2010/12/21 by Aaron S. Keys, Keys, Aaron S., Christopher R. Iacovella +3 · 1 citation
Materials Science · #Chemical Physics (physics.chem-ph) #Computer Vision and Pattern Recognition (cs.CV) #Enzyme Structure and Function #FOS: Computer and information sciences #FOS: Physical sciences #Pickering emulsions and particle stabilization #Soft Condensed Matter (cond-mat.soft) #Supramolecular Self-Assembly in Materials
paper · pdf · doi:10.48550/arxiv.1012.4527
openalex publication_date 2010/12/21 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
Order parameters based on spherical harmonics and Fourier coefficients already play a significant role in condensed matter research in the context of systems of spherical or point particles. Here, we extend these types of order parameter to more complex shapes, such as those encountered in nanoscale self-assembly applications. To do so, we build on a powerful set of techniques that originate in the computer science field of "shape matching." We demonstrate how shape matching techniques can be applied to identify unknown structures and create highly-specialized ad hoc order parameters. Additionally, we investigate the special symmetry properties of harmonic descriptors, and demonstrate how they can be exploited to provide optimal solutions to certain classes of problems. Our techniques can be applied to particle systems in general, both simulated and experimental, provided the particle positions are known.