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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…

Coevolving and competing species or game-theoretic strategies exhibit rich and complex dynamics for which a general theoretical framework based on finite populations is still lacking. Recently, an explicit mean-field description in the form…

We propose a statistical model for static and sliding friction between rough surfaces. Approximating the contact between rough surfaces by the contact of an ensemble of one-dimensional viscoelastic elements with a rough rigid surface, we…

Flocking behavior is observed in biological systems from the cellular to super-organismal length scales, and the mechanisms and purposes of this behavior are objects of intense interest. In this paper, we study the collective dynamics of…

Biological systems achieve precise control over ambient fluids through the self-organization of active protein structures including flagella, cilia, and cytoskeletal networks. In active structures individual proteins consume chemical energy…

Termites which are able to forage in the open can be often seen, in the field or in the lab: (i) wandering around, forming no observable pattern, or (ii) clustering themselves in a dense and almost immobile pack, or (iii) milling about in a…

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…

This paper presents a position-based flocking model for interacting agents, balancing cohesion-separation and alignment to achieve stable collective motion. The model modifies a position-velocity-based approach by approximating velocity…

Here we show that coupling to curvature has profound effects on collective motion in active systems, leading to patterns not observed in flat space. Biological examples of such active motion in curved environments are numerous: curvature…

Many types of motile cells perform durotaxis, namely, directed migration following gradients of substrate stiffness. Recent experiments have revealed that cell monolayers can migrate toward stiffer regions even when individual cells do not…

It is frequent for active or living entities to find themselves embedded in a surrounding medium. Resulting composite systems are usually classified as either active fluids or active solids. Yet, in reality, particularly in the biological…

Terracettes, striking, step-like landforms that stripe steep, vegetated hillslopes, have puzzled scientists for more than a century. Competing hypotheses invoke either slow mass-wasting or the relentless trampling of grazing animals, yet no…

We consider a compressible Euler system with singular velocity alignment, known as the Euler-alignment system, describing the flocking behaviors of large animal groups. We establish a local well-posedness theory for the system, as well as a…

Classic computational models of collective motion suggest that simple local averaging rules can promote many observed group level patterns. Recent studies, however, suggest that rules simpler than local averaging may be at play in real…

We present a model of soft active particles that leads to a rich array of collective behavior found also in dense biological swarms of bacteria and other unicellular organisms. Our model uses only local interactions, such as Vicsek-type…

Polar active matter - including animal herds, aggregates of motile cells and active colloids - often forms coordinated migration patterns, such as flocking. This orderly motion can be disrupted by full-integer topological defects…

Video-based high-density crowd analysis and prediction has been a long-standing topic in computer vision. It is notoriously difficult due to, but not limited to, the lack of high-quality data and complex crowd dynamics. Consequently, it has…

One of the most impressive features of moving animal groups is their ability to perform sudden coherent changes in travel direction. While this collective decision can be a response to an external perturbation, such as the presence of a…

We present existence, uniqueness and continuous dependence results for some kinetic equations motivated by models for the collective behavior of large groups of individuals. Models of this kind have been recently proposed to study the…

A fundamental question in complex systems is how to relate interactions between individual components ("microscopic description") to the global properties of the system ("macroscopic description"). Another fundamental question is whether…