16 citations · 28 across the 9 of their papers we have counts for
10 papers
Dimension-dependent symmetry breaking in a diffusive nonlocal interaction model
Dohyun Kim, Hansol Park, Woojoo Shim
We study the equilibrium structure and long-time behavior of a nonlinear Fokker--Planck equation with diffusion and nonlocal interactions generated by squared simplex volumes. For…
Logarithmic Velocity Alignment on Riemannian Manifolds
Hyunjin Ahn, Woojoo Shim
We introduce a logarithmic velocity alignment model for collective motion on Riemannian manifolds. The interaction law is defined by the covariant time derivative of logarithmic di…
Geometric Control of Moving Parallel Transport in Riemannian Cucker--Smale Dynamics with Bonding Forces
Hyunjin Ahn, Woojoo Shim
We study a Cucker--Smale type system with bonding forces on complete Riemannian manifolds with uniformly bounded curvature. On general manifolds, the time variation of parallel tra…
Finite-dimensional reduction of a Wasserstein gradient flow and sharp decay rates
Dohyun Kim, Hansol Park, Woojoo Shim
We study the Wasserstein gradient flow generated by a family of extended generalized variance functionals, defined as the expected squared -dimensional volume of a simplex, whic…
Asymptotic stability of the high-dimensional Kuramoto model on Stiefel manifolds
Dohyun Kim, Woojoo Shim
The aim of this article is to investigate the convergence properties of a heterogeneous consensus model on Stiefel manifolds. We consider each agent, without interaction, moving ac…
On the emergent dynamics of the infinite set of Kuramoto oscillators
Seung-Yeal Ha, Euntaek Lee, Woojoo Shim
We propose an infinite Kuramoto model for a countably infinite set of Kuramoto oscillators and study its emergent dynamics for two classes of network topologies. For a class of sym…
Higher-order interaction model from geometric measurements
Dohyun Kim, Hansol Park, Woojoo Shim
We introduce a higher simplicial generalization of the linear consensus model which shares several common features. The well-known linear consensus model is a gradient flow with a…
A Cucker-Smale inspired deterministic mean field game with velocity interactions
Filippo Santambrogio, Woojoo Shim
We introduce a mean field game model for pedestrians moving in a given domain and choosing their trajectories so as to minimize a cost including a penalization on the difference be…
Emergent behaviors of Cucker-Smale flocks on the hyperboloid
Hyunjin Ahn, Seung-Yeal Ha, Hansol Park +1
We study emergent behaviors of Cucker-Smale(CS) flocks on the hyperboloid in any dimensions. In a recent work \cite{H-H-K-K-M}, a first-order aggregation model on th…
Emergent behaviors of Thermodynamic Kuramoto ensemble on a regular ring lattice
Seung-Yeal Ha, Hansol Park, Tommaso Ruggeri +1
The temporal evolution of Kuramoto oscillators influenced by the temperature field often appears in biological oscillator ensembles. In this paper, we propose a generalized Kuramot…