Complex Dynamics and Algorithms for Disordered Matter

技术摘要：该奖项支持以计算为重点的理论研究和围绕复杂无序材料研究组织的教育工作。了解复杂材料的热力学和动力学对于理解磁记忆的稳定性和探索在介观“自旋冰”、涡旋物质或填充胶状二聚体等系统中看到的新型复杂集体效应是必要的。通过新算法的开发，该项目还将加强物理方法与计算机科学家开发的优化和采样研究之间的联系。微观非均相材料表现出不同寻常和迷人的特性。这些材料可以表现出复杂的记忆，例如通过磁滞或在变暖时再现其热历史。无序材料具有高度复杂的能量景观，表现出玻璃动力学，并且被认为在广泛的温度范围内处于临界状态。虽然存在启发式解析图，但数值模拟对于验证理论和探索哪种模型可以解释实验结果至关重要。在这个项目中，PI将通过发明、实施和利用先进的优化和动力学算法来促进对复杂和无序材料动力学的理解。自旋玻璃材料的两种新方法将应用于非平衡动力学：拼凑动力学，一种探索多时间尺度非平衡动力学的启发式方法，以及最近开发的精确采样技术，用于研究温度的影响。还将研究新的方法。该项目将探索真实物理系统空间结构中相关性对大容量内存效应和算法性能的重要性。对涡旋物质和胶体系统的模拟也将与实验结果进行比较。研究生、博士后研究员和本科生将接受高级计算方法和数据分析方面的培训。他们将学习和使用统计物理、凝聚态物理和计算方法之间的深刻关系。这项工作与计算机科学有很强的跨学科联系，包括为困难的优化和抽样问题开发解决方案。由于无序界面和磁体问题是无序和复杂性的原型模型，该领域的进展有助于更好地描述复杂系统，包括一般网络和优化问题的实际解决方案。PI将普遍提供计算机代码，并将开展外联工作。该奖项支持以计算为重点的理论研究，以及对无序和复杂物质的一般主题的教育。大多数材料都是不纯的，但人们对这些材料的了解通常不如纯材料。由于相互竞争的力量，不纯的材料需要很长时间才能放松或改变。这种极端的“玻璃化”行为可以在含有杂质的磁性材料和人工构建的系统中看到，例如填充的微观哑铃状珠子或超导材料条。这些系统具有长期记忆，能够以分布式的方式存储复杂的信息。PI的目标是开发新的计算方法来模拟这些材料。这些方法大大加快了计算速度，足以长时间模拟材料。更直接的蛮力计算通常非常慢。PI的新技术与计算机科学家和数学家开发的寻找最佳解决方案的技术密切相关，例如地图上不同地点之间的最短路线，以及从一组复杂的选择中随机选择项目。采用这些技术来研究材料模型，既提高了计算技术，也提高了我们对复杂材料的理解。PI将与本科生、研究生和一名博士后研究人员合作，培训他们在该领域使用的复杂计算技术和物理分析。这些方法的通用性提供了有价值的训练，使学生能够解决各种计算和科学问题。PI将向社区提供项目中使用的计算机代码。PI通过与材料相变和结构相关的演讲和活动与地区社区分享他的科学专业知识和热情。

TECHNICAL ABSTRACTThis award supports theoretical research with a computational emphasis and education efforts organized around the study of complex disordered materials. An understanding of the thermodynamics and dynamics of complex materials is necessary both to understand the stability of magnetic memory and to explore novel complex collective effects seen in systems such as mesoscopic "spin ice," vortex matter, or packed colloidal dimers. Through the development of novel algorithms, this project will also strengthen the connections between physical approaches and the study of optimization and sampling developed by computer scientists.Microscopically heterogeneous materials exhibit unusual and fascinating properties. These materials can exhibit intricate memory, for example through magnetic hysteresis or in a reprise of their thermal history upon warming. Disordered materials possess a highly complex energy landscape, exhibit glassy dynamics, and are believed to be in a critical state over a broad range of temperatures. Though heuristic analytic pictures exist, numerical simulations have been crucial to verifying theories and exploring which models explain experimental results.In this project, the PI will advance understanding of the dynamics of complex and disordered materials by inventing, implementing, and utilizing advanced algorithms for optimization and dynamics. Two new approaches to spin glass materials will be applied to non-equilibrium dynamics: patchwork dynamics, a heuristic method to explore non-equilibrium dynamics over many time scales, and a recently developed exact sampling technique, to study the effects of temperature. New methods will also be investigated. This project will explore the importance of the correlations in the spatial structure of real physical systems to bulk memory effects and to the performance of algorithms. Simulations on vortex matter and colloidal systems will also be compared with experimental work.Graduate students, a postdoctoral researcher, and undergraduate students will be trained in advanced computing methods and data analysis. They will learn and use the deep relationships between statistical physics and condensed matter physics and computational methods. This work has strong interdisciplinary connections with computer science and includes developing solvers for difficult optimization and sampling problems. As the problem of disordered interfaces and magnets are prototypical models of disorder and complexity, advances in this area contribute to a better description of complex systems, including both general networks and practical solutions to optimization problems. The PI will make computer codes generally available and will carry out outreach efforts.NON-TECHNICAL ABSTRACTThis award supports theoretical research with a computational emphasis and education on the general topic of matter that is disordered and complex. Most materials are impure, but these materials are generally less well understood than pure materials. Because of competing forces, impure materials can take a very long time to relax or change. This extreme "glassy" behavior is seen in magnetic materials with impurities and artificially constructed systems such as packed microscopic dumbbell shaped beads or strips of superconducting material. These systems have long term memories and can store complex information in a distributed fashion.The PI aims to develop new computational approaches to simulate these materials. These approaches speed up the computations sufficiently to be able to simulate materials over long times. More direct brute force calculations are often prohibitively slow. The PI's new techniques are closely connected to those developed by computer scientists and mathematicians to find optimal solutions, such as the shortest route between locations on a map and the random selection items from a complex set of choices. Adopting these techniques to the study of models for materials advances both the computational techniques and our understanding of complex materials.The PI will work with undergraduate students, graduate students, and a postdoctoral researcher, to train them in the sophisticated computational techniques and physical analyses that are used in this field. The generality of these methods provides valuable training that enables students to solve a variety of problems in computation and science. The PI will make the computer codes used in the project available to the community. The PI shares his scientific expertise and enthusiasm with the area community through presentations and activities related to phase transitions and structure in materials.