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Many particle physics models of matter admit solutions corresponding to stable or long-lived topological defects. In the context of standard cosmology it is then unavoidable that such defects will form during phase transitions in the very…

We study the spatio-temporal dynamics of a model of polar active fluid in two dimensions. The system exhibits a transition from an isotropic to a polarized state as a function of density. The uniform polarized state is, however, unstable…

Topological defects are singularities in material fields that play a vital role across a range of systems: from cosmic microwave background polarization to superconductors, and biological materials. Although topological defects and their…

In many active systems, swimmers collectively stir the surrounding fluid to stabilize some self-sustained vortices. The resulting nonequilibrium state is often referred to as active turbulence, by analogy with the turbulence of passive…

Active matter has played a pivotal role in advancing our understanding of non-equilibrium systems, leading to a fundamental shift in the study of biophysical phenomena. The foundation of active matter research is built on assumptions…

Point-like topological defects are singular configurations that occur in a variety of in and out of equilibrium systems with two-dimensional orientational order. As they are associated with a nonzero circuitation condition, the presence of…

Topological and geometrical properties and the associated topological defects find a rapidly growing interest in studying the interplay between mechanics and the collective behavior of cells on the tissue level. We here test if well studied…

To enhance the understanding of the behavior of active nematic, it is important to understand the behavior of topological defects. In this paper, we study the configuration of topological defects of a two-dimensional active nematic around a…

Collectively moving cellular systems often contain a proportion of dead cells or non-motile genotypes. When mixed, nematically aligning motile and non-motile agents are known to segregate spontaneously. However, the role that topological…

Meso-scale turbulence was originally observed experimentally in various suspensions of swimming bacteria, as well as in the collective motion of active colloids. The corresponding large-scale dynamical patterns were reproduced in a simple…

Topological defects are produced during phase transitions in the very early Universe. They arise in most unified theories of strong, weak and electromagnetic interactions. These lectures focus on the role of topological defects in…

Active systems, from bacterial suspensions to cellular monolayers, are continuously driven out of equilibrium by local injection of energy from their constituent elements and exhibit turbulent-like and chaotic patterns. Here we demonstrate…

Topological defects in active liquid crystals can be confined by introducing gradients of activity. Here, we examine the dynamical behavior of two defects confined by a sharp gradient of activity that separates an active circular region and…

Phase separation routinely occurs in both living and synthetic systems. These phases are often complex and distinguished by features including crystallinity, nematic order, and a host of other nonconserved order parameters. For systems at…

Remarkably, even under negligible inertia, the addition of microstructural agents can generate chaotic flow fields. Such behavior can arise in polymer solutions, leading to elastic turbulence, or from active, self-driven particles, which…

Living materials at different length scales manifest active nematic features such as orientational order, nematic topological defects, and active nematic turbulence. Using numerical simulations we investigate the impact of fluid inertia on…

Inspired by recent experiments that highlight the role of nematic defects in the morphogenesis of epithelial tissues, we develop a minimal framework to study the dynamics of an active curved surface driven by its nematic texture. Allowing…

We study a novel phase of active polar fluids, which is characterized by the continuous creation and destruction of dense clusters due to self-sustained turbulence. This state arises due to the interplay of the self-advection of the aligned…

We consider 1D integrable systems supporting ballistic propagation of excitations, perturbed by a localised defect that breaks most conservation laws and induces chaotic dynamics. Focusing on classical systems, we study an…

We consider a phenomenological continuum theory for an extensile, overdamped active nematic liquid crystal, applicable in the dense regime. Constructed from general principles, the theory is universal, with parameters independent of any…