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We use the Fokker-Planck equation and its moment equations to study the collective behavior of interacting particles in unsteady one-dimensional flows. Particles interact according to a long-range attractive and a short-range repulsive…

Fluid Dynamics · Physics 2014-08-05 Maryam Abedi , Mir Abbas Jalali

Recently, we proposed a self-propelled particle model with competing alignment interactions: nearby particles tend to align their velocities whereas they anti-align their direction of motion with particles which are further away [R.…

Soft Condensed Matter · Physics 2016-05-02 Robert Großmann , Pawel Romanczuk , Markus Bär , Lutz Schimansky-Geier

We study analytically the emergence of spontaneous collective motion within large bidimensional groups of self-propelled particles with noisy local interactions, a schematic model for assemblies of biological organisms. As a central result,…

Statistical Mechanics · Physics 2009-11-11 Eric Bertin , Michel Droz , Guillaume Gregoire

Starting from a particle model describing self-propelled particles interacting through nematic alignment, we derive a macroscopic model for the particle density and mean direction of motion. We first propose a mean-field kinetic model of…

Mathematical Physics · Physics 2019-10-08 Pierre Degond , Sara Merino-Aceituno

We study the structure and phase behavior of a binary mixture where one of the components is self-propelling in nature. The inter-particle interactions in the system were taken from the Asakura-Oosawa model, for colloid-polymer mixtures,…

Statistical Mechanics · Physics 2015-06-17 Subir K. Das , Sergei Egorov , Benjamin Trefz , Peter Virnau , Kurt Binder

We provide a numerical study of the macroscopic model of [3] derived from an agent-based model for a system of particles interacting through a dynamical network of links. Assuming that the network remodelling process is very fast, the…

We present an individual-based model describing disk-like self-propelled particles moving inside parallel planes. The disk directions of motion follow alignment rules inside each layer. Additionally, the disks are subject to interactions…

Adaptation and Self-Organizing Systems · Physics 2015-02-23 Pierre Degond , Laurent Navoret

Asymmetric obstacles can be exploited to direct the motion and induce sorting of run-and-tumbling particles. In this work, we show that flocking particles which follow the Vicsek model aligning rules experience a collective trapping in the…

Soft Condensed Matter · Physics 2019-12-02 Raul Martinez , Francisco Alarcon , Juan Luis Aragones , Chantal Valeriani

We study the collective dynamics of a population of particles/organisms subject to self-consistent attraction-repulsion interactions and an external velocity field. The starting point of our analysis is a mean-field kinetic model and we…

Analysis of PDEs · Mathematics 2025-11-04 Thierry Goudon , Antoine Mellet

We numerically study a discretized Vicsek model (DVM) with particles orienting in $q$ possible orientations in two dimensions. The study probes the significance of anisotropic orientation and microscopic interaction on the macroscopic…

Statistical Mechanics · Physics 2024-05-07 Mintu Karmakar , Swarnajit Chatterjee , Raja Paul , Heiko Rieger

We investigate the collective dynamics of self-propelled droplets, confined in a one dimensional micro-fluidic channel. On one hand, neighboring droplets align and form large trains of droplets moving in the same direction. On the other…

Soft Condensed Matter · Physics 2020-05-14 Pierre Illien , Charlotte de Blois , Yang Liu , Marjolein N. van der Linden , Olivier Dauchot

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 use a combination of unsupervised clustering and sparsity-promoting inference algorithms to learn locally dominant force balances that explain macroscopic pattern formation in self-organized active particle systems. The self-organized…

Soft Condensed Matter · Physics 2023-07-28 Dominik Sturm , Suryanarayana Maddu , Ivo F. Sbalzarini

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

We consider flocking of self-propelling agents in two dimensions, each of which communicates with its neighbors within a limited vision cone. Also, the communication occurs with some delay. The communication among the agents are modeled by…

Soft Condensed Matter · Physics 2018-03-13 Mihir Durve , Arnab Saha , Ahmed Sayeed

A macroscopic hydrodynamic system that couples a particle and a wave has recently renewed interest in the question as to what extent a classical system may reproduce quantum phenomena. Here we investigate single-particle diffraction with a…

Fluid Dynamics · Physics 2024-10-31 Giuseppe Pucci , Antoine Bellaigue , Alessia Cirimele , Giuseppe Ali , Anand U. Oza

Self-propelled particles with hydrodynamic interactions (microswimmers) have previously been shown to produce long-range ordering phenomena. Many theoretical explanations for these collective phenomena are connected to instabilities in the…

Soft Condensed Matter · Physics 2017-05-03 Yuzhou Qian , Peter R. Kramer , Patrick T. Underhill

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

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

When particles move at a constant speed and have the tendency to align their directions of motion, ordered large scale movement can emerge despite significant levels of noise. Many variants of this model of self-propelled particles have…

Biological Physics · Physics 2012-12-11 Matthias Meschede , Oskar Hallatschek