形状匹配表征结构及其在自组装中的应用
Characterizing Structure Through Shape Matching and Applications to Self Assembly
摘要：
序参量和关联函数等结构量常被用来研究凝聚态系统的物理行为和性质。虽然存在表征结构的标准量，但它们通常不足以处理纳米和微米尺度自组装的新兴领域中的问题，其中遇到的结构可能是复杂和不寻常的。计算机科学领域的“形状匹配”通过定义各种方法来量化任意复杂形状之间的相似性，为这个问题提供了一个强大的解决方案。凝聚态物质中使用的大多数序参量和关联函数在更广泛的方案中应用结构相似性的特定度量。通过用形状匹配量代替传统量，我们保留了更广泛方案的本质，但将其适用性扩展到更复杂的结构。在这里，我们回顾了一些标准的形状匹配技术，并讨论了如何使用它们来创建高度灵活的结构度量不同的系统，如自组装物质。我们提供了三个应用形状匹配方法来识别局部和全局结构，并跟踪复杂组装系统中的结构转换的概念验证示例问题。这里回顾的形状匹配方法适用于广泛的凝聚态系统，模拟和实验，粒子的位置是已知的或可以准确地成像。
英文摘要：
Structural quantities such as order parameters and correlation functions are often employed to gain insight into the physical behavior and properties of condensed matter systems. While standard quantities for characterizing structure exist, often they are insufficient for treating problems in the emerging field of nano and microscale self-assembly, where the structures encountered may be complex and unusual. The computer science field of "shape matching" offers a robust solution to this problem by defining diverse methods for quantifying the similarity between arbitrarily complex shapes. Most order parameters and correlation functions used in condensed matter apply a specific measure of structural similarity within the context of a broader scheme. By substituting shape matching quantities for traditional quantities, we retain the essence of the broader scheme, but extend its applicability to more complex structures. Here we review some standard shape matching techniques and discuss how they might be used to create highly flexible structural metrics for diverse systems such as self-assembled matter. We provide three proof-of-concept example problems applying shape matching methods to identifying local and global structures, and tracking structural transitions in complex assembled systems. The shape matching methods reviewed here are applicable to a wide range of condensed matter systems, both simulated and experimental, provided particle positions are known or can be accurately imaged.
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