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Ordered, collective motions commonly arise spontaneously in systems of many interacting, active units, ranging from cellular tissues and bacterial colonies to self-propelled colloids and animal flocks. Active phases are especially rich when…

How chirality propagates across scales remains an open question in many biological and synthetic systems. An especially clear manifestation of this propagation is found in in vitro gliding assays of cytoskeletal filaments on surfaces,…

In active matter systems, self-propelled particles can self-organize to undergo collective motion, leading to persistent dynamical behavior out of equilibrium. In cells, cytoskeletal filaments and motor proteins self-organize into complex…

Controlling the motion of active matter is a central issue that has recently garnered significant attention in fields ranging from non-equilibrium physics to chemical engineering and biology. Distinct methods for controlling active matter…

Collective motion in actively propelled particle systems is triggered on the very local scale by nucleation of coherently moving units consisting of just a handful of particles. These units grow and merge over time, ending up in a…

Active matter systems characterized by the interplay of chirality and self-alignment offer a rich landscape for the emergence of non-equilibrium collective behaviors and the development of autonomous materials. We present a versatile…

Living materials such as biological tissues or bacterial colonies are collections of heterogeneous entities of different sizes, capable of autonomous motion, and often capable of cooperating. Such a degree of complexity brings to collective…

Active matter comprises individual units that convert energy into mechanical motion. In many examples, such as bacterial systems and biofilament assays, constituent units are elongated and can give rise to local nematic orientational order.…

We introduce a minimal model for a collection of self-propelled apolar active particles, also called as `active nematic', on a two-dimensional substrate and study the order-disorder transition with the variation of density. The particles…

Active matter systems - such as a collection of active colloidal particles - operate far from equilibrium with complex inter-particle interactions that govern their collective dynamics. Predicting the collective dynamics of such systems may…

These lecture notes are designed to provide a brief introduction into the phenomenology of active matter and to present some of the analytical tools used to rationalize the emergent behavior of active systems. Such systems are made of…

The emergence of macroscopic order and patterns is a central paradigm in systems of (self-)propelled agents, and a key component in the structuring of many biological systems.The relationships between the ordering process and the underlying…

Active matter describes materials whose constituents are driven out of equilibrium by continuous energy consumption, for instance from ATP. Due to the orientable character of the constituents, active suspensions can attain liquid…

Active matter systems may be characterised by the conversion of energy into active motion, e.g. the self-propulsion of microorganisms. Artificial active colloids form models which exhibit essential properties of more complex biological…

Active matter systems evade the constraints of thermal equilibrium, leading to the emergence of intriguing collective behavior. A paradigmatic example is given by motor-filament mixtures, where the motion of motor proteins drives alignment…

Active forces occurring within cells can drive crucial biological processes that involve spontaneous organization and shape change, such as cell division. Motivated by recent in vitro experiments of nematic droplets of cytoskeletal…

Collective rotations are common in active matter, enhancing cohesion, transport, and mixing. They are typically attributed to chiral non-reciprocal dynamics due to intrinsic particle chirality, torque-generating interactions among units, or…

We study the spontaneous motion, binary collisions, and collective dynamics of "polar disks", i.e. purpose-built particles which, when vibrated between two horizontal plates, move coherently along a direction strongly correlated to their…

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…

We study a crystal composed of active units governed by self-alignment and chirality. The first mechanism acts as an effective torque that aligns the particle orientation with its velocity, while the second drives individual particles along…