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We analyse the asymptotic behavior for kinetic models describing the collective behavior of animal populations. We focus on models for self-propelled individuals, whose velocity relaxes toward the mean orientation of the neighbors. The…

Analysis of PDEs · Mathematics 2019-02-01 P. Aceves-Sánchez , M. Bostan , J. A. Carrillo , P. Degond

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

A kinetic-fluid model describing the evolutions of disperse two-phase flows is considered. The model consists of the Vlasov-Fokker-Planck equation for the particles (disperse phase) coupled with the compressible Navier-Stokes equations for…

Analysis of PDEs · Mathematics 2017-04-06 Fucai Li , Yanmin Mu , Dehua Wang

For the discrete Cucker-Smale's flocking model with a singular communication weight $\psi(s) = s^{-\alpha}$, with $0<\alpha<1/2$ , we prove that the velocity component of certain type of weak solutions is absolutly continuous. This result…

Analysis of PDEs · Mathematics 2014-12-22 Jan Peszek

We study the classical Cucker-Smale model in continuous time with a positive time delay $\tau$. As in the non-delayed case, unconditional flocking occurs when $\beta \leq 1/2$ for every $\tau>0$. Furthermore, we prove the exponential decay…

Analysis of PDEs · Mathematics 2020-08-24 Mauro Rodriguez Cartabia

We study quantitative estimates for the flocking and uniform-time classical limit to the relativistic Cucker-Smale (in short RCS) model introduced in \cite{Ha-Kim-Ruggeri-ARMA-2020}. Different from previous works, we do not neglect the…

Analysis of PDEs · Mathematics 2024-12-18 Seung-Yeal Ha , Tommaso Ruggeri , Qinghua Xiao

We propose a unified method for the large space-time scaling limit of \emph{linear} collisional kinetic equations in the whole space. The limit is of \emph{fractional} diffusion type for heavy tail equilibria with slow enough decay, and of…

Analysis of PDEs · Mathematics 2023-02-22 Emeric Bouin , Clément Mouhot

We present a stochastic version of the Cucker-Smale flocking dynamics based on a markovian $N$-particle system of pair interactions with unbounded and, in general, non-Lipschitz continuous interaction potential. We establish the infinite…

Probability · Mathematics 2022-03-17 Martin Friesen , Oleksandr Kutoviy

We prove the existence of weak solutions to kinetic flocking model with cut-off interaction function by using Schauder fixed pointed theorem and velocity averaging lemma. Under the natural assumption that the velocity support of the initial…

Analysis of PDEs · Mathematics 2015-10-07 Chunyin Jin

We consider a 1D-2V Vlasov-Fokker-Planck multi-species ionic description coupled to fluid electrons. We address temporal stiffness with implicit time stepping, suitably preconditioned. To address temperature disparity in time and space, we…

Plasma Physics · Physics 2018-05-09 William T. Taitano , Luis Chacon , Andrei N. Simakov

In this work, we perform modulation analysis of monokinetic limits from the kinetic Cucker- Smale model to the pressureless Euler alignment system. Two regimes are considered -- a strong Fokker- Planck force with vanishing noise and Knudsen…

Analysis of PDEs · Mathematics 2025-08-08 Alina Chertock , Roman Shvydkoy , Trevor Teolis

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

The purpose of this paper is to consider flocking formations of a second order dynamic system on a sphere with a Cucker-Smale type flocking operator and cooperative control. The flocking operator consists of a weighted control parameter and…

Dynamical Systems · Mathematics 2021-07-12 Sun-Ho Choi , Dohyun Kwon , Hyowon Seo

In this paper, we are concerned with the global well-posedness and time-asymptotic decay of the Vlasov-Fokker-Planck equation with local alignment forces. The equation can be formally derived from an agent-based model for self-organized…

Analysis of PDEs · Mathematics 2016-06-22 Young-Pil Choi

Birds in a flock move in a correlated way, resulting in large polarization of velocities. A good understanding of this collective behavior exists for linear motion of the flock. Yet observing actual birds, the center of mass of the group…

To study the kinetics of phase separation in active matter systems, we consider models that impose a Vicsek-type self-propulsion rule on otherwise passive particles interacting via the Lennard-Jones potential. Two types of kinetics are of…

Statistical Mechanics · Physics 2023-10-31 Tanay Paul , Nalina Vadakkayil , Subir K. Das

We present a systematic approach to regularity theory of the multi-dimensional Euler alignment systems with topological diffusion introduced in \cite{STtopo}. While these systems exhibit flocking behavior emerging from purely local…

Analysis of PDEs · Mathematics 2021-07-05 Daniel Lear , David N. Reynolds , Roman Shvydkoy

We present a new finite volume method for computing numerical approximations of a system of nonlocal transport equation modeling interacting species. This method is based on the work [F. Delarue, F. Lagoutire, N. Vauchelet, Convergence…

Analysis of PDEs · Mathematics 2019-12-16 Anissa Keurti , Thomas Rey

We extend to multi-dimensions the work of [1], where new fully explicit kinetic methods were built for the approximation of linear and non-linear convection-diffusion problems. The fundamental principles from the earlier work are retained:…

Numerical Analysis · Mathematics 2023-12-29 Gauthier Wissocq , Rémi Abgrall

In this paper, we propose a coupled system describing the interaction between the Relativistic Cucker-Smale model and the incompressible Navier-Stokes equations via a drag force, and establish a global existence theory as well as the…

Analysis of PDEs · Mathematics 2025-03-18 Shenglun Yan , Weiyuan Zou