Topological Framework for Analysis and Visualization of Atomistic Materials Simulations

非技术总结该奖项支持计算研究和教育，以开发计算工具来推进遵守牛顿定律的原子的计算机模拟。原子模拟是理解固体和液体、有机和无机材料以及生物和无生命系统行为的一种非常重要和广泛应用的方法。随着现代计算的快速发展，在这样的模拟中跟踪超过1万亿个原子的运动是可能的。科学家面临的一个关键挑战是确定如何从如此丰富的数据中提取意义。一种广泛应用的方法是表征原子的局部排列。众所周知，这很难以有意义的方式完成。考虑通过结晶温度冷却液体的例子。无序液体中的原子是如何组织形成晶体的？以高效和有意义的方式自动进行这种类型的结构分析，对物理、化学和生物系统的计算建模的快速增长提出了挑战。一个有用的解决方案将产生广泛的影响，从设计具有所需性质的材料到理解它们是如何失效的。PI将开发一种新的方法来确定模拟中每个原子周围的结构排列。基于拓扑学的数学思想，他们将开发实用的软件工具，用于确定局部结构，这些工具稳健、准确，计算效率足够高，即使是最大的模拟也能分析。与其他方法不同，PI的方法可以在不像在动态模拟中通常所做的那样将结构冷却到绝对零度的情况下应用。这一过程在计算上可能非常昂贵，并且使感兴趣的或寻找的现象的特征变得模糊。该软件将成为开源软件，允许所有科学家免费访问，并与该领域已广泛使用的可视化代码兼容。该项目将培训下一代开发算法和软件基础设施，使科学发现成为可能，并推动前沿。技术总结该奖项支持计算研究和教育，以开发用于分析原子环境中的局部结构的软件，这些软件出现在原子模拟中，以支持对凝聚态中的缺陷、相变和变形的理论和计算研究。传统上，连续的“序参数”被用来描述和识别点状物体的大系统中的结构；这类数据集包括例如通过分子动力学模拟和离散粒子实验获得的粒子坐标。连续有序参数通常被用来识别晶体结构中的缺陷或测量液体和玻璃中的无序。PI将开发一个以Voronoi单元拓扑为中心的新的数学框架。这将使研究人员能够在不猝灭的情况下研究高温下的原子机制。与目前可用的方法相比，这提供了计算和科学上的优势。PI将把注意力集中在三个研究目标上。首先，发展了一种适合于分析大点集局部结构的数学框架。特别是，Voronoi拓扑提供了对可能的粒子排列的配置空间的粗粒度细分。这个配置空间的几何和拓扑将提供对邻居的可能排列的洞察，这在不完美的系统中特别有价值。将特别关注晶体结构中缺陷的有限温度结构。其次，将开发和分发开源软件，以允许其他研究人员将这种自动化方法应用于他们自己的研究和进一步的方法开发。该软件将被设计成与计算材料科学和应用物理中广泛使用的其他软件包一起工作。基本算法在并行计算机上是有效的，使它们能够用于研究大规模系统。最后，将使用开发的理论和计算工具来研究在计算材料科学和应用物理中的应用。特别是，PIs将专注于高温相变的动力学，晶体环境中缺陷的迁移和演化，以及对液体和玻璃中“无序”的理解。该奖项支持培训下一代开发算法和软件基础设施，使科学发现成为可能，并推动前沿。

NONTECHNICAL SUMMARYThis award supports computational research and education to develop computational tools to advance computer simulation of atoms that obey Newton's laws. Atomistic simulation is a very important and widely applied approach for understanding the behavior of solids and liquids, organic and inorganic materials, and living and inanimate systems. With the rapid advance of modern computation, it is possible to track the motion of over a trillion atoms in such simulations. A key challenge to scientists is determining how to extract meaning from such rich data. One widely applicable approach is to characterize the local arrangement of atoms. This is notoriously difficult to do in a meaningful way. Consider the example of cooling a liquid through the crystallization temperature. How do the atoms in the disordered liquid organize to form a crystal? Automating this type of structure analysis in an efficient and meaningful manner challenges the rapid growth of computational modeling of physical, chemical and biological systems. A useful solution would have wide ranging impact from designing materials with desired properties to understanding how they fail.The PIs will develop a novel approach to identify structural arrangements around every atom in a simulation. Building on mathematical ideas from topology, they will develop practical software tools for local structure determination that is robust, accurate and sufficiently computationally efficient to analyze even the largest simulations. In contrast to others, the PIs' approach can be applied without cooling the structure to absolute zero as is usually done in dynamic simulation. This procedure can be computationally very costly and obscure the signatures of interesting or sought phenomena. The software will be made open source to allow free access to all scientists, and compatible with visualization codes that are already widely used in the field. This project will train the next generation in developing algorithms and software infrastructure that will enable scientific discovery and advance the frontiers.TECHNICAL SUMMARYThis award supports computational research and education to develop software for the analysis of local structure in atomic environments that arise in atomistic simulation in support of theoretical and computational studies of defects, phase transitions, and deformation in condensed matter. Traditionally, continuous "order parameters" are used to characterize and identify structure in large systems of point-like objects; data sets of this kind include particle coordinates as obtained through, for example, molecular dynamics simulations and discrete particle experiments. Continuous order parameters are routinely used to identify defects in crystal structures or to measure disorder in liquids and glasses. The PIs will develop a novel mathematical framework centered on Voronoi cell topology. This will allow researchers to study atomic mechanisms at high-temperature without quenching. This provides both computational and scientific advantages over currently available methods.The PIs will focus attention on three research goals. First, the development of a mathematical framework suitable for analyzing local structure in large point sets. In particular, Voronoi topology provides a coarse-grain subdivision of the configuration space of possible particle arrangements. The geometry and topology of this configuration space will provide insight into possible arrangements of neighbors that is especially valuable in imperfect systems. Particular attention will be paid to finite-temperature structure of defects in crystal structures. Second, open source software will be developed and distributed to allow other researchers to apply this automated approach for their own studies and further method development. The software will be designed to work with other software packages that are widely used in computational materials science and applied physics. The basic algorithms are efficient on parallel computers enabling their use in studying large-scale systems. Finally, applications in computational materials science and applied physics will be investigated using the theoretical and computational tools developed. In particular, the PIs will focus on the dynamics of high-temperature phase transformations, the migration and evolution of defects in crystalline environments and to the understanding of "disorder" in liquids and glasses.This award supports training the next generation in developing algorithms and software infrastructure that will enable scientific discovery and advance the frontiers.