arXiv research

Researchers calculate Hofer-Zehnder capacity for twisted tangent bundles over surfaces.

Normal forms prove dynamical results for magnetic fields on surfaces.

In this paper, we completely classify the magnetic curves (also N-magnetic curves with constant curvature) in a Galilean 3-space associated to a Killing vector field.

The Guillemin-Uribe trace formula is a semiclassical version of the Selberg trace formula and more general Duistermaat-Guillemin formula for elliptic operators on compact manifolds, which reflects the dynamics of magnetic geodesic flows in terms of eigenvalues of a natural differential operator (the magnetic Laplacian)…

Examples are presented of how the geometric notion of the mean curvature is used for general magnetic field configurations and magnetic surfaces. It is shown that the mean magnetic curvature is related to the variation of the absolute value of the magnetic field along its lines. Magnetic surfaces of constant mean curva…

Researchers compute trace formula for magnetic Laplacian on hyperbolic surfaces.

In a three-dimensional Riemannian manifold M that admits a unit Killing vector field $ξ$, we regard $ξ$ as a magnetic vector field. A magnetic Hopf surface is a surface obtained by Lie dragging the magnetic curve with $ξ$. Then we characterize Sasakian structure on M from magnetic Hopf surfaces. That is, we show that i…

In this paper, we present a Lichnerowicz type estimate and (higher order) Buser type estimates for the magnetic Laplacian on a closed Riemannian manifold with a magnetic potential. These results relate eigenvalues, magnetic fields, Ricci curvature, and Cheeger type constants.

We consider billiard ball motion in a convex domain of a constant curvature surface influenced by the constant magnetic field. We prove that if the billiard map is totally integrable then the boundary curve is necessarily a circle. This result is a manifestation of the so-called Hopf rigidity phenomenon which was recen…

Model predicts EMF of Ni-Mn-Ga MSMA, improved with GRNN.

We consider billiard ball motion in a convex domain on a constant curvature surface influenced by the constant magnetic field. We examine the existence of integral of motion which is polynomial in velocities. We prove that if such an integral exists then the boundary curve of the domain determines an algebraic curve in…

We consider billiard ball motion in a convex domain of the Euclidean plane bounded by a piece-wise smooth curve influenced by the constant magnetic field. We show that if there exists a polynomial in velocities integral of the magnetic billiard flow then every smooth piece $γ$ of the boundary must be algebraic and eith…

The problem of description of superintegrable systems (i.e., systems with closed trajectories in a certain domain) in the class of rotationally symmetric natural mechanical systems goes back to Bertrand and Darboux. We describe all superintegrable (in a domain of slow motions) systems in the class of rotationally symme…

Paper proves a spinor inequality for magnetic fields on spin manifolds.

Let $M$ be a closed oriented surface endowed with a Riemannian metric $g$ and let $Ω$ be a 2-form. We show that the magnetic flow of the pair $(g,Ω)$ has zero asymptotic Maslov index and zero Liouville action if and only $g$ has constant Gaussian curvature, $Ω$ is a constant multiple of the area form of $g$ and the mag…

Upper bounds for magnetic Laplacian eigenvalues on planar domains.

Constructs smooth integrable magnetic systems on a two-torus.

We prove the existence of harmonic spinor fields in axisymmetric Riemannian 3-manifolds having nonnegative scalar curvature and asymptotic to the usual constant time hypersurface of Melvin's magnetic universe. Such a spinor can be used in the proof of the uniqueness of the magnetized Schwarzschild solution.

Challenge to separate Earth's magnetic field from vehicle's magnetic field for accurate navigation.

Given a constant magnetic field on Euclidean space ${\mathbb R}^p$ determined by a skew-symmetric $(p\times p)$ matrix $Θ$, and a ${\mathbb Z}^p$-invariant probability measure $μ$ on the disorder set $Σ$ which is by hypothesis a Cantor set, where the action is assumed to be minimal, the corresponding Integrated Density…

A magnetic field is defined by the property that its divergence is zero in a three dimensional oriented Riemannian manifold. Each magnetic field generates a magnetic flow whose trajectories are curves called as magnetic curves. In this paper, we give a new variational approach to studies the magnetic flow asociated wit…

Study magnetic Laplacians on hyperbolic surfaces, revealing three regimes of eigenfunction behavior.

Researchers prove integrability of magnetic systems on spheres up to dimension 6.

Study magnetic Steklov eigenvalues on manifolds with boundary.

Proves magnetic geodesic flow on sphere is integrable with constant 2-form.

Two non-local asymptotic invariants of magnetic fields for the ideal magnetohydrodynamics are introduced. The velocity of variation of the invariants for a non-ideal magnetohydrodynamics with a small magnetic dissipation is estimated. By means of the invariants the spectra of electromagnetic fields are investigated. A …

We explicitly determine all magnetic curves corresponding to the Killing magnetic fields on the 3-dimensional Euclidean space.

Anomalies in the ambient magnetic field can be used as features in indoor positioning and navigation. By using Maxwell's equations, we derive and present a Bayesian non-parametric probabilistic modeling approach for interpolation and extrapolation of the magnetic field. We model the magnetic field components jointly by…

Improves magnetic field mapping using an array of magnetometers with noisy input.

Characterizes magnetic unit vector fields on Lie groups.

Efficiently maps indoor magnetic fields with SKI and D-SKI.

In this paper we study rigidity aspects of Zoll magnetic systems on closed surfaces. We characterize magnetic systems on surfaces of positive genus given by constant curvature metrics and constant magnetic functions as the only magnetic systems such that the associated Hamiltonian flow is Zoll, i.e. every orbit is clos…

Study magnetic field evolution in inhomogeneous axion stars.

Study reveals new geometric structures for magnetic field Hamiltonian systems.

The paper calculates dimensions of higher Landau levels on compact manifolds.

The article studies eigenvalues and spectrum of magnetic Dirac operators.

Study magnetic flows on 3D contact sub-Riemannian manifolds using Rumin complex.

We consider an open domain with a compact boundary in an Euclidean space and a Schroedinger operator with magnetic field on this domain. We give sufficient conditions on the rate of growth of the magnetic field near the boundary which guarantees essential self-adjointness of this operator. From the physical point of vi…

We present a method for scalable and fully 3D magnetic field simultaneous localisation and mapping (SLAM) using local anomalies in the magnetic field as a source of position information. These anomalies are due to the presence of ferromagnetic material in the structure of buildings and in objects such as furniture. We …

Consider a compact Riemannian manifold with boundary endowed with a magnetic field. A path taken by a particle of unit charge, mass, and energy is called a magnetic geodesic. It is shown that if everything is real-analytic, the topology, metric, and magnetic field are uniquely determined by the scattering relation of t…

The paper studies magnetic field effects on surface eigenvalues and spectral properties.

We consider a magnetic Schrödinger operator $H^h$, depending on a semiclassical parameter $h>0$, on a compact Riemannian manifold. We assume that there is no electric field. We suppose that the minimal value $b_0$ of the intensity of the magnetic field $b$ is strictly positive. We give a survey of the results on asympt…

Injectivity result for light ray transform on Lorentzian manifolds.

For a two-dimensional simple magnetic system, we study the attenuated magnetic ray transform $I_{A,Φ}$, with attenuation given by a unitary connection $A$ and a skew-Hermitian Higgs field $Φ$. We give a description for the range of $I_{A,Φ}$ acting on $\mathbb C^n$-valued tensor fields.

Magnetic manifold HMC improves sampling on constrained manifolds.

Magnetic geodesics describe the trajectory of a particle in a Riemannian manifold under the influence of an external magnetic field. In this article, we use the heat flow method to derive existence results for such curves. We first establish subconvergence of this flow to a magnetic geodesic under certain boundedness a…

In this paper we study the local magnetic ray transform of symmetric tensor fields up to rank two on a Riemannian manifold of dimension $\geq 3$ with boundary. In particular, we consider the magnetic ray transform of the combinations of tensors of different orders due to the nature of magnetic flows. We show that such …

This paper studies Hamilton-Jacobi equations for magnetic systems with constraints.