Emergent behaviors of Cucker–Smale flocks on Riemannian manifolds
SY Ha, D Kim, FW Schlöder - IEEE Transactions on Automatic …, 2020 - ieeexplore.ieee.org
In this article, we present a new Cucker-Smale model on smooth Riemannian manifolds
using the concepts of covariant derivative and parallel transport, and we also study its …
using the concepts of covariant derivative and parallel transport, and we also study its …
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 …
on complete smooth Riemannian manifolds. For this, we extend the TCS model on the …
Well-posedness and asymptotic behavior of an aggregation model with intrinsic interactions on sphere and other manifolds
RC Fetecau, H Park, FS Patacchini - Analysis and Applications, 2021 - World Scientific
We investigate a model for collective behavior with intrinsic interactions on Riemannian
manifolds. We establish the well-posedness of measure-valued solutions (defined via mass …
manifolds. We establish the well-posedness of measure-valued solutions (defined via mass …
The mean-field limit of the Cucker-Smale model on complete Riemannian manifolds
We study the mean-field limit of the Cucker-Smale (CS) model for flocking on complete
smooth Riemannian manifolds. For this, we first formally derive the kinetic manifold CS …
smooth Riemannian manifolds. For this, we first formally derive the kinetic manifold CS …
The nonlocal-interaction equation near attracting manifolds
FS Patacchini, D Slepčev - arXiv preprint arXiv:2106.01823, 2021 - arxiv.org
We study the approximation of the nonlocal-interaction equation restricted to a compact
manifold $\mathcal {M} $ embedded in $\mathbb {R}^ d $, and more generally compact sets …
manifold $\mathcal {M} $ embedded in $\mathbb {R}^ d $, and more generally compact sets …
Emergent behaviors of rotation matrix flocks
We derive an explicit form for the Cucker--Smale (CS) model on the special orthogonal
group SO(3) by identifying closed form expressions for geometric quantities such as …
group SO(3) by identifying closed form expressions for geometric quantities such as …
Well-posedness of an interaction model on Riemannian manifolds
RC Fetecau, FS Patacchini - arXiv preprint arXiv:2109.03959, 2021 - arxiv.org
We investigate a model for collective behaviour with intrinsic interactions on smooth
Riemannian manifolds. For regular interaction potentials, we establish the local well …
Riemannian manifolds. For regular interaction potentials, we establish the local well …
Learning interaction kernels for agent systems on riemannian manifolds
M Maggioni, J Miller, H Qiu, M Zhong - arXiv preprint arXiv:2102.00327, 2021 - arxiv.org
Interacting agent and particle systems are extensively used to model complex phenomena
in science and engineering. We consider the problem of learning interaction kernels in these …
in science and engineering. We consider the problem of learning interaction kernels in these …
An Intrinsic Aggregation Model on the Special Orthogonal Group SO(3): Well-posedness and Collective Behaviours
We consider a model for collective behaviour on Riemannian manifolds, with interactions
modelled through a smooth interaction potential that depends on the squared intrinsic …
modelled through a smooth interaction potential that depends on the squared intrinsic …
Aggregation-Diffusion Energies on Cartan–Hadamard Manifolds of Unbounded Curvature
RC Fetecau, H Park - The Journal of Geometric Analysis, 2024 - Springer
We consider an aggregation-diffusion energy on Cartan–Hadamard manifolds with sectional
curvatures that can grow unbounded at infinity. The energy corresponds to a macroscopic …
curvatures that can grow unbounded at infinity. The energy corresponds to a macroscopic …