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Related papers: On reduced inertial PDE models for Cucker-Smale fl…

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We analyze the one dimensional Cucker-Smale (in short CS) model with a weak singular communication weight $\psi(x) = |x|^{-\beta}$ with $\beta \in (0,1)$. We first establish a global-in-time existence of measure-valued solutions to the…

Analysis of PDEs · Mathematics 2020-06-16 Young-Pil Choi , Xiongtao Zhang

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

We study emergent behaviors of thermomechanical Cucker-Smale (TCS) ensemble confined in a harmonic potential field. In the absence of external force field, emergent dynamics of TCS particles has been extensively studied recently under…

Analysis of PDEs · Mathematics 2021-10-25 Hangjun Cho , Linglong Du , Seung-Yeal Ha

Exact results on particle-densities as well as correlators in two models of immobile particles, containing either a single species or else two distinct species, are derived. The models evolve following a descent dynamics through…

Statistical Mechanics · Physics 2012-11-12 Christophe Chatelain , Malte Henkel , Mário J. De Oliveira , Tânia Tomé

Many systems in physics, engineering, and biology exhibit multiscale stochastic dynamics, where low-dimensional slow variables evolve under the influence of high-dimensional fast processes. In practice, observations are often limited to a…

Machine Learning · Statistics 2026-05-12 Anan Saha , Arnab Ganguly

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 derive a sufficient condition for asymptotic flocking in the Cucker-Smale model with self-delay (also called reaction delay) and with non-symmetric interaction weights. The condition prescribes smallness of the delay length relative to…

Analysis of PDEs · Mathematics 2021-10-20 Jan Haskovec

In this work we derive and analyze coarse-grained descriptions of self-propelled particles with selective attraction-repulsion interaction, where individuals may respond differently to their neighbours depending on their relative state of…

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

In this paper, we deal with a Cucker-Smale model with time-dependent time delay and communication failures. Namely, we investigate the situation in which the agents involved in a flocking process can possibly suspend the exchange of…

Optimization and Control · Mathematics 2025-08-19 Elisa Continelli

We prove existence of global $C^1$ piecewise weak solutions for the discrete Cucker-Smale's flocking model with the communication weight $\psi(s)=s^{-\alpha}, 0<\alpha<1.$ We also discuss the possibility of finite in time alignment of the…

Analysis of PDEs · Mathematics 2013-02-19 Jan Peszek

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

Particle filters (PFs) are recursive Monte Carlo algorithms for Bayesian tracking and prediction in state space models. This paper addresses continuous-discrete filtering problems, where the hidden state evolves as an It\^o stochastic…

Computation · Statistics 2026-04-24 Utku Erdogan , Gabriel J. Lord , Joaquin Miguez

We prove that certain types of measure-valued mappings are monokinetic i.e. the distribution of velocity is concentrated in a Dirac mass. These include weak measure-valued solutions to the strongly singular Cucker-Smale model with…

Analysis of PDEs · Mathematics 2022-11-04 Michał Fabisiak , Jan Peszek

Spatial reaction-diffusion models have been employed to describe many emergent phenomena in biological systems. The modelling technique most commonly adopted in the literature implements systems of partial differential equations (PDEs),…

Quantitative Methods · Quantitative Biology 2015-10-05 Christian A. Yates , Mark B. Flegg

A stochastic PDE, describing mesoscopic fluctuations in systems of weakly interacting inertial particles of finite volume, is proposed and analysed in any finite dimension $d\in\mathbb{N}$. It is a regularised and inertial version of the…

Analysis of PDEs · Mathematics 2021-02-10 Federico Cornalba , Tony Shardlow , Johannes Zimmer

In this paper, we study the behavior of systems of individuals in confined environments that are driven by laws of self-organization. We propose that, under certain conditions, the long-term behavior of such systems will be global…

Classical Analysis and ODEs · Mathematics 2020-05-14 Veronica Kalicki

Inertial microfluidics has been limited to dilute particle concentrations due to defocusing (spreading out) at high particle concentrations. We observe a counterintuitive shift of focusing to the outer curved wall under high concentration…

We study the large-time behavior of continuum alignment dynamics based on Cucker-Smale (CS)-type interactions which involve short-range kernels, that is, communication kernels with support much smaller than the diameter of the crowd. We…

Analysis of PDEs · Mathematics 2019-05-22 Javier Morales , Jan Peszek , Eitan Tadmor

We introduce and discuss two nonlinear perturbed extensions of the Cucker-Smale model with asymmetric coupling weights. The first model assumes a finite collection of autonomous agents aiming to perform a consensus process in the presence…

Optimization and Control · Mathematics 2017-10-04 Christoforos Somarakis , Evripidis Paraskevas , John S. Baras , Nader Motee

To understand the process of pattern formation in a low-density granular flow, we propose a simple particle model. This model considers spherical particles moving over an inclined flat surface based on three forces: gravity as the driving…

Soft Condensed Matter · Physics 2019-04-24 Hirofumi Niiya , Akinori Awazu , Hiraku Nishimori