2025/12/13 by Vinesh Vijayan, T Ishwarya, Vijayan, Vinesh +5
Materials Science · Mathematics · Physics and Astronomy · #FOS: Physical sciences #Homotopy and Cohomology in Algebraic Topology #Mathematical Physics (math-ph) #Nonlinear Photonic Systems #Nonlocal and gradient elasticity in micro/nano structures
paper · pdf · doi:10.48550/arxiv.2512.12158
openalex publication_date 2025/12/13 · openalex created_date 2025/12/17 · openalex updated_date 2026/07/28
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.