Publications

@article{perrellaExistenceGlobalSymmetries2023,

title = {Existence of Global Symmetries of Divergence-Free Fields with First Integrals},

author = {David Perrella and Nathan Duignan and David Pfefferl\'{e}},

doi = {10.1063/5.0152213},

issn = {0022-2488},

year  = {2023},

date = {2023-05-01},

urldate = {2023-05-01},

journal = {Journal of Mathematical Physics},

volume = {64},

number = {5},

pages = {052705},

keywords = {differential geometry, flux-surfaces, MHD equilibrium, noether theorem, quasi-symmetry},

pubstate = {published},

tppubtype = {article}

}

@article{perrellaRectifiabilityDivergencefreeFields2022,

title = {Rectifiability of Divergence-Free Fields along Invariant 2-Tori},

author = {David Perrella and David Pfefferl\'{e} and Luchezar Stoyanov},

doi = {10.1007/s42985-022-00182-3},

issn = {2662-2971},

year  = {2022},

date = {2022-07-01},

urldate = {2022-07-01},

journal = {Partial Differential Equations and Applications},

volume = {3},

number = {4},

pages = {50},

keywords = {cohomology, differential geometry, flux-surfaces, magnetic coordinates, MHD equilibrium, rotational transform},

pubstate = {published},

tppubtype = {article}

}

@article{perrellaStefanSussmannTheoremNormal2021,

title = {A Stefan-Sussmann Theorem for Normal Distributions on Manifolds with Boundary},

author = {David Perrella and David Pfefferl\'{e} and Luchezar Stoyanov},

year  = {2021},

date = {2021-09-01},

urldate = {2021-09-01},

journal = {arXiv:2109.04845 [math]},

abstract = {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 entirety. Plain integral manifolds are not enough to "integrate" a normal distribution; the next best "integrals" are so-called neat integral manifolds with boundary. The conditions on the distribution for this integrability is expressed in terms of adapted collars and integrability of a pulled-back distribution on the interior and on the boundary.},

keywords = {differential geometry, foliations, Froebenius, integrability, manifolds, topology},

pubstate = {published},

tppubtype = {article}

}

@article{pfefferleGaugeFreedomMagnetostatics2021,

title = {Gauge Freedom in Magnetostatics and the Effect on Helicity in Toroidal Volumes},

author = {David Pfefferl\'{e} and Lyle Noakes and David Perrella},

doi = {10.1063/5.0038226},

issn = {0022-2488},

year  = {2021},

date = {2021-09-01},

urldate = {2021-09-01},

journal = {Journal of Mathematical Physics},

volume = {62},

number = {9},

pages = {093505},

publisher = {American Institute of Physics},

abstract = {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~curl~of a vector potential comes about because of homological considerations. With this in mind, we study gauge freedom in magnetostatics and its effect on the comparison between magnetic configurations through key quantities such as the magnetic helicity. For this, we apply the Hodge decomposition of k-forms on compact orientable Riemaniann manifolds with smooth boundary, as well as de Rham cohomology, to the representation of magnetic fields through potential one-forms in toroidal volumes. An advantage of the homological approach is the recovery of classical results without explicit coordinates and assumptions about the fields on the exterior of the domain. In particular, a detailed construction of minimal gauges and a formal proof of relative helicity formulas are presented.},

keywords = {algebraic topology, boundary value problems, cohomology, differential geometry, exterior calculus, gauge freedom, helicity, Hodge decomposition, magnetostatics},

pubstate = {published},

tppubtype = {article}

}