表征复杂颗粒形貌的谐波序参量
Harmonic Order Parameters for Characterizing Complex Particle Morphologies
摘要：
基于球谐函数和傅立叶系数的序参量在球形或点粒子系统的凝聚态研究中已经发挥了重要作用。在这里，我们将这些类型的序参量扩展到更复杂的形状，例如在纳米级自组装应用中遇到的形状。为了做到这一点，我们建立在一套强大的技术，起源于计算机科学领域的“形状匹配”。“我们演示了形状匹配技术如何应用于识别未知结构并创建高度专业化的\textit{ad hoc}序参量。此外，我们研究了谐波描述符的特殊对称性，并演示了如何利用它们为某些类别的问题提供最佳解决方案。我们的技术可以适用于粒子系统一般，模拟和实验，提供粒子的位置是已知的。
英文摘要：
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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