Curved Odd Elasticity
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.
Cite
@article{arxiv.2512.11037,
title = {Curved Odd Elasticity},
author = {Yuan Zhou and Lazaros Tsaloukidis and Jack Binysh and Yuchao Chen and Nikta Fakhri and Corentin Coulais and Piotr Surówka},
journal= {arXiv preprint arXiv:2512.11037},
year = {2025}
}
Comments
15 pages (including Supplementary Information), 6 figures