Related papers: The third order helicity of magnetic fields via li…
We construct a semiclassical theory for electrons in a non-Hermitian periodic system subject to perturbations varying slowly in space and time. We derive the energy of the wavepacket to first order in the gradients of the perturbations.…
An algorithm for calculating three gauge-invariant helicities (self-, mutual- and Berger relative helicity) for a magnetic field specified in a rectangular box is described. The algorithm is tested on a well-known force-free model (Low and…
Much work on turbulent three-dimensional dynamos has been done using triply periodic domains, in which there are no magnetic helicity fluxes. Here we present simulations where the turbulent intensity is still nearly homogeneous, but now…
We have tested the ability of driven turbulence to generate magnetic field structure from a weak uniform field using three dimensional numerical simulations of incompressible turbulence. We used a pseudo-spectral code with a numerical…
A second-order formalism for the theory of 3D spin-3 gravity is considered. Such a formalism is obtained by solving the torsion-free condition for the spin connection \omega^a_{\mu}, and substituting the result into the action integral. In…
We consider the Neumann Laplacian with constant magnetic field on a regular domain. Let $B$ be the strength of the magnetic field, and let $\lambda_1(B)$ be the first eigenvalue of the magnetic Neumann Laplacian on the domain. It is proved…
The energy of the stochastic magnetic field is bounded from below by a topological quantity expressing the degree of linkage of the field lines. When the bound is saturated one can assume that the storage of a certain magnetic energy…
Inspired by a paper by T. Chakradhar, K. Gittins, G. Habib and N. Peyerimhoff, we analyze their conjecture that the ground state energy of the magnetic Dirichlet-to-Neumann operator tends to infinity as the magnetic field tends to infinity.…
Three-dimensional topological solitons attract a great deal of interest in fields ranging from particle physics to cosmology but remain experimentally elusive in solid-state magnets. Here we numerically predict magnetic heliknotons, an…
Field line helicity measures the net linking of magnetic flux with a single magnetic field line. It offers a finer topological description than the usual global magnetic helicity integral, while still being invariant in an ideal evolution…
Through a direct comparison between numerical simulations in two and three dimensions, we investigate topological effects in reconnection. A simple estimate on increase in reconnection rate in three dimensions by a factor of $\sqrt{2}$,…
Magnetic helicity is a fundamental constraint in both ideal and resistive magnetohydrodynamics. Measurements of magnetic helicity density on the Sun and other stars are used to interpret the internal behaviour of the dynamo generating the…
This paper is devoted to a collection of results on nonlinear interpolation inequalities associated with Schr{\"o}dinger operators involving Aharonov-Bohm magnetic potentials, and to some consequences. As symmetry plays an important role…
To give a general description of the influences of electric fields or currents on magnetization dynamics, we developed a semiclassical theory for the magnetization implicitly coupled to electronic degrees of freedom. In the absence of…
A solution of a problem by V.I.Arnol'd about higher analog of the asymptotic Hopf invariant of divergence-free vector fields is presented. A higher invariant of magnetic fields, which is not expressed from the asymptotic linking numbers of…
We have proposed a method to calculate the relative magnetic helicity in a finite volume as given the magnetic field in the former paper (Yang et al. {\it Solar Physics}, {\bf 283}, 369, 2013). This method requires that the magnetic flux to…
Assuming locality, Lorentz invariance and parity conservation we obtain a set of differential equations governing the 3-point interactions of massless bosons, which in turn determines the polynomial ring of these amplitudes. We derive all…
Magnetic helicity is a quantity that underpins many theories of magnetic relaxation in electrically conducting fluids, both laminar and turbulent. Although much theoretical effort has been expended on magnetic fields that are everywhere…
K. Orr defined a Milnor-type invariant of links that lies in the third homotopy group of a certain space $K_\omega.$ The problem of non-triviality of this third homotopy group has been open. We show that it is an infinitely generated group.…
This work provides a concept for three-dimensional magnetic solitons based on mapping the homotopy path between various two-dimensional solutions onto the third spatial axis. The representative examples of statically stable configurations…