MSE Graduate Seminar: Structure, order, and extracopularity

Abstract:

Order is an aspect of a system’s structure that holds much insight. Despite the fact that many physical systems are well modeled as collections of interacting particles, a general approach to quantifying the absolute degree of order immediately surrounding a particle has yet to be described. Thus motivated, this seminar presents a quantity E that captures the amount of pairwise informational redundancy among the bonds formed by a particle. Particles with larger E have less diversity in bond angles and thus simpler neighborhoods. We demonstrate that E is, in principle, able to distinguish a wide range of structures and conjecture that it is maximized by the icosahedral geometry under the constraint of equal sphere packing. An algorithm for computing E is described and results from its application to the structural characterization of crystals and glasses are discussed. These findings are generally consistent with existing knowledge on the structure of such systems. We compare E to the Steinhardt order parameter Q6 and polyhedral template matching (PTM). We observe that E has resolution comparable to Q6 and robustness similar to PTM, despite being much simpler than the former and far more informative than the latter.