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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…

Chiral active materials are abundant in nature, including the cytoskeleton with attached motor proteins, rotary clusters of bacteria flagella, and self-spinning starfish embryos. These materials break both time reversal and mirror-image…

Soft Condensed Matter · Physics 2025-10-17 Cheng-Tai Lee , Tom C. Lubensky , Tomer Markovich

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

During the last decades active particles have attracted an incipient attention as they have been observed in a broad class of scenarios, ranging from bacterial suspension in living systems to artificial swimmers in nonequilibirum systems.…

Statistical Mechanics · Physics 2023-12-19 Antonio A. Valido , Mattia Coccolo , Miguel A. F. Sanjuán

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

Non-reciprocal interactions in elastic media give rise to rich non-equilibrium behaviors, but controllable experimental realizations of such odd elastic phenomena remain scarce. Building on recent breakthroughs in electrical analogs of…

Soft Condensed Matter · Physics 2025-03-19 Harry Walden , Alexander Stegmaier , Jörn Dunkel , Alexander Mietke

We study a two-dimensional chiral active crystal composed of underdamped chiral active particles. These particles, characterized by intrinsic handedness and persistence, interact via linear forces derived from harmonic potentials. Chirality…

Soft Condensed Matter · Physics 2024-12-25 Umberto Marini Bettolo Marconi , Lorenzo Caprini

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

We theoretically investigate self-oscillating waves of an active material, which have recently been introduced as a non-symmetric part of the elastic moduli, termed odd elasticity. Using Purcell's three-link swimmer model, we reveal that an…

Soft Condensed Matter · Physics 2022-06-22 Kenta Ishimoto , Clément Moreau , Kento Yasuda

We present the linear response theory for an elastic solid composed of active Brownian particles with intrinsic individual chirality, deriving both a normal mode formulation and a continuum elastic formulation. Using this theory, we compute…

Soft Condensed Matter · Physics 2025-08-21 Amir Shee , Silke Henkes , Cristián Huepe

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

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

Active hydrodynamic theories are a powerful tool to study the emergent ordered phases of internally driven particles such as bird flocks, bacterial suspension and their artificial analogues. While theories of orientationally ordered phases…

Soft Condensed Matter · Physics 2019-03-06 Ananyo Maitra , Martin Lenz

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 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 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

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

Models of active nematics in biological systems normally require complexity arising from the hydrodynamics involved at the microscopic level as well as the viscoelastic nature of the system. Here we show that a minimal, space-independent,…

Soft Condensed Matter · Physics 2022-06-27 Emmanuel L. C. VI M. Plan , Huong Le Thi , Julia M. Yeomans , Amin Doostmohammadi

Active cholesterics are chiral in both their structure, which has continuous screw symmetry, and their active stresses, which include contributions from torque dipoles. Both expressions of chirality give rise to curl forces in the…

Soft Condensed Matter · Physics 2025-12-04 Gareth P. Alexander , S. J. Kole , Ananyo Maitra , Sriram Ramaswamy

A recent surge of discoveries has sparked significant interest in active systems where a particle moves autonomously in resonance with its self-generated wave field, leading to notable wave-mediated effects including new propulsion…

Soft Condensed Matter · Physics 2026-05-26 Austin M. Blitstein , Rodolfo R. Rosales , Pedro J. Sáenz
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