26th Australian Institute of Physics Congress and the Australian and New Zealand Conference on Optics and Photonics

Testing Hyperuniformity in Self-Assembled Point Structures Using Persistent Homology and Ideal Structure Estimation

Not scheduled

1h 30m

Belinda Hutchinson Building (The University of Sydney )

Contributed Oral AIP | Theoretical Physics (TPG) Parallel sessions

Description

Hyperuniform point patterns suppress density fluctuations at long wavelengths and provide an important framework for understanding order in crystals, quasicrystals, and disordered condensed matter. However, identifying hyperuniformity from finite, thermally fluctuating simulation data remains challenging, because conventional descriptors such as the pair-correlation function and structure factor are strongly affected by finite-size effects, boundary effects, and thermal noise. In this work, I present a geometric and topological approach for characterizing structural order in self-assembled point patterns generated by molecular dynamics simulations with an oscillating pair potential.

First, persistent homology based on alpha-shape filtrations is used to quantify short- and medium-range order directly from three-dimensional particle configurations. The resulting persistence diagrams encode the formation and disappearance of connected components, loops, and cavities across length scales, allowing packing and covering-related radii to be extracted in a parameter-free way. These topological signatures distinguish crystalline, quasicrystalline, and disordered simulated structures and provide information complementary to conventional real-space and reciprocal-space measures.

Second, I discuss why short-range geometric characterization alone cannot fully capture hyperuniformity. Counterexamples based on Delone sets, Meyer sets, and epsilon-net-like point patterns show that bounded local geometry does not necessarily imply suppressed long-range number fluctuations. This motivates the need to combine local structural descriptors with a long-range density-fluctuation criterion.

Finally, I introduce an ideal-structure estimation method for testing hyperuniformity in thermally fluctuating self-assembled data. By projecting noisy simulation configurations toward ideal point structures while preserving the underlying geometric organization, the method aims to separate thermal fluctuations from intrinsic structural disorder. This provides a pathway to determine whether apparently disordered self-assembled phases are genuinely non-hyperuniform, or whether an underlying ideal configuration may exhibit hidden hyperuniform order.