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Related papers: Singular Cucker-Smale Dynamics

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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 study the large-time behavior of hydrodynamic model which describes the collective behavior of continuum of agents, driven by pairwise alignment interactions with additional external potential forcing. The external force tends to compete…

Analysis of PDEs · Mathematics 2020-07-15 Ruiwen Shu , Eitan Tadmor

We consider a particle system with a mean-field-type interaction perturbed by some common and individual noises. When the interacting kernels are sublinear and only locally Lipschitz-continuous, relying on arguments based on the tightness…

Probability · Mathematics 2020-07-27 Angelo Rosello

We present a new stochastic particle system on networks which describes the flocking behavior and pattern formation. More precisely, we consider Cucker-Smale particles with decentralized formation control and multiplicative noises on…

Dynamical Systems · Mathematics 2022-04-20 Young-Pil Choi , Doeun Oh , Oliver Tse

In this work we study propagation of chaos for solutions of the Liouville equation for the classical discrete Cucker-Smale system. Assuming that the communication kernel satisfies the heavy tail condition -- known to be necessary to induce…

Analysis of PDEs · Mathematics 2021-12-09 Vinh Nguyen , Roman Shvydkoy

In this paper we propose a numerical study of macroscopic models for collective cell migration, focusing on a multi-dimensional pressureless Euler-type model with non-local interactions coupled with chemotaxis, rigorously derived from…

Numerical Analysis · Mathematics 2025-08-06 Marta Menci , Roberto Natalini , Tommaso Tenna

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 investigate the pressureless fractional Euler-alignment system with nonlinear velocity couplings, referred to as the $p$-Euler-alignment system. This model features a nonlinear velocity alignment force, interpreted as a density-weighted…

Analysis of PDEs · Mathematics 2024-09-17 Young-Pil Choi , Michał Fabisiak , Jan Peszek

We derive a novel thermodynamically consistent Navier--Stokes--Cahn--Hilliard system with dynamic boundary conditions. This model describes the motion of viscous incompressible binary fluids with different densities. In contrast to previous…

Analysis of PDEs · Mathematics 2023-10-25 Andrea Giorgini , Patrik Knopf

We present a simple proof of asymptotic consensus in the discrete Hegselmann-Krause model and flocking in the discrete Cucker-Smale model with renormalization and variable delay. It is based on convexity of the renormalized communication…

Dynamical Systems · Mathematics 2020-06-30 Jan Haskovec

In this paper, we study global existence and large time behaviors of strong solutions to the kinetic Cucker--Smale model coupled with the three dimensional incompressible Navier--Stokes equations in the whole space. Using the maximal…

Analysis of PDEs · Mathematics 2021-12-28 Chunyin Jin

We consider a hydrodynamic model of self-organized evolution of agents, with singular interaction kernel $\phi_\alpha(x)=1/|x|^{1+\alpha}$ ($0<\alpha<2$), in the presence of an additional external force. Well-posedness results are already…

Analysis of PDEs · Mathematics 2018-12-05 Trevor M. Leslie

Many classical examples of models of self-organized dynamics, including the Cucker-Smale, Motsch-Tadmor, multi-species, and several others, include an alignment force that is based upon density-weighted averaging protocol. Those protocols…

Analysis of PDEs · Mathematics 2024-03-14 Roman Shvydkoy

This paper considers the Keller-Segel model coupled to stochastic Navier-Stokes equations (KS-SNS, for short), which describes the dynamics of oxygen and bacteria densities evolving within a stochastically forced 2D incompressible viscous…

Analysis of PDEs · Mathematics 2024-08-02 Lei Zhang , Bin Liu

An implicit Euler finite-volume scheme for a nonlocal cross-diffusion system on the one-dimensional torus, arising in population dynamics, is proposed and analyzed. The kernels are assumed to be in detailed balance and satisfy a weak…

Numerical Analysis · Mathematics 2023-02-23 Ansgar Jüngel , Stefan Portisch , Antoine Zurek

We consider in this work the convergence of a split-step Euler type scheme (SSM) for the numerical simulation of interacting particle Stochastic Differential Equation (SDE) systems and McKean-Vlasov Stochastic Differential Equations…

Probability · Mathematics 2023-03-28 Xingyuan Chen , Goncalo dos Reis

We rigorously show the mean-field limit for a large class of swarming individual based models with local sharp sensitivity regions. For instance, these models include nonlocal repulsive-attractive forces locally averaged over sharp vision…

Analysis of PDEs · Mathematics 2016-05-06 José A. Carrillo , Young-Pil Choi , Maxime Hauray , Samir Salem

The generic alignment conjecture states that for almost every initial data on the torus solutions to the Cucker-Smale system with a strictly local communication align to the common mean velocity. In this note we present a partial resolution…

Dynamical Systems · Mathematics 2025-08-12 Roman Shvydkoy

This paper presents a unified mathematical theory of swarms where the dynamics of social behaviors interacts with the mechanical dynamics of self-propelled particles. The term behavioral swarms is introduced to characterize the specific…

Adaptation and Self-Organizing Systems · Physics 2020-06-24 Nicola Bellomo , Seung-Yeal Ha , Nisrine Outada

The cohesive collective motion (flocking, swarming) of autonomous agents is ubiquitously observed and exploited in both natural and man-made settings, thus, minimal models for its description are essential. In a model with continuous space…

Statistical Mechanics · Physics 2015-01-12 Illes J. Farkas , Jeromos Kun , Yi Jin , Gaoqi He , Mingliang Xu
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