Multiscale geometrical and topological learning in the analysis of soft matter collective dynamics

Abstract

Understanding the behavior and evolution of a dynamical many-body system by analyzing patterns in their experimentally captured images is a promising method relevant for a variety of living and non-living self-assembled systems. The arrays of moving liquid crystal skyrmions studied here are a representative example of hierarchically organized materials that exhibit complex spatiotemporal dynamics driven by multiscale processes. Joint geometric and topological data analysis (TDA) offers a powerful framework for investigating such systems by capturing the underlying structure of the data at multiple scales. In the TDA approach, we introduce the $\Psi$-function, a robust numerical topological descriptor related to both the spatiotemporal changes in the size and shape of individual topological solitons and the emergence of regions with their different spatial organization. The geometric method based on the analysis of vector fields generated from images of skyrmion ensembles offers insights into the nonlinear physical mechanisms of the system's response to external stimuli and provides a basis for comparison with theoretical predictions. The methodology presented here is very general and can provide a characterization of system behavior both at the level of individual pattern-forming agents and as a whole, allowing one to relate the results of image data analysis to processes occurring in a physical, chemical, or biological system in the real world.

arXiv comment13 pages, 6 figures

References in corpus (23)

• Skyrmion Lattice in a Chiral Magnet
• A roadmap for the computation of persistent homology
• Optical skyrmions in evanescent electromagnetic fields
• Particle-like topologies in light
• Topological Data Analysis of Biological Aggregation Models
• Persistent Homology Analysis for Materials Research and Persistent Homology Software: HomCloud
• Two-dimensional skyrmions and other solitonic structures in confinement-frustrated chiral nematics
• Diversity of knot solitons in liquid crystals manifested by linking of preimages in torons and hopfions
• Electric-field-induced nematic-cholesteric transition and 3-D director structures in homeotropic cells
• Review: Topology of solitons and singular defects in chiral liquid crystals
• Computer simulation of topological defects around a colloidal particle or droplet dispersed in a nematic host
• Analysis of Kolmogorov Flow and Rayleigh-Bénard Convection using Persistent Homology
• Rotational and translational diffusion of anisotropic gold nanoparticles in liquid crystals controlled by varying surface anchoring
• Schools of skyrmions with electrically tunable elastic interactions
• Comparing skyrmions and merons in chiral liquid crystals and magnets
• Topological data analysis and machine learning
• Tracking collective cell motion by topological data analysis
• Topological carnival: electrically-powered motions of toron crystallites in chiral liquid crystals
• Topological packing statistics distinguish living and non-living matter
• Photonic band structure design using persistent homology
• Directed Motion of Liquid Crystal Skyrmions With Oscillating Fields
• A Fast and Scalable Computational Topology Framework for the Euler Characteristic
• Persistent Homology for Structural Characterization in Disordered Systems