Statics and Dynamics of Materials with Quenched Disorder

这个项目是对无序控制的物质系统的理论探索。无序在材料中普遍存在，是从多孔导体或纳米点阵列中的电子传输到胶体系统的动力学和磁性薄膜中的磁畴壁的各种实验的核心。主要研究人员(PI)将使用(1)非均匀磁体和具有竞争相互作用的界面以及(2)具有随机钉扎的材料中的颗粒流动的模型进行广泛的数值模拟。PI还将寻求更好的描述，即用于研究无序材料的算法与模型的理论图像之间的明显联系。这些链条将计算机科学方法和物理图像联系在一起，这在图论和统计力学中共享基本的数学基础。智力优势：通过粗粒度模型描述材料，这些模型利用(主要)经典自由度捕捉基本的能量学和动力学，为凝聚态物质的相和动力学提供了基本的洞察。这类模型的模拟既提供了定量的预测，也提供了定性的描述；它们对于理解无序材料的集体行为尤其必要，对于无序材料的集体行为往往缺乏明确的解析答案。PI研究并开发了优化算法来研究无序磁体(如随机场伊辛磁铁和自旋玻璃)的低温行为，并将改进模拟以建立更连贯的无序系统图像。PI还将开发新的方案来计算弛豫和加速玻璃系统的动力学，以便在广泛的时间范围内研究老化和记忆效应。更好地理解研究基态和动力学的算法将与这些模型的物理图像密切相关。凝聚态系统中输运的研究包含许多不同的问题，取决于量子效应是否重要，温度的作用，相互作用的强度等。PI将研究一组与自由度相关的问题，这些问题最好在介观尺度上描述，其中量子效应可以忽略不计，温度不大。这些问题包括电子在小颗粒阵列之间的传输，多孔介质中的粘性流体，以及超导体中的磁涡。将详细研究由PI和合作者开发的用于研究具有守恒定律的塑性流动的各向异性粗晶模型。除了研究这些系统的随机性外，PI还将模拟设计的准周期系统对交流驱动的响应，例如可能用胶体粒子实现的响应。更广泛的影响：该项目特定科学目标的进展将与更广泛的利益密切相关。PI将培养研究生和博士后研究人员，重点是直接模拟、先进算法和凝聚态物理之间的重叠。要研究的模型是无序材料的原型，并启发了一系列系统的物理图像，包括无序存在的量子临界点和生物聚合物的折叠。在理解无序系统的静力学和动力学方面的进展，包括磁畴结构和磁滞，最终将应用于材料的开发，包括磁记忆。这项工作将加强计算机科学(组合优化算法及其运行时间)和物理学(长度、尺度和动力学、无限维材料)中的思想之间的联系。由国际和平研究所开发的计算机程序将普遍可用。PI通过与凝聚态物理相关的演讲和活动，积极地与当地社区分享科学。非技术摘要：这个理论项目将探索由无序决定其性质的材料和凝聚态系统。经典固态材料的特征是原子以完美的顺序排列。然而，大多数材料都有一定程度的无序，有些材料的独特性质归因于无序的存在。这项研究将主要使用数值方法(计算)来研究无序对各种当前感兴趣的材料的影响。所使用的数值方法和所描述的物理图像之间的联系可以导致具有更广泛应用的计算机代码的进步。这些联系也将继续进行。

This project is a theoretical exploration of material systems that are controlled by disorder. Disorder is prevalent in materials and is central to experiments ranging from electronic transport in porous conductors or nanoscopic dot arrays through the dynamics of colloidal systems and of domain walls in magnetic films. The principal investigator ( PI) will carry out extensive numerical simulations using models of (1) inhomogeneous magnets and interfaces with competing interactions and (2) the flow of particles in materials with random pinning. The PI will also pursue a better description the apparent connections between the algorithms used to study disordered materials and the theoretical pictures of the models. These strands link computer science methods and physical pictures, which share a fundamental mathematical basis in graph theory and statistical mechanics.Intellectual merit: The description of materials by coarse-grained models, which capture the essential energetics and dynamics using (mostly) classical degrees of freedom, has provided fundamental insight into the phases and dynamics of condensed matter. Simulations of such models provide both quantitative predictions and qualitative descriptions; they are especially needed for understanding the collective behavior of disordered materials, for which clear analytic answers are often lacking.The PI has studied and developed optimization algorithms to study the low temperature behavior of such models for disordered magnets, such as the random field Ising magnet and spin glasses, and will improve simulations to build more coherent pictures of disordered systems. The PI will also develop new schemes for computing barriers to relaxation and accelerating the dynamics of glassy systems, in order to study aging and memory effects over a wide range of time scales. Better understanding of algorithms for studying ground states and dynamics will be closely linked to physical pictures of these models.The study of transport in condensed matter systems encompasses many distinct problems, depending on whether quantum effects are important, the role of temperature, the strength of the interactions, etc. The PI will study the set of problems relevant to degrees of freedom that are best described at the mesoscopic scale, where quantum effects are negligible and the temperature is not large. Such problems include the transport of electrons between arrays of small particles, viscous fluids in porous media, and magnetic vortices in superconductors.An anisotropic coarse-grained model, developed by the PI and collaborators for studying plastic flow with conservation laws, will be studied in detail. In addition to investigating randomness in these systems, the PI will simulate the response of designed quasiperiodic systems to ac drives, such as might be realized with colloidal particles.Broader impact: Progress on the specific scientific goals of this project will be closely connected with more general benefits. The PI will train graduate students and postdoctoral researchers, with an important focus on the overlap between direct simulation, advanced algorithms, and condensed matter physics. The models to be studied are prototypes for disordered materials and have inspired physical pictures for a wide range of systems, including quantum critical points in the presence of disorder and the folding of biopolymers. Progress on understanding the statics and dynamics of disordered systems, including domain structure and hysteresis, has eventual application to materials development, including magnetic memories. This work will strengthen connections between ideas in computer science (algorithms for combinatorial optimization and their running time) and physics (lengths scales and dynamics infinite-dimensional materials). The computer programs developed by the PI will be made generally available. The PI is active in sharing science with the local community through presentations and activities related to condensed matter physics.Non-Technical Abstract: This theoretical project will explore materials and condensed systems whose properties are determined by disorder. Classic solid state materials are characterized by atoms arranged in perfect order. Yet most materials have some degree of disorder and some owe their unique properties to the presence of disorder. This research will use primarily numerical methods (computation) to study the effects of disorder on a variety of materials of current interest. The connection between the numerical methods used and the physical picture described can lead to advances in computer codes that have wider application. These connections will also be pursued.