(184n) Creating Flexible Order Parameters Using Shape Matching II: Harmonic Descriptors

In many computer science applications, a technique known as "shape matching" is used to identify unknown structures. Common applications include retrieving fingerprints from a criminal database or verifying signatures electronically. In the context of materials research, we can use shape matching methods to identify and characterize structures formed by particle systems. Our scheme involves associating "shape descriptors" with structural patterns of interest in our particle systems and then characterizing the patterns by comparing shape descriptors with reference structures. Here, we provide a detailed description of the methods used to create different types of shape descriptors, with a particular focus on a powerful class of "harmonic descriptors." To aid in the development and dissemination of these techniques, we have implemented a C++/python library to perform shape matching analysis, which will be made available at matforge.org and codeblue.umich.edu.