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Stress-strain constitutive relations in solids with an internal angular degree of freedom can be modelled using Cosserat (also called micropolar) elasticity. In this paper, we explore the phenomenology for a natural extension of Cosserat…

Soft Condensed Matter · Physics 2023-12-19 Piotr Surówka , Anton Souslov , Frank Jülicher , Debarghya Banerjee

Chiral active fluids are materials composed of self-spinning rotors that continuously inject energy and angular momentum at the microscale. Out-of-equilibrium fluids with active-rotor constituents have been experimentally realized using…

Soft Condensed Matter · Physics 2017-11-22 Debarghya Banerjee , Anton Souslov , Alexander G. Abanov , Vincenzo Vitelli

Odd elasticity describes the unusual elastic response of solids whose stress-strain relationship is not compatible with an elastic potential. Here, we present a study of odd elasticity in a driven granular matter system composed of grains…

Soft Condensed Matter · Physics 2023-12-01 Rosalind Huang , Rituparno Mandal , Colin Scheibner , Vincenzo Vitelli

Rheological properties of chiral active materials have been an important area of research in the recent past, in particular regarding odd terms in their mechanical response. While much progress has been made in the study of odd viscous…

Soft Condensed Matter · Physics 2025-09-08 Debarghya Banerjee , Peter Sollich

Active chiral viscoelastic materials exhibit elastic responses perpendicular to the applied stresses, referred to as odd elasticity. We use a covariant formulation of viscoelasticity combined with an entropy production analysis to show that…

Soft Condensed Matter · Physics 2022-05-30 Ruben Lier , Jay Armas , Stefano Bo , Charlie Duclut , Frank Jülicher , Piotr Surówka

Chiral active matter is predicted to exhibit odd elasticity, with nontraditional elastic response arising from a combination of chirality, being out of equilibrium, and the presence of nonreciprocal interactions. One of the resulting…

Soft Condensed Matter · Physics 2025-11-10 Sang Hyun Choi , Zhi-Feng Huang , Nigel Goldenfeld

Active crystals are highly ordered structures that emerge from the self-organization of motile objects, and have been widely studied in synthetic and bacterial active matter. Whether collective crystallization phenomena can occur in groups…

Non-reciprocal interactions fueled by local energy consumption can be found in biological and synthetic active matter at scales where viscoelastic forces are important. Such systems can be described by "odd" viscoelasticity, which assumes…

Soft Condensed Matter · Physics 2023-10-31 Carlos Floyd , Aaron R. Dinner , Suriyanarayanan Vaikuntanathan

Odd elasticity encompasses active elastic systems whose stress-strain relationship is not compatible with a potential energy. As the requirement of energy conservation is lifted from linear elasticity, new anti-symmetric (odd) components…

Soft Condensed Matter · Physics 2025-07-15 Michele Fossati , Colin Scheibner , Michel Fruchart , Vincenzo Vitelli

Hooke's law states that the forces or stresses experienced by an elastic object are proportional to the applied deformations or strains. The number of coefficients of proportionality between stress and strain, i.e., the elastic moduli, is…

A wide range of physical and biological systems, including colloidal magnets, granular spinners, and starfish embryos, are characterized by strongly rotating units that give rise to odd viscosity and odd elasticity. These active systems can…

Soft Condensed Matter · Physics 2025-02-28 Lorenzo Caprini , Umberto Marini Bettolo Marconi

Chiral surface waves are surface-localized modes that propagate unidirectionally along a boundary, enabling directed transport and minimal back-scattering. While first identified in quantum systems, they were recently shown to emerge in…

Soft Condensed Matter · Physics 2026-03-24 Cheng-Tai Lee , Tomer Markovich

Crystallography typically studies collections of point particles whose interaction forces are the gradient of a potential. Lifting this assumption generically gives rise in the continuum limit to a form of elasticity with additional moduli…

Soft Condensed Matter · Physics 2021-12-30 Lara Braverman , Colin Scheibner , Bryan VanSaders , Vincenzo Vitelli

Elasticity typically refers to a material's ability to store energy, while viscosity refers to a material's tendency to dissipate it. In this review, we discuss fluids and solids for which this is not the case. These materials display…

Soft Condensed Matter · Physics 2023-03-29 Michel Fruchart , Colin Scheibner , Vincenzo Vitelli

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…

Soft Condensed Matter · Physics 2025-12-15 Yuan Zhou , Lazaros Tsaloukidis , Jack Binysh , Yuchao Chen , Nikta Fakhri , Corentin Coulais , Piotr Surówka

In equilibrium liquid crystals, chirality leads to a variety of spectacular three-dimensional structures, but chiral and achiral phases with the same broken continuous symmetries have identical long-time, large-scale dynamics. In this…

Soft Condensed Matter · Physics 2021-06-23 S. J. Kole , Gareth P. Alexander , Sriram Ramaswamy , Ananyo Maitra

Odd viscoelastic materials are constrained by fewer symmetries than their even counterparts. The breaking of these symmetries allow these materials to exhibit different features, which have attracted considerable attention in recent years.…

Soft Condensed Matter · Physics 2024-08-21 Charlie Duclut , Stefano Bo , Ruben Lier , Jay Armas , Piotr Surówka , Frank Jülicher

In common fluids, viscosity is associated with dissipation. However, when time-reversal-symmetry is broken a new type of non-dissipative `viscosity' may emerge. Recent theories and experiments on classical 2D systems with active spinning…

Soft Condensed Matter · Physics 2021-07-28 Tomer Markovich , Tom C. Lubensky

Chiral active materials display odd dynamical effects in both their elastic and viscous responses. We show that the most symmetric mesophase with two-dimensional odd elasticity in three dimensions is chiral, polar and columnar, with…

Soft Condensed Matter · Physics 2025-01-03 S. J. Kole , Gareth P. Alexander , Ananyo Maitra , Sriram Ramaswamy

Odd viscosity couples stress to strain rate in a dissipationless way. It has been studied in plasmas under magnetic fields, superfluid ${\rm He}^3$, quantum-Hall fluids, and recently in the context of chiral active matter. In most of these…

Soft Condensed Matter · Physics 2024-09-04 Tomer Markovich , Tom C. Lubensky
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