Computational Studies of Complex and Frustrated Systems

复杂和受挫系统的计算研究

• 批准号: 1208046
• 负责人: Jonathan Machta
• 金额: $ 30.74万
• 依托单位: University of Massachusetts Amherst
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2012
• 资助国家: 美国
• 起止时间: 2012-09-01 至 2016-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1208046&HistoricalAwards=false
• 关键词: Computational; Studies; Complex; Frustrated; Systems

TECHNICAL SUMMARYThis award supports theoretical and computational research in statistical physics and condensed matter physics organized in three related projects. 1. The PI will develop algorithms for simulating frustrated spin systems and related systems with rough free energy landscapes. The PI aims to improve both the parallel tempering and the population annealing algorithms. 2. The PI will carry out a large-scale computational study of Ising spin glass models. The primary goal of this research is to resolve the controversy over whether, in finite-dimensional systems, spin glass ordering occurs in the simple way as proposed in the droplet picture with only two thermodynamically pure states or through the more complex replica symmetry breaking scenario involving a large multiplicity of pure states. In this study, the PI and collaborators will carry out large scale simulations of Ising spin glasses and analyze the statistics of the overlap distribution using new observables that sharply distinguish these scenarios. The problem of packing hard objects will also be studied using both parallel tempering and population annealing. 3. The last area involves the application of the theory of parallel computational complexity to problems in statistical physics. The notion of P-completeness in parallel computational complexity theory will be extended to sampling problems and applied to prove that growth models such as diffusion limited aggregation are inherently sequential. This work extends and builds on early results that show that diffusion limited aggregation and other processes in statistical physics are P-complete. This project has a significant emphasis on education and much of the budget is devoted to supporting graduate and undergraduate students who will be trained in the concepts and techniques of statistical, condensed matter, and computational physics. NON-TECHNICAL SUMMARYThis award supports theoretical research and education in statistical and condensed matter physics. The research consists of several related projects that involve computation and concepts that cross disciplinary boundaries.The PI aims to develop computer algorithms that can overcome the computational challenges of materials that exhibit frustration or barriers to finding the true solution among many possibilities, such as the folded structure of a protein. This general class of problems is important not only in the physical sciences but also in computer science and engineering where they are called combinatorial optimization problems. Spin glasses provide an example of frustration. They are magnetic materials with random interactions between the atomic scale magnetic constituents in these materials often referred to as spins. The random interactions lead to "frustration" spins receive conflicting signals from different neighbors as to which way they should orient themselves. Due to frustration spin glasses take a very long time to reach equilibrium. This is also true for computer simulations of models of spin glasses; they require very long computation times. The PI aims to develop computer algorithms that can overcome the challenges of simulating frustrated systems. The algorithms will then be used to carry out a large scale computational study of spin glasses that will help to resolve a long-standing and fundamental controversy in the theory of disordered materials. The PI will be able to carry out more extensive simulations for lower temperatures than has been possible up to now, and utilize new techniques that can more sharply distinguish between the existence of many equilibrium states or a single pair of states. The PI also seeks to understand whether computational difficulty of simulations of materials systems on computers with processors that can work in parallel has a fundamental connection to the physical system. The PI will study diffusion limited aggregation, a growth process that describes, for example, mineral deposition and snowflake growth, and creates complex patterns. The question is whether patterns that arise from this process can be generated rapidly by a parallel computer or whether the pattern formation process itself is fundamentally sequential one and not parallelizable. These results may guide the understanding of whether parallelization on a computer will lead to higher performance for a particular problem, and a new way to measure the inherent complexity of a material or other physical system.This project has a significant emphasis on education and much of the budget is devoted to supporting graduate and undergraduate students who will be trained in the concepts and techniques of statistical, condensed matter, and computational physics.

技术摘要这一奖项支持在三个相关项目中组织的统计物理学和凝结物理学的理论和计算研究。 1。PI将开发算法，用于模拟具有粗糙的自由能景观的沮丧的旋转系统和相关系统。 PI旨在改善平行回火和人口退火算法。 2。PI将对Ising自旋玻璃模型进行大规模计算研究。 这项研究的主要目的是解决争议在有限维系统中，自旋玻璃排序以简单的方式发生在液滴图片中，只有两个热力学纯净的状态，还是通过更复杂的复制复制对称性破坏场景，涉及涉及纯种状态的大量多样性。 在这项研究中，PI和合作者将使用新的可观察到的新观测值分析重叠分布的统计数据，从而进行大规模的模拟。 包装硬物体的问题也将使用平行回火和人口退火研究。 3。最后一个领域涉及将平行计算复杂性理论应用于统计物理学中问题。 平行计算复杂性理论中P完整性的概念将扩展到采样问题，并应用于证明诸如扩散限制聚集之类的生长模型本质上是顺序的。 这项工作扩展并建立在早期结果的基础上，表明扩散有限的聚集和统计物理学中的其他过程是P的。 该项目对教育有很大的重视，大部分预算都致力于支持研究生和本科生，这些学生将接受统计，凝结物和计算物理学的概念和技术培训。非技术摘要这一奖项支持统计和凝结物理学的理论研究和教育。 该研究由几个涉及跨学科边界的计算和概念的相关项目组成。PI旨在开发计算机算法，这些算法可以克服材料的计算挑战，这些材料的计算挑战表现出挫败感或障碍，无法在许多可能性中找到真正的解决方案，例如蛋白质的折叠结构。这种一般的问题不仅在物理科学中，而且在计算机科学和工程学中也很重要，在这些科学和工程中，它们被称为组合优化问题。 自旋眼镜提供了挫败感的例子。它们是这些材料中原子尺度磁成分之间具有随机相互作用的磁性材料，通常称为自旋。随机相互作用导致“挫败感”旋转从不同邻居那里获得相互矛盾的信号，以表明自己的方式。 由于挫败感，旋转眼镜需要很长时间才能达到平衡。 对于旋转眼镜模型的计算机模拟也是如此。他们需要很长的计算时间。 PI旨在开发计算机算法，以克服模拟挫败系统的挑战。然后，该算法将用于对自旋眼镜进行大规模计算研究，这将有助于解决无序材料理论中的长期和根本的争议。 与现在相比，PI将能够为较低的温度进行更广泛的模拟，并利用新技术可以更明显地区分许多平衡状态或一对状态。 PI还试图了解具有可以并行工作的处理器上材料系统模拟的计算难度是否与物理系统具有基本联系。 PI将研究扩散限制聚集，这是一个描述例如矿物沉积和雪花生长的生长过程，并创造了复杂的模式。 问题是，是否可以通过平行计算机快速生成此过程的模式，或者模式形成过程本身是否从根本上是顺序的，而不是平行的。 这些结果可以指导了解计算机上的并行化是否会导致特定问题的更高绩效，并是一种衡量材料或其他物理系统固有复杂性的新方法。该项目对教育有很大的重视，并且大部分预算致力于支持研究生和本科生，这些学生将在统计和凝结，凝结性，计算性和计算性的概念和技术中受过培训。