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We review the observations and the basic laws describing the essential aspects of collective motion -- being one of the most common and spectacular manifestation of coordinated behavior. Our aim is to provide a balanced discussion of the…

Statistical Mechanics · Physics 2012-08-16 Tamás Vicsek , Anna Zafeiris

Designing microscopic and nanoscopic self-propelled particles and characterising their motion has become a major scientific challenge over the past decades. To this purpose, phoretic effects, namely propulsion mechanisms relying on local…

Soft Condensed Matter · Physics 2021-04-09 Pierre Illien , Ramin Golestanian , Ayusman Sen

Granular materials are involved in most industrial and environmental processes, as well as many civil engineering applications. Although significant advances have been made in understanding the statics and dynamics of cohesionless grains…

Soft Condensed Matter · Physics 2025-11-21 Ram Sudhir Sharma , Alban Sauret

Collective motion is a manifestation of emergent phenomena in medium-heavy and heavy nuclei. A relatively large number of constituent nucleons contribute coherently to nuclear excitations (vibrations, rotations) that are characterized by…

Nuclear Theory · Physics 2022-03-18 Z. P. Li , D. Vretenar

Swarming or collective motion of living entities is one of the most common and spectacular manifestations of living systems having been extensively studied in recent years. A number of general principles have been established. The…

Cell Behavior · Quantitative Biology 2014-06-06 Elod Mehes , Tamas Vicsek

In this review article, we focus on collective motion in externally driven colloidal suspensions, as well as how these collective effects can be harnessed for use in microfluidic applications. We highlight the leading role of hydrodynamic…

Soft Condensed Matter · Physics 2018-11-01 Michelle Driscoll , Blaise Delmotte

Self-powered motion in catalytic colloidal particles provides a compelling example of active matter, i.e. systems that engage in single-particle and collective behavior far from equilibrium. The long-time, long-distance behavior of such…

Soft Condensed Matter · Physics 2017-10-25 Young-Moo Byun , Paul E. Lammert , Yiying Hong , Ayusman Sen , Vincent H. Crespi

Active solids such as cell collectives, colloidal clusters, and active metamaterials exhibit diverse collective phenomena, ranging from rigid body motion to shape-changing mechanisms. The nonlinear dynamics of such active materials remains…

Soft Condensed Matter · Physics 2024-06-21 Claudio Hernández-López , Paul Baconnier , Corentin Coulais , Olivier Dauchot , Gustavo Düring

These lecture notes were prepared for the 2018 Summer School on `Active Matter and Non-equilibrium Statistical Physics' at l'\'{E}cole de Physique des Houches. They survey metabolic activity across a wide range of living organisms, and…

Soft Condensed Matter · Physics 2019-03-25 Eric R. Dufresne

We review theoretical models of individual motility as well as collective dynamics and pattern formation of active particles. We focus on simple models of active dynamics with a particular emphasis on nonlinear and stochastic dynamics of…

Other Condensed Matter · Physics 2015-06-04 Pawel Romanczuk , Markus Bär , Werner Ebeling , Benjamin Lindner , Lutz Schimansky-Geier

Recent experiments have led to active colloidal molecules which aggregate from non-motile building blocks and acquire self-propulsion through their non-reciprocal interactions. Here, we model the collective behavior of such active molecules…

Soft Condensed Matter · Physics 2023-08-04 Sebastian Fehlinger , Benno Liebchen

From the formation of animal flocks to the emergence of coordinate motion in bacterial swarms, at all scales populations of motile organisms display coherent collective motion. This consistent behavior strongly contrasts with the difference…

Soft Condensed Matter · Physics 2013-11-11 Antoine Bricard , Jean-Baptiste Caussin , Nicolas Desreumaux , Olivier Dauchot , Denis Bartolo

With the aim of understanding the emergence of collective motion from local interactions of organisms in a "noisy" environment, we study biologically inspired, inherently non-equilibrium models consisting of self-propelled particles. In…

Biological Physics · Physics 2009-10-31 A. Czirok , T. Vicsek

Active matter spans a wide range of time and length scales, from groups of cells and synthetic self-propelled particles to schools of fish, flocks of birds, or even human crowds. The theoretical framework describing these systems has shown…

Granular materials are ubiquitous in our daily lives. While they have been a subject of intensive engineering research for centuries, in the last decade granular matter attracted significant attention of physicists. Yet despite a major…

Soft Condensed Matter · Physics 2009-11-11 Igor S. Aranson , Lev S. Tsimring

The term active matter describes diverse systems, spanning macroscopic (e.g. shoals of fish and flocks of birds) to microscopic scales (e.g. migrating cells, motile bacteria and gels formed through the interaction of nanoscale molecular…

Soft Condensed Matter · Physics 2010-03-11 Gautam I. Menon

We study the interplay between collective and incoherent single-particle motion in a model of two chains of particles whose interaction comprises a non-integrable part. In the perturbative regime, but for a general form of the interaction,…

Quantum Physics · Physics 2015-05-20 Jens Hammerling , Boris Gutkin , Thomas Guhr

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…

Soft Condensed Matter · Physics 2021-07-19 Abraham Mauleon-Amieva , Michael P. Allen , C. Patrick Royall

The study of systems with sustained energy uptake and dissipation at the scale of the constituent particles is an area of central interest in nonequilibrium statistical physics. Identifying such systems as a distinct category -- Active…

Statistical Mechanics · Physics 2017-06-07 Sriram Ramaswamy

Collective behavior in animals has long been modeled through self-propelled particle models, which reproduce striking group-level phenomena through abstract interaction forces. Yet these models are fundamentally descriptive: they leave open…

Robotics · Computer Science 2026-05-19 Vito Mengers , Bao Duc Cao , Oliver Brock
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