2025/12/13 by Vinesh Vijayan, T Ishwarya, Vijayan, Vinesh +5
Materials Science · Mathematics · Physics and Astronomy · #Action (physics) #Conservation law #Curvature #Dislocation #Equations of motion #FOS: Physical sciences #Homotopy and Cohomology in Algebraic Topology #Mathematical Physics (math-ph) #Motion (physics) #Negative curvature #Nonlinear Photonic Systems #Nonlocal and gradient elasticity in micro/nano structures #Torsion (gastropod)
paper · pdf · doi:10.48550/arxiv.2512.12158
published in arXiv (Cornell University) (Cornell University)
openalex publication_date 2025/12/13 · openalex created_date 2025/12/17 · openalex updated_date 2026/08/05
We develop a unified Cartan geometric framework where dislocations and disclinations correspond to torsion and curvature of the material coframe connection, respectively, and phase defects emerge as U(1) vortices. This single action principle produces coupled equations of motion and conservation laws governing these defects. Our theory predicts a universal Magnus-like force exerted by curvature on moving dislocations, as well as disclination-driven reconnection events. These phenomena offer experimentally testable signatures in colloidal crystals and mechanical metamaterials.