Curved Odd Elasticity

2025/12/11 by Yuan Zhou, Zhou, Yuan, Lazaros Tsaloukidis +11
Physics and Astronomy · #FOS: Physical sciences #Soft Condensed Matter (cond-mat.soft) #cond-mat.soft

paper · pdf · doi:10.48550/arxiv.2512.11037

19 pages (including Supplemental Material), 10 figures

arxiv created 2026/08/03 · arxiv updated 2026/08/04

Abstract

Living materials such as membranes, cytoskeletal assemblies, cell collectives and tissues can often be described as active solids---materials that are energized from within, with elastic response about a well defined reference configuration. These materials often live in complex and curved manifolds, yet most descriptions of active solids are flat. Here, we explore the interplay between curvature and non-reciprocal elasticity via a covariant effective theory on curved manifolds in combination with numerical simulations. We find that curvature spatially patterns activity, gaps the spectrum, modifies exceptional points and introduces non-Hermitian defect modes. Together these results establish a foundation for hydrodynamic and rheological models on curved manifolds, with direct implications for living matter and active metamaterials.

Citations

• Emergent odd viscoelasticity in chiral soft glassy materials
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Related

• Integer defects, flow localization, and bistability on curved active surfaces
• Active Filaments on Curved Surfaces: From Single Filaments to Dilute Suspensions
• A Twist On Active Membranes: Odd Mechanics, Spontaneous Flows and Shape Instabilities
• Nonlinear morphoelastic energy based theory for stimuli responsive elastic shells
• Emergent Dynamics of Active Systems on Curved Environments