics is involved: where do such complex structures come from, and how can they be understood? With my group, I am investigating these and other systems by nonlinear analysis, and large-scale computer simulation. We make use of ideas and analogies developed in other contexts, particularly those developed in the theory of critical phenomena -- namely the deep understanding of fluctuations, correlations, scale invariance, interface dynamics, and the focus on universal issues as manifested through modeling and large-scale simulation -- to understand the origin of complex structures. Over the last several years, while continuing to study phase transitions and nonlinear elastic issues in complex materials, I have moved my group to study more on elastic issues with soft materials, active matter, and biological systems. Most of this work involves developing models and approaches, and analyzing those models analytically and especially numerically. Over the next five years my group will generalize work we have done on such systems, and we will extend our phase-field treatment of soft systems to incorporate some of the useful features of our phase-field crystal formalism.