245 citations · 1.1k across the 44 of their papers we have counts for
6 papers · 1 filter
Geometric order parameter equations
Darryl D. Holm, Vakhtang Putkaradze
Aggregation of particles whose interaction potential depends on their mutual orientation is considered. The aggregation dynamics is derived using a version of Darcy's law and a var…
Lagrangian analysis of alignment dynamics for isentropic compressible magnetohydrodynamics
J. D. Gibbon, D. D. Holm
After a review of the isentropic compressible magnetohydrodynamics (ICMHD) equations, a quaternionic framework for studying the alignment dynamics of a general fluid flow is explai…
Formation and Evolution of Singularities in Anisotropic Geometric Continua
Darryl D. Holm, Vakhtang Putkaradze
Evolutionary PDEs for geometric order parameters that admit propagating singular solutions are introduced and discussed. These singular solutions arise as a result of the competiti…
Lagrangian particle paths and ortho-normal quaternion frames
J. D. Gibbon, D. D. Holm
Experimentalists now measure intense rotations of Lagrangian particles in turbulent flows by tracking their trajectories and Lagrangian-average velocity gradients at high Reynolds…
Singular solutions for geodesic flows of Vlasov moments
John Gibbons, Darryl D. Holm, Cesare Tronci
The Vlasov equation for the collisionless evolution of the single-particle probability distribution function (PDF) is a well-known example of coadjoint motion. Remarkably, the prop…
Length-scale estimates for the LANS-alpha equations in terms of the Reynolds number
John D. Gibbon, Darryl D. Holm
Foias, Holm & Titi \cite{FHT2} have settled the problem of existence and uniqueness for the 3D \lans equations on periodic box . There still remains the problem, first i…