A velocity alignment model on quotient spaces of the Euclidean space

@article{Park2021AVA,
  title={A velocity alignment model on quotient spaces of the Euclidean space},
  author={Hansol Park},
  journal={Journal of Mathematical Analysis and Applications},
  year={2021}
}
  • Hansol Park
  • Published 2 June 2021
  • Mathematics
  • Journal of Mathematical Analysis and Applications
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SHOWING 1-10 OF 23 REFERENCES

Emergent dynamics of a thermodynamic Cucker-Smale ensemble on complete Riemannian manifolds

We study emergent collective behaviors of a thermodynamic Cucker-Smale (TCS) ensemble on complete smooth Riemannian manifolds. For this, we extend the TCS model on the Euclidean space to a complete…

Emergent behaviors of Cucker–Smale flocks on the hyperboloid

We study emergent behaviors of Cucker-Smale(CS) flocks on the hyperboloid $\mathbb{H}^d$ in any dimensions. In a recent work \cite{H-H-K-K-M}, a first-order aggregation model on the hyperboloid was…

Emergent Behaviors of Cucker–Smale Flocks on Riemannian Manifolds

A new Cucker–Smale model on smooth Riemannian manifolds is presented using the concepts of covariant derivative and parallel transport, and its emergent dynamics is studied under an a priori assumption on the energy functional.

A Dynamical Systems Approach for the Shape Matching of Polytopes Along Rigid-Body Motions

We present a dynamical systems approach for geometric matchings in an ensemble of polytopes along rigid-body motions. Each polytope can be characterized by a vertex set and edge or faces determined…

Self-organization on Riemannian manifolds

We consider an aggregation model that consists of an active transport equation for the macroscopic population density, where the velocity has a nonlocal functional dependence on the density, modelled…

Emergent Behaviors of Rotation Matrix Flocks

Abstract. We derive an explicit form for the Cucker-Smale (CS) model on the special orthogonal group SOp3q by identifying closed form expressions for geometric quantities such as covariant derivative…

Global-in-time weak measure solutions and finite-time aggregation for nonlocal interaction equations

In this paper we provide a well-posedness theory for weak measure solutions of the Cauchy problem for a family of nonlocal interaction equations. These equations are continuum models for interacting…

Global Weak Solutions for Kolmogorov–Vicsek Type Equations with Orientational Interactions

We study the global existence and uniqueness of weak solutions to kinetic Kolmogorov–Vicsek models that can be considered as non-local, non-linear, Fokker–Planck type equations describing the…

Riemannian Geometry

THE recent physical interpretation of intrinsic differential geometry of spaces has stimulated the study of this subject. Riemann proposed the generalisation, to spaces of any order, of Gauss's…

Interaction ruling animal collective behavior depends on topological rather than metric distance: Evidence from a field study

It is argued that a topological interaction is indispensable to maintain a flock's cohesion against the large density changes caused by external perturbations, typically predation, and supported by numerical simulations.