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Active matter encompasses different nonequilibrium systems in which individual constituents convert energy into non-conservative forces or motion at the microscale. This review provides an elementary introduction to the role of topology in…

Soft Condensed Matter · Physics 2022-06-28 Suraj Shankar , Anton Souslov , Mark J. Bowick , M. Cristina Marchetti , Vincenzo Vitelli

The spontaneous emergence of collective flows is a generic property of active fluids and often leads to chaotic flow patterns characterised by swirls, jets, and topological disclinations in their orientation field. However, the ability to…

Soft Condensed Matter · Physics 2017-03-07 Tyler N. Shendruk , Amin Doostmohammadi , Kristian Thijssen , Julia M. Yeomans

Topological defects in systems with liquid-crystalline order are crucial in determining their large-scale properties. In active systems, they are known to have properties impossible at equilibrium: for example, $+1/2$ defects in…

Soft Condensed Matter · Physics 2026-02-17 Giacomo Marco La Montagna , Sumeja Burekovic , Ananyo Maitra , Cesare Nardini

In active nematic liquid crystals activity is able to drive chaotic spatiotemporal flows referred to as active turbulence. Active turbulence has been characterized through theoretical and experimental work as a low Reynolds number…

Soft Condensed Matter · Physics 2022-11-30 C. Rorai , F. Toschi , I. Pagonabarraga

Liquid crystals inevitably possess topological defect excitations generated through boundary conditions, applied fields or in quenches to the ordered phase. In equilibrium pairs of defects coarsen and annihilate as the uniform ground state…

Soft Condensed Matter · Physics 2013-06-05 Luca Giomi , Mark J. Bowick , Xu Ma , M. Cristina Marchetti

In pulsating active matter, topological defects are motile despite the absence of any macroscopic flows and microscopic self-propulsion. We reveal that this motility arises from a ratchet effect: the mechanochemical coupling between local…

Soft Condensed Matter · Physics 2026-05-26 Luca Casagrande , Alessandro Manacorda , Etienne Fodor

The effects of an electric field on the flow patterns and defect dynamics of two-dimensional active nematics are numerically investigated. We found that field-induced director reorientation causes anisotropic active turbulence characterized…

Soft Condensed Matter · Physics 2023-07-20 Yutaka Kinoshita , Nariya Uchida

Dense active matter, from bacterial suspensions and microtubule bundles driven by motor proteins to cellular monolayers and synthetic Janus particles, is characterised by mesoscale turbulence, the emergence of chaotic flow structures. By…

Soft Condensed Matter · Physics 2016-06-22 Sumesh P. Thampi , Amin Doostmohammadi , Tyler N. Shendruk , Ramin Golestanian , Julia M. Yeomans

Our understanding of the mechanism by which topological defects are formed in symmetry breaking phase transitions has recently changed. We examine the non-equilibrium dynamics of defect formation for weakly-coupled global O(N) theories…

High Energy Physics - Theory · Physics 2010-11-01 A. J. Gill , R. J. Rivers

Colloidal inclusions in nematic fluids induce topological defects that govern their dynamics. These defects create well-understood rheological behavior in passive nematics, but the interplay between colloid-associated defects and…

Soft Condensed Matter · Physics 2025-03-26 Timofey Kozhukhov , Benjamin Loewe , Kristian Thijssen , Tyler N. Shendruk

By means of the variational method and numerical simulations, we demonstrate the existence of stable 3D nonlinear modes, viz. vortex ``bullets'', in the form of pulsed beams carrying orbital angular momentum, that can self-trap in a 2D…

Topological defects are ubiquitous on surfaces with orientational order fields. Here, we study equilibrium states generated by the feedback between geometry and nematic order on fluid membranes with an integer topological defect. When the…

Soft Condensed Matter · Physics 2024-11-14 D. J. G. Pearce , C. Thibault , Q. Chaboche , C. Blanch-Mercader

Polar active matter of self-propelled particles sustain spontaneous flows through the full-integer topological defects. We study theoretically the effect of both polar and dipolar active forces on the flow profile around $\pm 1$ defects and…

Soft Condensed Matter · Physics 2023-03-14 Jonas Rønning , Julian Renaud , Amin Doostmohammadi , Luiza angheluta

We numerically study two-dimensional active nematics with periodic activity patterning. For stripes of activity, we observe a transition from two-dimensional to one-dimensional active turbulence as the maximum active force and distance…

Soft Condensed Matter · Physics 2025-03-11 Cody D. Schimming , C. J. O. Reichhardt , C. Reichhardt

When a nematic liquid crystal is confined in a porous medium with strong anchoring conditions, topological defects, called disclinations, are stably formed with numerous possible configurations. Since the energy barriers between them are…

Soft Condensed Matter · Physics 2015-06-12 Takeaki Araki

We study the collective dynamics of self-propelled rods in an inhomogeneous motility field. At the interface between two regions of constant but different motility, a smectic rod layer is spontaneously created through aligning interactions…

Soft Condensed Matter · Physics 2018-02-14 Jens Grauer , Hartmut Löwen , Liesbeth M. C. Janssen

We propose an ``active XY model'' that incorporates key elements of both the classical XY model and the Vicsek model to study the role of topological defects in active matter systems. This model features self-propelled particles with XY…

Soft Condensed Matter · Physics 2026-04-17 Shun Inoue , Satoshi Yukawa

Active turbulence in dense active systems is characterized by high vorticity on a length scale that is large compared to that of individual entities. We describe the properties of active turbulence as momentum propagation is screened by…

Soft Condensed Matter · Physics 2014-12-24 Sumesh P. Thampi , Ramin Golestanian , Julia M. Yeomans

We use numerical simulations and linear stability analysis to study the dynamics of an active liquid crystal film on a substrate in the regime where the passive system would be isotropic. Extensile activity builds up local orientational…

Soft Condensed Matter · Physics 2023-09-26 Fernando Caballero , Zhihong You , M. Cristina Marchetti

We propose an agent-based model of active flexible rods. Inspired by cytoskeletal flows, we introduce activity by an internal flow that contributes to the dissipative forces. The active force between our agents is central and reciprocal,…

Soft Condensed Matter · Physics 2026-03-06 Mathieu Dedenon , Carles Blanch-Mercader , Karsten Kruse , Jens Elgeti