arXiv subjects

Abel H. G. Milor

Publications and source records attributed to Abel H. G. Milor.

4 recordsLinked to original sources

arXiv2026

Construction of minimal integrity basis for anisotropic hyperelasticity via structural tensors

We present minimal integrity bases for all common anisotropies in hyperelasticity via the structural tensor concept, which can be used to formulate any algebraic invariant function in the elements of the respective bases. Hence, the provided minimal integrity bases are of great interest for formulating a concise but general anisotropic material model. Our work covers results for the 11 types of anisotropy that arise from the classical 7 crystal systems, as well as findings for 4 additional non-crystal anisotropies derived from the cylindrical, spherical, and icosahedral symmetry systems. By using well-known results from literature about structural tensors, isotropic invariants, and isotropic extension, functional bases are directly determined. A simple analytical-numerical approach is employed to identify polynomial relations between the invariants of these functional bases, thereby enabling the construction of functional bases of reduced cardinality. After that, we show that the determined reduced functional bases are also minimal integrity bases by identifying polynomial relations to known integrity bases from literature. Furthermore, fundamental concepts from invariant theory, including the Hironaka decomposition of invariant rings and the closely related Hilbert series, are employed to further validate the results. Alongside the presented findings, this article also aims to provide an introductory overview of the complex field of modeling anisotropic materials, especially for researchers with an engineering background.

cond-mat.mtrl-sci↗

arXiv2026

Grain-Growth Stagnation from Vacancy-Diffusion-Limited Disconnection Climb

Grain growth in polycrystals typically stagnates at long times. We identify disconnection climb, limited by vacancy diffusion, as a fundamental microscopic mechanism underlying this behavior. Using a phase-field crystal framework extended to model vacancy diffusion, we resolve grain-boundary migration on diffusive time scales and show that disconnection climb rates correlate with the characteristic grain size at which growth arrests. These results link vacancy transport, disconnection dynamics, and microstructural evolution, establishing vacancy diffusion as a key governing factor.

cond-mat.mtrl-sci↗

arXiv2025

A topological approach to the Cahn-Hilliard equation and hyperuniform fields

Hyperuniform structures are disordered, correlated systems in which density fluctuations are suppressed at large scales. Such a property generalizes the concept of order in patterns and is relevant across diverse physical systems. We present a numerical characterization of hyperuniform scalar fields that leverages persistent homology. Topological features across different lengths are represented in persistence diagrams, while similarities or differences between patterns are quantified through Wasserstein distances between these diagrams. We apply this framework to numerical solutions of the Cahn-Hilliard equation, a canonical model for generating hyperuniform scalar fields. We validate the approach against known features of the Cahn-Hilliard equation, including its scaling properties, convergence to the sharp interface limit, and self-similarity of the solutions. We then generalize the approach by studying Gaussian random fields exhibiting different degrees and classes of hyperuniformity, showing how the proposed approach can be exploited to reconstruct global properties from local topological information. Overall, we show how hyperuniform characteristics systematically correlate with distributions of topological features in disordered correlated fields. We expect this analysis to be applicable to a wide range of scalar fields, particularly those involving interfaces and free boundaries.

cond-mat.soft↗

arXiv2025

Inferring traits of hyperuniformity from local structures via persistent homology

Hyperuniformity refers to the suppression of density fluctuations at large scales. Typical for ordered systems, this property also emerges in several disordered physical and biological systems, where it is particularly relevant to understand mechanisms of pattern formation and to exploit peculiar attributes, e.g., interaction with light and transport phenomena. While hyperuniformity is a global property, ideally defined for infinitely extended systems, several disordered correlated systems have finite size. It has been shown in [Phys. Rev. Research 6, 023107 (2024)] that global hyperuniform characteristics systematically correlate with distributions of topological properties representative of local arrangements. In this work, building on this information, we explore and assess the inverse relationship between hyperuniformity and local structures in point patterns as described by persistent homology. Standard machine learning algorithms trained on persistence diagrams are shown to detect hyperuniformity of periodic point patterns with high accuracy. Therefore, we demonstrate that the information on patterns' local structures allows for characterizing whether finite size arrangements are analogous to those realized in hyperuniform patterns. Then, addressing more quantitative aspects, we show that parameters defining hyperuniformity globally can be reconstructed by comparing persistence diagrams of targeted patterns with reference ones. We also explore the generation of patterns entailing given topological properties. The results of this study pave the way for advanced analysis of hyperuniform patterns including local information, and introduce basic concepts for their inverse design.

cond-mat.stat-mech↗