Coarsening dynamics of fingerprint labyrinthine patterns: Machine learning assisted characterization

TL;DR

This study investigates the slow, defect-driven coarsening of fingerprint labyrinthine patterns using a combination of theoretical modeling and machine learning, revealing unique dynamics distinct from traditional stripe phases.

Contribution

It introduces a machine learning method to identify and analyze localized defects in complex pattern systems, advancing understanding of their coarsening behavior.

Findings

Defect motion is constrained by stripe geometry, leading to slow coarsening.

Point-like defects dominate the coarsening process, unlike grain boundary-driven mechanisms.

Machine learning enables real-space defect tracking and statistical analysis.

Abstract

Fingerprint labyrinthine patterns exhibit a level of structural complexity beyond simple stripe phases, combining local stripe order with a dense network of point-like defects. Unlike symmetry-breaking phases, where coarsening proceeds via diffusive defect annihilation, or conventional stripe phases, where curvature-driven motion of extended grain boundaries dominates, the coarsening of fingerprint labyrinths is governed primarily by localized junction and terminal defects. Using the Turing-Swift-Hohenberg equation, we study the nonequilibrium relaxation of fingerprint labyrinthine patterns following a quench. To go beyond conventional Fourier-based diagnostics, we employ a template-matching convolutional neural network (TM-CNN) to identify and track junctions and terminals directly in real space, enabling a quantitative characterization of defect statistics and spatial correlations. We show that, although these point-like defects drive coarsening, their motion is strongly constrained by the surrounding stripe geometry, leading to slow, nondiffusive dynamics that are qualitatively distinct from both conventional phase ordering and stripe coarsening. Together, these results establish defect-mediated dynamics as the central organizing principle of fingerprint labyrinthine coarsening and demonstrate the effectiveness of machine-learning-assisted approaches for complex pattern-forming systems.