23 citations · 36 across the 11 of their papers we have counts for
11 papers
Asymmetry of curl eigenfields solving Woltjer's variational problem
Daniel Peralta-Salas, David Perrella, David Pfefferlé
We construct families of rotationally symmetric toroidal domains in for which the eigenfields associated to the first (positive) Ampèrian curl eigenvalue are symmetri…
Humanity's Last Exam
Long Phan, Alice Gatti, Ziwen Han +1168
Benchmarks are important tools for tracking the rapid advancements in large language model (LLM) capabilities. However, benchmarks are not keeping pace in difficulty: LLMs now achi…
Closed orbits of MHD equilibria with orientation-reversing symmetry
David Perrella
As a generalisation of the periodic orbit structure often seen in reflection or mirror symmetric MHD equilibria, we consider equilibria with other orientation-reversing symmetries.…
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…
Characterization of admissible quasisymmetries
J. W. Burby, N. Kallinikos, R. S. MacKay +2
We solve "half" the problem of finding three-dimensional quasisymmetric magnetic fields that do not necessarily satisfy force balance. This involves determining which hidden symmet…
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…
Linearisability of divergence-free fields along invariant 2-tori
David Perrella, David Pfefferlé, Luchezar Stoyanov
We find conditions under which the restriction of a divergence-free vector field to an invariant toroidal surface is linearisable. The main results are similar in conclusio…
Integrability of normal distributions Part 2: Neat foliations by manifolds with boundary
David Perrella, David Pfefferlé, Luchezar Stoyanov
This paper completes the foundations of neatly integrable normal distribution theory on manifolds with boundary. Normal distributions are those which contain vectors transverse to…
A Stefan-Sussmann theorem for normal distributions on manifolds with boundary
David Perrella, David Pfefferlé, Luchezar Stoyanov
An analogue of the Stefan-Sussmann Theorem on manifolds with boundary is proven for normal distributions. These distributions contain vectors transverse to the boundary along its e…
Gauge freedom in magnetostatics and the effect on helicity in toroidal volumes
David Pfefferlé, Lyle Noakes
Magnetostatics defines a class of boundary value problems in which the topology of the domain plays a subtle role. For example, representability of a divergence-free field as the c…