148 citations · 1.1k across the 66 of their papers we have counts for
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Kinetic models of heterogeneous dissipation
Darryl D. Holm, Vakhtang Putkaradze, Cesare Tronci
We suggest kinetic models of dissipation for an ensemble of interacting oriented particles, for example, moving magnetized particles. This is achieved by introducing a double brack…
Emergent singular solutions of non-local density-magnetization equations in one dimension
Darryl D. Holm, Lennon O. Naraigh, Cesare Tronci
We investigate the emergence of singular solutions in a non-local model for a magnetic system. We study a modified Gilbert-type equation for the magnetization vector and find that…
Double bracket dissipation in kinetic theory for particles with anisotropic interactions
Darryl D. Holm, Vakhtang Putkaradze, Cesare Tronci
We derive equations of motion for the dynamics of anisotropic particles directly from the dissipative Vlasov kinetic equations, with the dissipation given by the double bracket app…
Vlasov moments, integrable systems and singular solutions
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 Lie-Poisson Hamiltonian system. Remarkably, the o…
Geometric dissipation in kinetic equations
Darryl D. Holm, Vakhtang Putkaradze, Cesare Tronci
A new symplectic variational approach is developed for modeling dissipation in kinetic equations. This approach yields a double bracket structure in phase space which generates kin…
Geometric gradient-flow dynamics with singular solutions
Darryl D. Holm, Vakhtang Putkaradze, Cesare Tronci
The gradient-flow dynamics of an arbitrary geometric quantity is derived using a generalization of Darcy's Law. We consider flows in both Lagrangian and Eulerian formulations. The…