79 citations · 638 across the 61 of their papers we have counts for
9 papers · 1 filter
An efficient geometric method for incompressible hydrodynamics on the sphere
Paolo Cifani, Milo Viviani, Klas Modin
We present an efficient and highly scalable geometric method for two-dimensional ideal fluid dynamics on the sphere. The starting point is Zeitlin's finite-dimensional model of hyd…
Canonical scale separation in two-dimensional incompressible hydrodynamics
Klas Modin, Milo Viviani
A two-dimensional inviscid incompressible fluid is governed by simple rules. Yet, to characterise its long-time behaviour is a knotty problem. The fluid evolves according to Euler'…
Integrability of point-vortex dynamics via symplectic reduction: a survey
Klas Modin, Milo Viviani
Point-vortex dynamics describe idealized, non-smooth solutions to the incompressible Euler equations on 2-dimensional manifolds. Integrability results for few point-vortices on var…
Geometric Hydrodynamics: from Euler, to Poincaré, to Arnold
Klas Modin
These are lecture notes for a short winter course at the Department of Mathematics, University of Coimbra, Portugal, December 6--8, 2018. The course was part of the 13th Internatio…
Symmetry reduction for central force problems
Robert I McLachlan, Klas Modin, Olivier Verdier
We given an elementary illustration of symmetry reduction for central force problems, drawing phase portraits of the reduced dynamics as the intersection of Casimir and energy leve…
Geometry of discrete-time spin systems
Robert I. McLachlan, Klas Modin, Olivier Verdier
Classical Hamiltonian spin systems are continuous dynamical systems on the symplectic phase space . In this paper we investigate the underlying geometry of a time discreti…