Author(s): Tetiana Orlova, Amaranta Membrillo Solis, Hayley R. O. Sohn, Tristan Madeleine, Giampaolo D’Alessandro, Ivan I. Smalyukh, Malgosia Kaczmarek, and Jacek Brodzki Understanding the fundamental principles of dynamic many-body systems from their temporally and spatially varying pattern images provides valuable insights into living and abiotic matter. Using liquid-crystalline skyrmion arrays as a model system, the authors apply geometric and topological data analysis to uncover their multiscale structure, motion, and shape changes of individual structures. Their approach relies on the Ψ function, a new topological descriptor that distinguishes pure translational dynamics from transformations in soliton geometry or spatial reorganization. This general framework connects image-based ana…
Author(s): Tetiana Orlova, Amaranta Membrillo Solis, Hayley R. O. Sohn, Tristan Madeleine, Giampaolo D’Alessandro, Ivan I. Smalyukh, Malgosia Kaczmarek, and Jacek Brodzki Understanding the fundamental principles of dynamic many-body systems from their temporally and spatially varying pattern images provides valuable insights into living and abiotic matter. Using liquid-crystalline skyrmion arrays as a model system, the authors apply geometric and topological data analysis to uncover their multiscale structure, motion, and shape changes of individual structures. Their approach relies on the Ψ function, a new topological descriptor that distinguishes pure translational dynamics from transformations in soliton geometry or spatial reorganization. This general framework connects image-based analysis with the underlying physical or biological processes. It can be applied to cellular organization, active matter, nanomaterials, and complex self-assembled systems. [Phys. Rev. Materials 10, 015602] Published Fri Jan 09, 2026