Nonequilibrium and metastable structures

我的兴趣在于了解和预测非平衡结构和亚稳态结构的性质。其中包括玻璃、分相合金和流体、外延生长的薄膜、凝固晶体、聚合物塑料，甚至微观和宏观尺度上的生物系统。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，它们如何自组装，是由非平衡加工历史决定的。这就产生了从纳米到微米的复杂结构。应用程序通过动态调整形态来利用这种复杂的结构，例如，将材料在应力下的故障率降至最低。合金是通过非平衡处理在相界捕获晶格缺陷来强化的，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，而是具有可调微结构的非平衡材料。通常，这些复杂的结构以一种内在和深刻的方式涉及到尺度不变性，其中占主导地位的长度尺度渐进地控制着结构在所有尺度上的演变。因此，涉及到物理学中的一个基本问题：这种复杂的结构从何而来，如何理解它们？我和我的团队正在通过非线性分析和大规模的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发展的思想和类比，特别是在临界现象理论中发展的思想和类比--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所表现出的普遍问题的关注--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，我带领我的团队更多地研究软材料、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，并对这些模型进行分析，特别是数值分析。在接下来的五年里，我的团队将总结我们在这类系统上所做的工作，我们将扩展我们对软系统的相场处理，以纳入我们相场晶体形式主义的一些有用的特征。

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.