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arXiv · 2512.11037

Curved Odd Elasticity

Yuan Zhou·Lazaros Tsaloukidis·Jack Binysh·Yuchao Chen·Nikta Fakhri·Corentin Coulais·Piotr Surówka
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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.

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Yuan Zhou, Lazaros Tsaloukidis, Jack Binysh, Yuchao Chen, Nikta Fakhri, Corentin Coulais, Piotr Surówka. 2026-08-03. Curved Odd Elasticity. https://arxiv.org/abs/2512.11037

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