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A wide range of living and artificial active matter exists in close contact with substrates and under strong confinement, where in addition to dipolar active stresses, quadrupolar active stresses can become important. Here, we numerically…

The interplay of nonlinearity and topology results in many novel and emergent properties across a number of physical systems such as chiral magnets, nematic liquid crystals, Bose-Einstein condensates, photonics, high energy physics, etc. It…

The persistent dynamics in systems out of equilibrium, particularly those characterized by annihilation and creation of topological defects, is known to involve complicated spatiotemporal processes and is deemed difficult to control. Here…

We comprehend the role of imperfections in materials consisting of interacting particles, arising from different origins on their universal features. Specifically, we report the static and dynamic responses in a cluster of Coulomb…

Active matter, composed of self-propelled entities, forms a wide class of out-of-equilibrium systems that display striking collective behaviors among which the so-called active turbulence where spatially and time disordered flow patterns…

Half-vortices have been recently shown to be the elementary topological defects supported by a spinor cavity exciton-polaritons condensates with spin anisotropic interactions (Y. G. Rubo, Phys. Rev. Lett. 99, 106401 (2007)). A half vortex…

Turing patterns are stationary, wave-like structures that emerge from the nonequilibrium assembly of reactive and diffusive components. While they are foundational in biophysics, their classical formulation relies on a single characteristic…

Topological defects, which are singular points in a director field, play a major role in shaping active systems. Here, we experimentally study topological defects and the flow patterns around them, that are formed during the highly rapid…

Monolayers of anisotropic cells exhibit long-ranged orientational order and topological defects. During the development of organisms, orientational order often influences morphogenetic events. However, the linkage between the mechanics of…

Using the Born-Oppenheimer approximation, we present a general description of topological defects dynamics in $p$-atic materials on curved surfaces, and simplify it in the case of active nematics. We find that activity induces a geometric…

Self-propulsion is a quintessential aspect of biological systems, which can induce nonequilibrium phenomena that have no counterparts in passive systems. Motivated by biophysical interest together with recent advances in experimental…

The potential role of cosmic topological defects has raised interest in the astrophysical community for many years now. In this set of notes, we give an introduction to the subject of cosmic topological defects and some of their possible…

The configurational and melting properties of large two-dimensional clusters of charged classical particles interacting with each other via the Coulomb potential are investigated through the Monte Carlo simulation technique. The particles…

As a method for controlling active materials, researchers have suggested designing patterns of activity on a substrate, which should guide the motion of topological defects. To investigate this concept, we model the behavior of a single…

Active matter, comprising many active agents interacting and moving in fluids or more complex environments, is a commonly occurring state of matter in biological and physical systems. By its very nature active matter systems exist in…

We use classical molecular dynamics combined with the recently developed metadynamics method [A. Laio and M. Parrinello, Procs. Natl. Acad. Sci. USA 99, 20 (2002)] to study the process of bulk melting in hexagonal ice. Our simulations show…

Collective cell migration governs a range of physiological and pathological processes, from tissue morphogenesis to cancer invasion, in which topological defects arise as an inevitable consequence of frequent cellular rearrangement and…

We establish how active stress globally affects the morphology of disclination lines of a three dimensional active nematic liquid crystal under chaotic flow. Thanks to a defect detection algorithm based on the local nematic orientation, we…

Point-like motile topological defects control the universal dynamics of diverse two-dimensional active nematics ranging from shaken granular rods to cellular monolayers. A comparable understanding in higher dimensions has yet to emerge. We…

We present a theory of active, permeating, polar gels, based on a two-fluid model. An active relative force between the gel components creates a steady-state current. We analyze its stability, while considering two polar coupling terms to…