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Cooperative transport is a striking phenomenon where multiple agents join forces to transit a payload too heavy for the individual. While social animals such as ants are routinely observed to coordinate transport at scale, reproducing the…

How do flocks, herds and swarms proceed through disordered environments? This question is not only crucial to animal groups in the wild, but also to virtually all applications of collective robotics, and active materials composed of…

Soft Condensed Matter · Physics 2016-10-17 Alexandre Morin , Nicolas Desreumaux , Jean-Baptiste Caussin , Denis Bartolo

Interactions among neighboring birds in a flock cause an alignment of their flight directions. We show that the minimally structured (maximum entropy) model consistent with these local correlations correctly predicts the propagation of…

Animal swarms displaying a variety of typical flocking patterns would not exist without underlying safe, optimal and stable dynamics of the individuals. The emergence of these universal patterns can be efficiently reconstructed with…

Adaptation and Self-Organizing Systems · Physics 2015-06-17 Csaba Virágh , Gábor Vásárhelyi , Norbert Tarcai , Tamás Szörényi , Gergő Somorjai , Tamás Nepusz , Tamás Vicsek

We consider collective dynamics of self-propelling particles in two dimensions. They can align themselves according to the direction of propulsion of their neighbours, together with a random perturbation (i.e. rotational fluctuation). They…

Soft Condensed Matter · Physics 2019-04-01 Shubhashis Rana , Md. Samsuzzaman , Arnab Saha

Coordinated collective motion in bird flocks and fish schools inspires algorithms for cohesive swarm robotics. This paper presents a position-based flocking model that achieves persistent velocity alignment without velocity sensing. By…

When birds come together to form a flock, the distribution of their individual velocities narrows around the mean velocity of the flock. We argue that, in a broad class of models for the joint distribution of positions and velocities, this…

Statistical Mechanics · Physics 2016-06-01 Michele Castellana , William Bialek , Andrea Cavagna , Irene Giardina

Long arrays of identical, self-propelling flapping flyers are inherently unstable and thus unlikely to exist without active control mechanisms. One approach to enable long in-line formations is to enforce a constant separation between the…

Fluid Dynamics · Physics 2026-01-21 Javier Chico-Vázquez , Christiana Mavroyiakoumou

The aim of the present paper is to elucidate the transition from collective to random behavior exhibited by various mathematical models of bird flocking. In particular, we compare Vicsek's model [Viscek et al., Phys. Rev. Lett. 75, 1226 --…

Adaptation and Self-Organizing Systems · Physics 2015-06-17 H. Christodoulidi , K. van der Weele , Ch. G. Antonopoulos , T. Bountis

We report a motility-induced pinning transition in the active Ising model for a self-propelled particle system with discrete symmetry. This model was known to exhibit a liquid-gas type flocking phase transition, but a recent study reveals…

Statistical Mechanics · Physics 2026-04-09 Chul-Ung Woo , Jae Dong Noh

We study a model for flocking given by a $n$-particle system under which each particle jumps forward by a random amount, independently sampled from a given distribution $\theta$, with rate given by a non-increasing function $w$ of its…

Probability · Mathematics 2024-04-23 Sayan Banerjee , Amarjit Budhiraja , Dilshad Imon

In a system of noisy self-propelled particles with interactions that favor directional alignment, collective motion will appear if the density of particles increases beyond a certain threshold. In this paper, we argue that such a threshold…

Soft Condensed Matter · Physics 2010-03-29 Chiu Fan Lee

We present the first decentralized multi-copter flock that performs stable autonomous outdoor flight with up to 10 flying agents. By decentralized and autonomous we mean that all members navigate themselves based on the dynamic information…

We bound the time it takes for a group of birds to reach steady state in a standard flocking model. We prove that (i) within single exponential time fragmentation ceases and each bird settles on a fixed flying direction; (ii) the flocking…

Computational Geometry · Computer Science 2009-05-27 Bernard Chazelle

We consider the interplay between persistent motion, which is a generic property of active particles, and a recoil interaction which causes particles to jump apart on contact. The recoil interaction exemplifies an active contact interaction…

Statistical Mechanics · Physics 2023-02-10 Matthew J Metson , Martin R Evans , Richard A Blythe

We study a simple swarming model on a two-dimensional lattice where the self-propelled particles exhibit a tendency to align ferromagnetically. Volume exclusion effects are present: particles can only hop to a neighboring node if the node…

Biological Physics · Physics 2013-02-18 Fernando Peruani , Tobias Klauss , Andreas Deutsch , Anja Voss-Boehme

Collective behavior in biological systems was first captured by the Vicsek model, in which particles align their velocities in the average direction of neighbors, leading to coherent motion and showing an order-disorder transition. However,…

Soft Condensed Matter · Physics 2026-02-26 Mohit Gaur , Arnab Saha , Subhajit Paul

Sea urchin feeding fronts are a striking example of spatial pattern formation in an ecological system. If it is assumed that urchins are asocial, and that they move randomly, then the formation of these dense fronts is an apparent paradox.…

Populations and Evolution · Quantitative Biology 2007-05-23 Edward R Abraham

We present a model of active particles interacting through a dynamic, heterogeneous environment, leading to emergent collective behaviors without direct agent-to-agent communication. Expanding the resource-dependent framework introduced in…

Biological Physics · Physics 2026-01-22 Gaston Briozzo , Gustavo J. Sibona , Fernando Peruani

Field control provides a practical route to programmable active matter, yet how weak fields modify non-equilibrium coexistence and interfaces remains unclear. To address this, we study a minimal flocking model of active Potts particles…

Soft Condensed Matter · Physics 2026-03-30 Mintu Karmakar , Matthieu Mangeat , Swarnajit Chatterjee , Heiko Rieger , Raja Paul