Related papers: Magnetic flatness and E. Hopf's theorem for magnet…
It is shown that a magnetic monopole appears as the tension state of the primary electric charge at its motion through each section of the path equal to the particle's de Broglie wavelength. This conclusion is followed from a submicroscopic…
In this paper, we prove a global rigidity theorem for negatively curved Finsler metrics on a compact manifold of dimension n>2. We show that for such a Finsler manifold, if the flag curvature is a scalar function on the tangent bundle, then…
The oft-neglected issue of the causal structure in the flat spacetime approach to Einstein's theory of gravity is considered. Consistency requires that the flat metric's null cone be respected, but this does not happen automatically. After…
Assume that a Hamiltonian system is monotone. In this paper, we give several characterizations on when such a system is Anosov. Assuming that a monotone Hamiltonian system has no conjugate point, we show that there are two distributions…
The rigidity of the positive mass theorem states that the only complete asymptotically flat manifold of nonnegative scalar curvature and zero mass is Euclidean space. We prove a corresponding stability theorem for spaces that can be…
A topological constraint on the dynamics of a magnetic field in a flux tube arises from the fixed point indices of its field line mapping. This can explain unexpected behaviour in recent resistive-magnetohydrodynamic simulations of magnetic…
Evidence of flat-band magnetism and half-metallicity in compressed twisted bilayer graphene is provided with first-principles calculations. We show that dynamic band-structure engineering in twisted bilayer graphene is possible by…
This paper is concerned with the vanishing viscosity and magnetic resistivity limit for the two-dimensional steady incompressible MHD system on the half plane with no-slip boundary condition on velocity field and perfectly conducting wall…
Magnetic field are transported and tangled by turbulence, even as they lose identity due to nonideal or resistive effects. On balance field lines undergo stretch-twist-fold processes. The curvature field, a scalar that measures the tangling…
Starting with a static, spherically symmetric spacetime incorporating critical (unstable) closed null geodesics, a family of models for equilibrium states of non-isolated compact objects is obtained by solving the Einstein equations for an…
In a bounded domain $\mathcal{O}\subset\mathbb{R}^3$ of class $C^{1,1}$, we consider a stationary Maxwell system with the boundary conditions of perfect conductivity. It is assumed that the magnetic permeability is given by a constant…
Physical experiments and numerical simulations have revealed a remarkable stabilizing phenomenon: a background magnetic field stabilizes and dampens electrically conducting fluids. This paper provides a rigorous mathematical justification…
Recent studies have demonstrated that in fully developed turbulence, the effective magnetic pressure of a large-scale field (non-turbulent plus turbulent contributions) can become negative. In the presence of strongly stratified turbulence,…
In this paper, we consider a special relative K\"ahler fibration that satisfies a homogenous Monge-Amp\`ere equation, which is called a Monge-Amp\`ere fibration. There exist two canonical types of generalized Weil-Petersson metrics on the…
Changes in magnetic helicity are often discussed across a variety of fields, from condensed matter physics to early universe cosmology. It is frequently stated that the helicity change is given by the integral of the gauge field strength…
Let $M$ be a compact real-analytic manifold, equipped with a real-analytic Riemannian metric $g,$ and let $\beta$ be a closed real-analytic 2-form on $M$, interpreted as a magnetic field. Consider the Hamiltonian flow on $T^*M$ that…
We demonstrate the Parker Magnetostatic Theorem in terms of a small neighborhood in solution space containing continuous force-free magnetic fields in small deviations from the uniform field. These fields are embedded in a perfectly…
We study stationary, electrically charged fluid structures encircling a rotating compact object with a dipole magnetic field oriented along the rotation axis. This situation is described in an idealized way by the Kerr metric and a magnetic…
Solutions to the compressible Euler equations in all dimensions have been shown to develop finite-time singularities from smooth initial data such as shocks and cusps. There is an extraordinary list of results on this subject. When the…
We first describe the action of the fundamental group of a closed surface of variable negative curvature on the oriented geodesics in its universal covering in terms of a naturally-defined flat connection whose holonomy lies in the group of…