Vehicular traffic, crowds, and swarms: From kinetic theory and multiscale methods to applications and research perspectives
This paper presents a review and critical analysis on the modeling of the dynamics of
vehicular traffic, human crowds and swarms seen as living and, hence, complex systems. It …
vehicular traffic, human crowds and swarms seen as living and, hence, complex systems. It …
A rigorous derivation from the kinetic Cucker–Smale model to the pressureless Euler system with nonlocal alignment
We consider the kinetic Cucker–Smale model with local alignment as a mesoscopic
description for the flocking dynamics. The local alignment was first proposed by Karper …
description for the flocking dynamics. The local alignment was first proposed by Karper …
[图书][B] Dynamics and analysis of alignment models of collective behavior
R Shvydkoy - 2021 - Springer
Collective phenomena occur in nature, technology, and social behavior in a vast variety of
contexts. For example, birds and fish use their sensory abilities to communicate and align …
contexts. For example, birds and fish use their sensory abilities to communicate and align …
Eulerian dynamics with a commutator forcing
R Shvydkoy, E Tadmor - Transactions of Mathematics and its …, 2017 - academic.oup.com
We study a general class of Euler equations driven by a forcing with a commutator structure
of the form, where is the velocity field and is the 'action'which belongs to a rather general …
of the form, where is the velocity field and is the 'action'which belongs to a rather general …
On the mathematics of swarming: emergent behavior in alignment dynamics
E Tadmor - arXiv preprint arXiv:2102.09134, 2021 - ams.org
. System 1 is a canonical model for alignment dynamics in which pairwise interactions steer
towards average heading. Alignment originated in pioneering works Rey87 VCBCS95 …
towards average heading. Alignment originated in pioneering works Rey87 VCBCS95 …
Eulerian dynamics with a commutator forcing II: Flocking
R Shvydkoy, E Tadmor - arXiv preprint arXiv:1701.07710, 2017 - arxiv.org
We continue our study of one-dimensional class of Euler equations, introduced in\cite
{ST2016}, driven by a forcing with a commutator structure of the form $[\aL_\phi …
{ST2016}, driven by a forcing with a commutator structure of the form $[\aL_\phi …
Sticky particle Cucker–Smale dynamics and the entropic selection principle for the 1D Euler-alignment system
We develop a global wellposedness theory for weak solutions to the 1D Euler-alignment
system with measure-valued density, bounded velocity, and locally integrable …
system with measure-valued density, bounded velocity, and locally integrable …
Swarming: hydrodynamic alignment with pressure
E Tadmor - Bulletin of the American Mathematical Society, 2023 - ams.org
We study the swarming behavior of hydrodynamic alignment. Alignment reflects steering
toward a weighted average heading. We consider the class of so-called $ p $-alignment …
toward a weighted average heading. We consider the class of so-called $ p $-alignment …
Global regularity of two-dimensional flocking hydrodynamics
We study the systems of Euler equations that arise from agent-based dynamics driven by
velocity alignment. It is known that smooth solutions to such systems must flock, namely the …
velocity alignment. It is known that smooth solutions to such systems must flock, namely the …
Singular cucker–smale dynamics
This chapter is dedicated to the singular models of flocking. We give an overview of the
existing literature starting from microscopic Cucker–Smale (CS) model with singular …
existing literature starting from microscopic Cucker–Smale (CS) model with singular …