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pro vyhledávání: '"Peszek, Jan"'
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 fractional
Externí odkaz:
http://arxiv.org/abs/2409.10501
We compare the multi-dimensional generalisation of the Aw-Rascle model with the pressureless Euler-alignment system, in which the communication weight is matrix-valued. Our generalisation includes the velocity offset in the form of a gradient of a no
Externí odkaz:
http://arxiv.org/abs/2409.07593
Autor:
Peszek, Jan, Rodiac, Rémy
We study the mean-field limits of critical points of interaction energies with Coulombian singularity. An important feature of our setting is that we allow interaction between particles of opposite signs. Particles of opposite signs attract each othe
Externí odkaz:
http://arxiv.org/abs/2404.13433
Autor:
Fabisiak, Michał, Peszek, Jan
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 singularity of orde
Externí odkaz:
http://arxiv.org/abs/2211.01448
Autor:
Mucha, Piotr B., Peszek, Jan
The paper examines the problems related to the well-posedness of the Cucker-Smale model with communication restricted to the $q$-closest neighbors, known also as the Cucker-Dong model. With agents oscillating on the boundary of different clusters, th
Externí odkaz:
http://arxiv.org/abs/2210.05319
Autor:
Peszek, Jan, Poyato, David
We introduce a multi-dimensional variant of the kinetic Cucker-Smale model with singular and matrix-valued communication weight, which reduces to the singular kinetic Cucker-Smale equation in the one-dimensional case. We propose an appropriate notion
Externí odkaz:
http://arxiv.org/abs/2207.14764
Autor:
Minakowski, Piotr, Peszek, Jan
We present a data segmentation method based on a first-order density-induced consensus protocol. We provide a mathematically rigorous analysis of the consensus model leading to the stopping criteria of the data segmentation algorithm. To illustrate o
Externí odkaz:
http://arxiv.org/abs/2204.10585
Autor:
Peszek, Jan, Poyato, David
Publikováno v:
Calc. Var. Partial Differ. Equ. 62 (2023), 258
We introduce an optimal transport topology on the space of probability measures over a fiber bundle, which penalizes the transport cost from one fiber to another. For simplicity, we illustrate our construction in the Euclidean case $\mathbb{R}^d\time
Externí odkaz:
http://arxiv.org/abs/2203.08104
The paper introduces a model of collective behavior where agents receive information only from sufficiently dense crowds in their immediate vicinity. The system is an asymmetric, density-induced version of the Cucker-Smale model with short-range inte
Externí odkaz:
http://arxiv.org/abs/2001.11550
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 show that if
Externí odkaz:
http://arxiv.org/abs/1812.03567