Harmonic Order Parameters for Characterizing Complex Particle Morphologies

Details Harmonic Order Parameters for Characterizing Complex Particle Morphologies Harmonic Order Parameters for Characterizing Complex Particle Morphologies

2010-12-21

arxiv.org/abs/1012.4527v1

Physics

Condensed Matter

Soft Condensed Matter

13 pages, 9 figures, J. Chem. Phys., submitted

Scientific paper

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 \textit{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.

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