18 citations · 80 across the 17 of their papers we have counts for
17 papers
All field strengths are possible locally in Boozer coordinates
Taylor J. Klotz, Nathan Duignan, Joshua W. Burby +1
The magnetic field strength is a central design object in the theory of magnetic confinement of plasma. Desirable confinement properties such as quasi-symmetry and omnigenity are c…
Blow-Up, Asymptotics, and Improbability of Collision Singularities in the n-Body Problem
Nathan Duignan, Manuel Quaschner
We study finite-time singularities in -body systems with pair potentials that are homogeneous of degree , where , that are not necessarily attractive and with bounded…
Generalizing Hamiltonian Mechanics with Closed Differential Forms
Nathan Duignan, Naoki Sato
Classical Hamiltonian mechanics, characterized by a single conserved Hamiltonian (energy) and symplectic geometry, `hides' other invariants into symmetries of the Hamiltonian or in…
Global realisation of magnetic fields as 1D Hamiltonian systems
Nathan Duignan, David Perrella, David Pfefferlé
The paper reviews the notion of D non-autonomous Hamiltonian systems, portraying their dynamics as the flow of the Reeb field related to a closed two-form of maximal…
Asymmetry of MHD equilibria for generic adapted metrics
Robert Cardona, Nathan Duignan, David Perrella
Ideal magnetohydrodynamic (MHD) equilibria on a Riemannian 3-manifold satisfy the stationary Euler equations for ideal fluids. A stationary solution admits a large set of ``ada…
Existence of global symmetries of divergence-free fields with first integrals
David Perrella, Nathan Duignan, David Pfefferlé
The relationship between symmetry fields and first integrals of divergence-free vector fields is explored in three dimensions in light of its relevance to plasma physics and magnet…