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…
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48 results for “magnetic confinement”
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…
New theorem links symmetries to first integrals in plasma physics.
problem Understanding the relationship between symmetries and first integrals in divergence-free fields.
method Developed a Noether-type Theorem reformulation for three-dimensional divergence-free vector fields.
result Converse of the Noether-type Theorem holds on the toroidal region, proving the existence of flux coordinates.
Turbulent field fluctuations in gyrokinetic and fluid plasmasphysics.plasm-ph
Deep learning compares turbulence models in plasma physics.
problem Predicting edge plasma turbulence in magnetic fusion reactors.
method Physics-informed deep learning framework for comparing two-fluid and gyrokinetic models.
result Good overall agreement between two-fluid theory and gyrokinetic models in turbulent field fluctuations.
Conditions found for linearizing divergence-free fields on invariant tori.
problem Linearizing divergence-free vector fields on invariant tori.
method Assuming a solution to the cohomological equation and using Bers' results in pseudo-analytic function theory.
result The field on is either identically zero or nowhere vanishing, with a linearizable form.
We probe the character of knotting in open, confined polymers, assigning knot types to open curves by identifying their projections as virtual knots. In this sense, virtual knots are transitional, lying in between classical knot types, which are useful to classify the ambiguous nature of knotting in open curves. Modell…
Study confined subgroups in groups with contracting elements, showing their growth rate is strictly greater than half of the ambient growth rate.
problem Understanding the growth rate of confined subgroups in groups with contracting elements.
method Through boundary actions, analyzing the Hopf decomposition and quotient growth.
result Confined subgroups have a growth rate strictly greater than half of the ambient growth rate.
Fast algorithm samples confined polygons efficiently.
problem Sampling confined random equilateral closed polygons efficiently.
method Uses symplectic geometry to sample moment polytope, leading to a linear-time algorithm.
result Explicit formulas for expected distances and total curvature of vertices to the origin.
CONFINE enhances neural networks' interpretability without sacrificing accuracy.
problem Lack of interpretability in deep neural networks, especially in healthcare.
method CONFINE uses conformal prediction to generate prediction sets with robust uncertainty estimates.
result CONFINE achieves correct efficiency up to 3.3% higher than original accuracy.
5D SCFTs can have confining vacua with strings and unbroken symmetries.
problem Investigating phases of 5D SCFTs by varying couplings.
method Using geometric realisation of M-theory on metrically conical Calabi-Yau threefolds.
result Many 5D SCFTs have couplings leading to massive, confining vacua with strings and unbroken symmetries.
New framework shows -simplicity for groups without certain subalgebras.
problem Characterizing -simplicity of groups.
method Introducing confined subalgebras and Uniformly Recurrent States.
result A countable discrete group is -simple if it has no non-trivial amenable confined subalgebras.
Extends confining subset theory to describe hyperbolic actions of solvable groups with higher rank abelianizations.
problem Describing hyperbolic actions of solvable groups with higher rank abelianizations.
method Extends confining subset theory to apply to solvable groups with higher rank abelianizations.
result Complete description of hyperbolic actions of generalized solvable Baumslag-Solitar groups.
Sharp growth tightness proven for group quotients.
problem Growth behavior of group quotients by confined subgroups.
method Statistically convex-cocompact action with contracting elements.
result Sharp growth tightness proven, with applications to uniformly recurrent subgroups.
Study on membranes under confinement, proving existence and regularity of minimizers.
problem Existence and regularity of minimizers for constrained Helfrich energy.
method Elliptic system analysis, careful study of measure-valued Lagrange multiplier.
result Optimal regularity for solutions throughout branch points, rigid behavior for unit ball minimizers.
Minimal submanifolds confined in space are highly restricted.
problem Understanding minimal submanifolds in confined spaces.
method Analyzing structural restrictions and volume growth properties.
result Proper minimal immersions with sublinear height growth must have Euclidean volume growth.
The study examines knot probabilities in confined lattice polygons.
problem Determining the relative knotting probabilities in confined lattice knots.
method Used Monte Carlo algorithms to enumerate conformations of lattice knots in a confined volume.
result Relative knotting probabilities are small, with the model dominated by unknots.
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.
Neural networks' optimization dynamics are confined to a single basin despite connected basins in the loss landscape.
problem Neural networks' optimization dynamics are confined to a single basin despite connected basins in the loss landscape.
method Identifying entropic barriers arising from the interplay between curvature variations along low-loss paths and noise in optimization dynamics.
result Curvature-induced entropic forces bias noisy dynamics back toward the endpoints, explaining the confinement and connectivity of solutions.
Extends E. Hopf's theorem to magnetic systems without conjugate points.
problem Proving magnetic curvature non-positive for magnetic systems without conjugate points.
method Using magnetic curvature introduced by the first author, proving magnetic flatness conditions.
result Magnetic flatness is a rigid condition with specific metric and curvature properties.
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…
Compatibility equations adapted to magnetic geometry.
problem No specific problem stated; magnetic geometry is the setting.
method Established compatibility equations in magnetic geometry.
result Analogues of Gauss, Ricci, and Codazzi-Mainardi equations in magnetic geometry.
We consider the problem of minimizing the bending or elastic energy among Jordan curves confined in a given open set . We prove existence, regularity and some structural properties of minimizers. In particular, when is convex we show that a minimizer is necessarily a convex curve. We also provide an example of a…
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.
Magnetic Brunn-Minkowski inequalities on Riemannian manifolds
problem Establishing equivalence between Brunn-Minkowski inequalities and magnetic Ricci curvature
method Using magnetic geodesics
result Proving a sharp, undistorted Brunn-Minkowski inequality
Study shows finiteness of magnetic hypersurfaces on closed manifolds.
problem Understanding the finiteness of magnetic hypersurfaces on closed manifolds.
method Introduced a dynamical version of the second fundamental form to generalize a previous result.
result Real-analytic negatively -curved magnetic systems on closed real-analytic manifolds have only finitely many closed totally -magnetic hypersurfaces.
The paper studies magnetic curves in -manifolds and their properties.
problem Understanding magnetic trajectories in -manifolds.
method Proving magnetic trajectories are -slant curves and providing parametrizations.
result Normal magnetic curves in -manifolds are -slant curves with specific curvature functions.
New tensors help solve magnetic flow integrability.
problem Integrability of magnetic flows on specific manifolds.
method Introduced magnetic Killing symmetric tensors to construct first integrals.
result Proved integrability of invariant magnetic flows on 2-step nilmanifolds.
Study magnetic geodesics on Heisenberg groups and manifolds.
problem Dynamics of magnetic flows on Heisenberg groups.
method Explicit description of magnetic geodesics, determination of lengths.
result Density of periodic magnetic geodesics and marked magnetic length spectrum rigidity.
We study the problem of so-called geometric quantum confinement in a class of two-dimensional incomplete Riemannian manifold with metric of Grushin type. We employ a constant-fibre direct integral scheme, in combination with Weyl's analysis in each fibre, thus fully characterising the regimes of presence and absence of…
Paper introduces magnetic Hodge Laplacian for differential forms.
problem No specific problem stated; general spectral analysis of differential forms.
method Introduced magnetic Hodge Laplacian, discussed spectral results.
result Similarities and differences with magnetic Laplacian on functions.
Study of bound states in quantum layers with confining potentials.
problem Investigating bound states in quantum layers with confining potentials.
method Developed a general approach using parallel coordinates based on the surface but outside its cut locus.
result Discrete eigenvalues exist for certain quantum layers with positive total Gauss curvature.
Physics-informed machine learning techniques for edge plasma turbulence modelling in computational theory and experimentphysics.plasm-ph
Physics-informed ML models improve turbulence understanding in fusion plasmas.
problem Improving turbulence modeling in fusion plasma devices.
method Physics-informed deep learning framework constrained by PDEs.
result Direct quantitative comparisons of turbulent fields between theory and gyrokinetic models.
We explicitly determine all magnetic curves corresponding to the Killing magnetic fields on the 3-dimensional Euclidean space.
Classifies quantum particle behavior on a special cylinder.
problem Quantum confinement and transmission on a Grushin cylinder.
method Characterizes self-adjoint realizations of the Laplace-Beltrami operator.
result Identifies physically meaningful extensions of the Hamiltonian.
Study of magnetic geodesics on Heisenberg nilmanifolds.
problem Existence and properties of closed magnetic geodesics on Heisenberg nilmanifolds.
method Analyzing conditions for the existence of closed magnetic geodesics on compact quotients of Heisenberg nilmanifolds.
result Existence of contractible closed magnetic geodesics for any energy level below the Mañé critical value.
Study magnetic Steklov eigenvalues on manifolds with boundary.
problem Eigenvalue problem for magnetic Steklov operators on compact manifolds.
method Equivalent characterizations, bounds, comparison results.
result Established bounds for the smallest eigenvalue of magnetic Steklov operators.
Study magnetic potentials on Anosov manifolds using spectral data.
problem Recover magnetic potentials from spectral data on Anosov manifolds.
method Utilize principal wave trace invariants and magnetic Schrödinger operator.
result Spectral data uniquely determines magnetic and electric potentials on Anosov manifolds.
Study magnetic curvature on Lie groups, extending Milnor's work.
problem Exploring magnetic curvatures on Lie groups.
method Computing magnetic curvatures and analyzing algebraic properties.
result Extending results from Milnor's classic paper on left-invariant metrics.
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 shows magnetic trajectories in Berger spheres are homogeneous.
problem Homogeneity of contact magnetic trajectories in Berger spheres.
method Proved every contact magnetic trajectory is a product of a homogeneous geodesic and a charged Reeb flow.
result Contact magnetic trajectories in Berger spheres are homogeneous.
Extends magnetic flow theory results to higher dimensions.
problem Magnetic flows on manifolds of arbitrary dimension.
method New Pestov identities and adapted Riemannian geometry concepts.
result Established tensor tomography and ergodicity results for magnetic flows.
The paper explores how magnetic systems' spectra can identify metrics and 1-forms.
problem Can the marked magnetic action spectrum of magnetic systems with Anosov flow determine the metric and 1-form?
method The paper addresses this question in two settings: locally for systems with close metrics and 1-forms, and for metrics in the same conformal class.
result The paper answers the question affirmatively in both settings.
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.
Metrics are isometric for certain Anosov magnetic systems.
problem Isometry of metrics for Anosov magnetic systems.
method Conjugacy isotopic to the identity, volume-preserving conjugacy, cohomology class.
result Isometric metrics for conjugate Anosov magnetic systems.
Study on magnetic Dirac operators and their spectrum.
problem Understanding the spectrum of magnetic Dirac operators.
method Analysis of magnetic Dirac operators over complete Riemannian manifolds.
result Find sufficient conditions for maximal or discrete spectrum.
In a three-dimensional Riemannian manifold M that admits a unit Killing vector field , we regard as a magnetic vector field. A magnetic Hopf surface is a surface obtained by Lie dragging the magnetic curve with . Then we characterize Sasakian structure on M from magnetic Hopf surfaces. That is, we show that i…
A quasiclassical method approximates magnetic monopole eigenvalues.
problem Describing eigenvalues of magnetic Laplacian in non-exact magnetic fields.
method Applying multidimensional WKB method to nontrivial line bundles.
result Demonstrated for Dirac magnetic monopole on a sphere.
Researchers compute trace formula for magnetic Laplacian on hyperbolic surfaces.
problem Analyzing the magnetic Laplacian on compact hyperbolic surfaces.
method Computed the trace formula for magnetic Laplacian energies above the Mane critical level.
result Asymptotic behavior of trace formula coefficients near the Mane critical level.