245 citations · 667 across the 24 of their papers we have counts for
4 papers · 1 filter
Geodesic flows on semidirect-product Lie groups: geometry of singular measure-valued solutions
Darryl D. Holm, Cesare Tronci
The EPDiff equation (or dispersionless Camassa-Holm equation in 1D) is a well known example of geodesic motion on the Diff group of smooth invertible maps (diffeomorphisms). Its re…
The Euler-Poincare theory of Metamorphosis
Darryl D. Holm, Alain Trouve, Laurent Younes
In the pattern matching approach to imaging science, the process of ``metamorphosis'' is template matching with dynamical templates. Here, we recast the metamorphosis equations of…
Geometry of Vlasov kinetic moments: a bosonic Fock space for the symmetric Schouten bracket
John Gibbons, Darryl D Holm, Cesare Tronci
The dynamics of Vlasov kinetic moments is shown to be Lie-Poisson on the dual Lie algebra of symmetric contravariant tensor fields. The corresponding Lie bracket is identified with…
Nonlocal orientation-dependent dynamics of molecular strands
Darryl D. Holm, Vakhtang Putkaradze
Time-dependent Hamiltonian dynamics is derived for a curve (molecular strand) in that experiences both nonlocal (for example, electrostatic) and elastic interactions…