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In this study, we introduce a minimal model for a collection of polar self-propelled particles (SPPs) on a two-dimensional substrate where each particle has a different ability to interact with its neighbours. The SPPs interact through a…

Statistical Mechanics · Physics 2021-02-02 Jay Prakash Singh , Sudipta Pattanayak , Shradha Mishra

In this paper we present our detailed investigations on the nature of the phase transition in the scalar noise model (SNM) of collective motion. Our results confirm the original findings of Vicsek et al. [Phys. Rev. Lett. 75 (1995) 1226]…

Adaptation and Self-Organizing Systems · Physics 2009-11-11 Mate Nagy , Istvan Daruka , Tamas Vicsek

Collective movement is observed widely in nature, where individuals interact locally to produce globally ordered, coherent motion. In typical models of collective motion, each individual takes the average direction of multiple neighbors,…

Quantitative Methods · Quantitative Biology 2026-01-23 Yogesh Kumar KC , Arshed Nabeel , Srikanth Iyer , Vishwesha Guttal

Understanding collective self-organization in active matter, such as bird flocks and fish schools, remains a grand challenge in physics. Interactions that induce alignment are essential for flocking; however, alignment alone is generally…

Soft Condensed Matter · Physics 2025-07-01 Julian Giraldo-Barreto , Viktor Holubec

We study a model of flocking in order to describe the transitions during the collective motion of organisms in three dimensions (e.g., birds). In this model the particles representing the organisms are self-propelled, i.e., they move with…

Biological Physics · Physics 2015-06-26 A. Czirok , M. Vicsek , T. Vicsek

We study a collection of polar self-propelled particles (SPPs) on a two-dimensional substrate in the presence of random quenched rotators. These rotators act like obstacles which rotate the orientation of the SPPs by an angle determined by…

Statistical Mechanics · Physics 2018-12-19 Rakesh Das , Manoranjan Kumar , Shradha Mishra

We consider a collective behavior model in which individuals try to imitate each others' velocity and have a preferred speed. We show that a phase change phenomenon takes place as diffusion decreases, bringing the system from a "disordered"…

Analysis of PDEs · Mathematics 2017-03-28 Alethea B. T. Barbaro , José A. Cañizo , José A. Carrillo , Pierre Degond

The Vicsek model for the self-propelled particles is investigated with the respect to the introduction of the stochastic perturbation of the dynamics. It is shown that such a dependence can be thought in terms of the isomorphism of the…

Statistical Mechanics · Physics 2010-11-11 A. A. Chepizhko , V. L. Kulinskii

We study a system of self-propelled particles (SPPs) in which individual particles are allowed to switch between a fast aligning and a slow nonaligning state depending upon the degree of the alignment in the neighborhood. The switching is…

Biological Physics · Physics 2022-04-19 Kunal Bhattacharya , Abhijit Chakraborty

Understanding the organization of collective motion in biological systems is an ongoing challenge. In this Paper we consider a minimal model of self-propelled particles with variable speed. Inspired by experimental data from schooling fish,…

Biological Physics · Physics 2015-06-04 Shradha Mishra , Kolbjørn Tunstrøm , Iain D. Couzin , Cristián Huepe

We present a study of pedestrian motion along a corridor in a non-panic regime (e.g., schools, hospitals or airports). Such situations have been discussed so far within the Social Force Model (SFM). We suggest to enrich this model by…

Applications · Statistics 2019-12-06 Juan Cruz Moreno , M. Leticia Rubio Puzzo , Wolfgang Paul

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

Self-propelled particle (SPP) systems are intrinsically out of equilibrium systems, where each individual particle converts energy into work to move in a dissipative medium. When interacting through a velocity alignment mechanism, and the…

Biological Physics · Physics 2014-05-20 Julien Barre , Raphael Chetrite , Massimiliano Muratori , Fernando Peruani

The emergence of collective motion, also known as flocking or swarming, in groups of moving individuals who orient themselves using only information from their neighbors is a very general phenomenon that is manifested at multiple spatial…

Statistical Mechanics · Physics 2016-04-26 David A. Quint , Ajay Gopinathan

Many systems in nature, from ferromagnets to flocks of birds, exhibit ordering phenomena on the large scale. In physical systems order is statistically robust for large enough dimensions, with relative fluctuations due to noise vanishing…

Statistical Mechanics · Physics 2017-04-05 Andrea Cavagna , Irene Giardina , Asja Jelic , Edmondo Silvestri , Massimiliano Viale

We investigate the influence of obstacles on the collective motion of self propelled objects in the framework of the Vicsek model. The obstacles are arranged in a square lattice and have circular shape. We show that by increasing the radius…

Soft Condensed Matter · Physics 2023-08-09 Horacio Serna , Wojciech T. Góźdź

Via molecular dynamics simulations we have studied kinetics of vapor-"solid" phase transition in an active matter model in which self-propulsion is introduced via the well-known Vicsek rule. The overall density of the particles is chosen in…

Soft Condensed Matter · Physics 2020-11-05 Subhajit Paul , Arabinda Bera , Subir K. Das

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…

Soft Condensed Matter · Physics 2020-05-19 Jeffrey M. Moore , Tyler N. Thompson , Matthew A. Glaser , Meredith D. Betterton

By introducing a predictive mechanism with small-world connections, we propose a new motion protocol for self-driven flocks. The small-world connections are implemented by randomly adding long-range interactions from the leader to a few…

Data Analysis, Statistics and Probability · Physics 2009-02-03 Hai-Tao Zhang , Michael Z. Q. Chen , Tao Zhou

A model of self-driven particles similar to the Vicsek model [Phys. Rev. Lett. 75 (1995) 1226] but with metric-free interactions is studied by means of a novel Enskog-type kinetic theory. In this model, N particles of constant speed v0 try…

Statistical Mechanics · Physics 2012-08-21 Yen-Liang Chou , Rylan Wolfe , Thomas Ihle