Topological Framework for Analysis and Visualization of Atomistic Materials Simulations

University Of Pennsylvania, Philadelphia PA

Investigators

Abstract

NONTECHNICAL SUMMARY This 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 SUMMARY This 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.