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Related papers: Flocking Beyond One Species: Novel Phase Coexisten…

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Flocking is a prime example of how robust collective behavior can emerge from simple interaction rules. The flocking transition has been studied extensively since the inception of the original Vicsek model. Here, we introduce a novel…

Soft Condensed Matter · Physics 2024-09-18 Eloise Lardet , Raphaël Voituriez , Silvia Grigolon , Thibault Bertrand

Self-propelled particles with anti-aligning interactions generally do not form a polar order. However, in this Letter, we show that when multiple types of such particles coexist and interact through aligning interactions between different…

Soft Condensed Matter · Physics 2025-12-08 Takahiro Oki , Tetsuhiro S. Hatakeyama , Seiya Nishikawa , Shuji Ishihara , Toshinori Namba

Natural systems are inextricably affected by noise. Within recent decades, the manner in which noise affects the collective behavior of self-organized systems, specifically, has garnered considerable interest from researchers and developers…

Optimization and Control · Mathematics 2016-07-12 Ge Chen

Flocking is ubiquitous in nature and emerges due to short- or long-range alignment interactions among self-propelled agents. Two unfriendly species that antialign or even interact nonreciprocally show more complex collective phenomena,…

Statistical Mechanics · Physics 2025-12-17 Jiwon Choi , Jae Dong Noh , Heiko Rieger

We consider the two-species Vicsek model (TSVM) consisting of two kinds of self-propelled particles, A and B, that tend to align with particles from the same species and to antialign with the other. The model shows a flocking transition…

Statistical Mechanics · Physics 2025-05-02 Swarnajit Chatterjee , Matthieu Mangeat , Chul-Ung Woo , Heiko Rieger , Jae Dong Noh

We show that even weak nonreciprocal alignment leads to large-scale structure formation in flocking mixtures. By combining numerical simulations of a binary Vicsek model and the analysis of coarse-grained continuum equations, we demonstrate…

Statistical Mechanics · Physics 2026-02-16 Charlotte Myin , Benoît Mahault

In this paper, we present a two-species Vicsek model, that describes alignment interactions of self-propelled particles which can either move or not. The model consists in two populations with distinct Vicsek dynamics that interact only via…

Mathematical Physics · Physics 2014-01-08 Laurent Navoret

We study a system of self-propelled particles whose alignment with neighbors depends on the degree of local alignment. We show that such a local conformity interaction naturally yields a Vicsek-type model with pairwise and three-body…

Statistical Mechanics · Physics 2025-12-23 Iván León , Riccardo Muolo , Hiroya Nakao , Keisuke Taga

Natural flocks need to cope with various forms of heterogeneities, for instance, their composition, motility, interaction, or environmental factors. Here, we study the effects of such heterogeneities on the flocking dynamics of the…

Statistical Mechanics · Physics 2025-12-15 Aditya Kumar Dutta , Matthieu Mangeat , Heiko Rieger , Raja Paul , Swarnajit Chatterjee

The theoretical understanding of pattern formation in active systems remains a central problem of interest. Heterogeneous flocks made up of multiple species can exhibit a remarkable diversity of collective states that cannot be obtained…

Statistical Mechanics · Physics 2025-12-23 Eloise Lardet , Letian Chen , Thibault Bertrand

The synchronization of self-propelled particles (SPPs) is a fascinating instance of emergent behavior in living and man-made systems, such as colonies of bacteria, flocks of birds, robot ensembles, and many others. The recent discovery of…

Adaptation and Self-Organizing Systems · Physics 2018-10-12 Nikita Kruk , Yuri Maistrenko , Heinz Koeppl

We investigate collective behavior in a $Q$-species Vicsek model with a nonreciprocal velocity alignment interaction. This system is characterized by a constant phase shift $\alpha$ in the inter-species velocity alignment rule. While the…

Statistical Mechanics · Physics 2025-12-23 Chul-Ung Woo , Heiko Rieger , Jae Dong Noh

Systems composed of interacting self-propelled particles (SPPs) display different forms of order-disorder phase transitions relevant to collective motion. In this paper we propose a generalization of the Vicsek model characterized by an…

Adaptation and Self-Organizing Systems · Physics 2021-04-14 Pau Clusella , Romualdo Pastor-Satorras

The flocking of self-propelled particles in heterogeneous environments is relevant to both natural and artificial systems. The Vicsek model is a canonical choice to investigate such systems due to the minimal number of parameters required…

Computational Physics · Physics 2024-12-11 Eighdi Aung , Nicole Abaid , James E. McClure

We generalize the Vicsek model to describe the collective behaviour of polar circle swimmers with local alignment interactions. While the phase transition leading to collective motion in 2D (flocking) occurs at the same interaction to noise…

Statistical Mechanics · Physics 2017-08-09 Benno Liebchen , Demian Levis

There is growing interest in multi-species active matter systems with reciprocal and non-reciprocal interactions. While such interactions have been explored in continuous symmetry models, less is known about multi-species discrete-symmetry…

Statistical Mechanics · Physics 2025-05-01 Matthieu Mangeat , Swarnajit Chatterjee , Jae Dong Noh , Heiko Rieger

We study a binary metric-free Vicsek model involving two species of self-propelled particles aligning with their Voronoi neighbors, focusing on a weakly nonreciprocal regime, where species $A$ aligns with both $A$ and $B$, but species $B$…

Soft Condensed Matter · Physics 2025-04-04 Tian Tang , Yu Duan , Yu-qiang Ma

We introduce a Vicsek-like flocking model with a minimal form of time-delayed orientational interactions, in which the delays occur on a time scale that is well-separated from other time scales in the model. We achieve this by implementing…

Soft Condensed Matter · Physics 2025-05-19 Charles R. Packard , Daniel M. Sussman

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

Self-propelled particles with alignment, displaying ordered collective motions such as swarming, can be investigated by the well-known Vicsek model. However, challenges still remain regarding the nature of the associated phase transition.…

Statistical Mechanics · Physics 2024-11-12 Ruizhe Yan , Jie Su , Jin Wang
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