The paper topologically characterizes near force-free magnetic fields using Giroux correspondence.
problem Characterizing near force-free magnetic fields.
method Using Giroux correspondence and topological tools.
result Conditions for sufficiency of topological characterization of force-free magnetic fields.
The paper establishes a connection between force-free fields and conformally geodesic fields.
problem Understanding the relationship between force-free fields and conformally geodesic fields.
method Developed an equivalence between force-free fields and conformally geodesic fields, generalized to arbitrary dimensions.
result Established that stationary points of hierarchies of L2 and L1-optimization problems are related by a conformal change of metric. Study shows unique determination of conformal factors and magnetic fields near convex boundary points.
problem Determining conformal factors and magnetic fields from partial lens data.
method Using partial data for conformal metrics on compact manifolds with boundary in the presence of a magnetic field.
result Unique determination of conformal factor and magnetic field near strictly convex boundary points.
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…
Study local magnetic ray transform of tensor fields on Riemannian manifolds.
problem Stable inversion of magnetic ray transforms of tensor fields up to rank two.
method Analyzes magnetic ray transforms of tensor fields of different orders on Riemannian manifolds with boundary.
result Stable inversion of magnetic ray transforms near strictly convex boundary points.
New Beltrami vector fields with polyhedral symmetries discovered.
problem Finding Beltrami vector fields with specific symmetries.
method Constructing vector fields with polyhedral symmetries using solutions to the Helmholtz equation.
result All simplest Beltrami fields with polyhedral symmetries are calculated.
In this paper we produce a lower bound for the number of periodic orbits of certain Hamiltonian vector fields near Bott-nondegenerate symplectic critical submanifolds. This result is then related to the problem of finding closed orbits of the motion of a charged low energy particle on a Riemannian manifold under the in…
We consider open manifolds which are interiors of a compact manifold with boundary, and Riemannian metrics asymptotic to a conformally cylindrical metric near the boundary. We show that the essential spectrum of the Laplace operator on functions vanishes under the presence of a magnetic field which does not define an i…
Challenge to separate Earth's magnetic field from vehicle's magnetic field for accurate navigation.
problem Separate Earth's magnetic field from vehicle's magnetic field for accurate magnetic navigation.
method Use machine learning (ML) and integrate physics of magnetic navigation (SciML) to remove aircraft magnetic field from total magnetic field.
result A model can be constructed to effectively remove aircraft magnetic field from the dataset.
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…
For Hamiltonian flows we establish the existence of periodic orbits on a sequence of level sets approaching a Bott-nondegenerate symplectic extremum of the Hamiltonian. As a consequence, we show that a charge on a compact manifold with a nondegenerate (i.e. symplectic) magnetic field has periodic orbits on a sequence o…
Bayesian model interpolates indoor magnetic fields using Gaussian processes.
problem Interpolation and extrapolation of the ambient magnetic field for indoor positioning.
method Bayesian non-parametric probabilistic modeling with Gaussian processes.
result The model provides a computationally efficient tool for magnetic field estimation and updates.
For a compact Riemannian manifold with boundary, endowed with a magnetic potential α, we consider the problem of restoring the metric g and the magnetic potential α from the values of the Mañé action potential between boundary points and the associated linearized problem. We study simple magnetic systems. In this…
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 …
Study classifies magnetic curves in Galilean space tied to Killing vectors.
problem Classifying magnetic curves in Galilean space.
method Complete classification of magnetic curves associated to Killing vector fields.
result Completely classified magnetic curves in Galilean 3-space.
We explicitly determine all magnetic curves corresponding to the Killing magnetic fields on the 3-dimensional Euclidean space.
Improves magnetic field mapping using an array of magnetometers with noisy input.
problem Improving magnetic field maps in indoor environments with noisy magnetometer data.
method Uses Gaussian process regression with an array of magnetometers, incorporating known array positions and relative magnetometer locations.
result The method produces higher quality magnetic field maps compared to using a single magnetometer.
Characterizes magnetic unit vector fields on Lie groups.
problem Classifying magnetic unit vector fields on Lie groups.
method Characterization through critical points of Landau Hall and Dirichlet energy functionals.
result Classification of all magnetic left invariant unit vector fields on 3-dimensional Lie groups.
A scalable 3D magnetic field SLAM method using smartphone data.
problem Scalable 3D magnetic field SLAM in buildings and objects.
method Gaussian process model, reduced-rank regression, hexagonal tiling, Rao-Blackwellised particle filter.
result Accurate position and orientation estimates from smartphone data.
Efficiently maps indoor magnetic fields with SKI and D-SKI.
problem Computing large-scale magnetic field maps in indoor environments.
method Structured kernel interpolation (SKI) with derivatives (D-SKI) for Gaussian process regression.
result Achieves better accuracy and faster computation than state-of-the-art methods.
The study characterizes Sasakian manifolds from magnetic Hopf surfaces.
problem Characterizing Sasakian manifolds from magnetic Hopf surfaces.
method Using a unit Killing vector field and Lie dragging a magnetic curve, the study characterizes Sasakian structures.
result If a magnetic Hopf surface is a constant mean curvature surface, then the manifold M is a Sasakian manifold.
Study rigidity of Hamiltonians near a minimum in symplectic and magnetic settings.
problem Rigidity of Hamiltonians near a minimum in symplectic and magnetic settings.
method Analyzing Hamiltonian systems near a compact symplectic Morse-Bott minimum, focusing on Zoll flows and magnetic forms.
result A constant curvature quantity characterizes complex space forms among Kähler manifolds.
The paper estimates magnetic Laplacian eigenvalues using Ricci curvature and magnetic fields.
problem Estimating eigenvalues of the magnetic Laplacian on manifolds.
method Lichnerowicz and Buser type estimates related to Ricci curvature and magnetic fields.
result Relates eigenvalues, magnetic fields, Ricci curvature, and Cheeger type constants.
Study magnetic field evolution in inhomogeneous axion stars.
problem Magnetic field evolution in axion stars with spatial inhomogeneity.
method Derived new induction equation for magnetic field, analyzed CS waves interactions, and considered compact domain effects.
result Spatial inhomogeneity of pseudoscalar field significantly affects magnetic field evolution.
Study reveals new geometric structures for magnetic field Hamiltonian systems.
problem Understanding Hamiltonian systems in magnetic fields.
method Investigation of symplectic-Haantjes geometry.
result Non-trivial symplectic-Haantjes manifolds found.
The article studies eigenvalues and spectrum of magnetic Dirac operators.
problem Fundamental mathematical properties of magnetic Dirac operators remain unexplored.
method Eigenvalue estimates and explicit spectrum computation for specific cases.
result Explicit computation of spectrum for magnetic fields on specific manifolds.
Normal forms prove dynamical results for magnetic fields on surfaces.
problem Existence and rigidity of Zoll flows on surfaces.
method Proved normal forms for strong magnetic fields and used them to derive dynamical results.
result Flow cannot be Zoll unless specific conditions hold.
Study magnetic flows on 3D contact sub-Riemannian manifolds using Rumin complex.
problem Understanding magnetic flows on 3D contact sub-Riemannian manifolds.
method Introducing horizontal magnetic flows via closed Rumin differential two-forms and analyzing the lifted sub-Riemannian structure.
result Horizontal magnetic flows can be interpreted as geodesic flows on a suitably lifted structure, which is of Engel type when the magnetic field is non-vanishing.
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…
The paper studies magnetic field effects on surface eigenvalues and spectral properties.
problem Understanding magnetic effects on surface eigenvalues and spectral properties.
method Provided precise spectral asymptotics expansion for the magnetic Dirichlet-to-Neumann map on surfaces.
result The spectrum of the magnetic Dirichlet-to-Neumann map uniquely determines the number and length of boundary components, parallel transport, and magnetic flux.
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…
New findings on magnetic geodesic flows and periodic motions.
problem Characterizing superintegrable systems in magnetic geodesic flows.
method Analyzing rotationally symmetric magnetic geodesic flows.
result All sufficiently slow motions in a central magnetic field are periodic under specific curvature and homogeneity conditions.
We consider a magnetic Schrödinger operator Hh, 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 b0 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.
problem Injectivity of light ray transform on Lorentzian manifolds.
method Explicit relationship between geodesic and magnetic vector fields.
result Injectivity up to natural obstruction under certain conditions.
New definition of magnetic charge density for monopoles, smooth in core.
problem Defining magnetic charge density for non-abelian monopoles.
method Definition based on zero-modes of Dirac operator, expansion in 1/r.
result Smooth charge density induces magnetic field matching conventional asymptotic field.
For a two-dimensional simple magnetic system, we study the attenuated magnetic ray transform IA,Φ, with attenuation given by a unitary connection A and a skew-Hermitian Higgs field Φ. We give a description for the range of IA,Φ acting on Cn-valued tensor fields.
Magnetic manifold HMC improves sampling on constrained manifolds.
problem Sampling from distributions restricted to embedded manifolds.
method Introduces magnetic manifold HMC, a generalization of HMC for constrained manifolds.
result Magnetic manifold HMC outperforms canonical manifold-constrained HMC.
Study magnetic geodesics on surfaces avoiding lightlike points.
problem Understanding geodesics on surfaces with singularities.
method Analytical proof and numerical solutions.
result Magnetic geodesics avoid points with lightlike tangent planes.
Study shows magnetic billiards are algebraically non-integrable in most cases.
problem Non-integrability of magnetic billiards in convex domains.
method Analyzing polynomial integrals of motion in magnetic billiard flows.
result Magnetic billiards are algebraically non-integrable for most smooth boundary curves.
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…
The paper surveys the Guillemin-Uribe trace formula for magnetic Laplacians.
problem Analyzing dynamics of magnetic geodesic flows through eigenvalues.
method Semiclassical version of the Selberg trace formula for magnetic Laplacians.
result Concrete examples computed for specific magnetic fields.
This paper studies Hamilton-Jacobi equations for magnetic systems with constraints.
problem Understanding dynamics of magnetic systems with geometric constraints.
method Developed Hamilton-Jacobi equations for magnetic systems with nonholonomic constraints.
result Revealed relationships between magnetic structures, constraints, and dynamics.
New invariant connects magnetic lines to Arf-invariants.
problem Understanding the properties of magnetic field lines.
method Developed a new invariant and proved its ergodicity.
result The new invariant is not a function of pairwise linking numbers.
The Hamiltonian flow of the standard metric Hamiltonian with respect to the twisted symplectic structure on the cotangent bundle describes the motion of a charged particle on the base. We prove that under certain natural hypotheses the number of periodic orbits on low energy levels for this flow is at least the sum of …
Paper studies non-associativity in quantum systems with magnetic fields.
problem Non-associativity of magnetic translations in quantum systems.
method Quantum field theory approach with n-component fermions. result Non-associativity described by a 3-cocycle of Rn with values in S1. Study shows non-integrability of magnetic billiards on curved surfaces.
problem Non-existence of polynomial integrals for magnetic billiards.
method Examined billiard motion on constant curvature surfaces with magnetic fields.
result For most magnetic field values, billiard motion lacks polynomial integrals.
We solved the Schr{ö}dinger equation for a particle in a uniform magnetic field in the n-dimensional torus. We obtained a complete set of solutions for a broad class of problems; the torus T^n = R^n / Λ is defined as a quotient of the Euclidean space R^n by an arbitrary n-dimensional lattice Λ. The lattice is not neces…
The paper calculates fractional quantum numbers on complex orbifolds with strong magnetic fields.
problem Understanding fractional quantum numbers in complex orbifolds with strong magnetic fields.
method The study uses Landau Hamiltonians on complex, compact 2D orbifolds and a nontrivial generalisation of the Nahm transform.
result Fractional quantum numbers are calculated as conductance and charge transport is refined.