Related papers: Magnetic Curves in $C$-manifolds
We analyze spectral properties of a quantum graph in the form of a ring chain with a $\delta$ coupling in the vertices exposed to a homogeneous magnetic field perpendicular to the graph plane. We find the band spectrum in the case when the…
We study conformal field theories (CFTs) on curved spaces including both orientable and unorientable manifolds possibly with boundaries. We first review conformal transformations on curved manifolds. We then compute the identity components…
The current paper is devoted to the study of integral curves of constant type in parabolic homogeneous spaces. We construct a canonical moving frame bundle for such curves and give the criterium when it turns out to be a Cartan connection.…
A normal subgroup of the (extended) mapping class group of a surface is said to be geometric if its automorphism group is the mapping class group. We prove that in the case of the Cantor tree surface, every normal subgroup is geometric. We…
Observational evidence for dynamo action in spiral galaxies is reviewed, and the capabilities of various theories in explaining the basic features of galactic magnetic fields are discussed. Mean-field dynamo models appear to be unique in…
After a short introduction on how we get information of the magnetic fields from radio observations I discuss the results concerning the magnetic field structure in galaxies: Large-scale regular magnetic field pattern of spiral structure…
We present new mathematical alternatives for explaining rotation curves of spiral galaxies in the MOND context. For given total masses, it is shown that various mathematical alternatives to MOND, while predicting flat rotation curves for…
We analyze the transport properties of curved, three-dimensional graphite samples in strong magnetic fields. Focusing on a millimeter-scale graphite cylinder as a prototypical curved object, we perform longitudinal and Hall voltage…
Magnetic winding is a fundamental topological quantity that underpins magnetic helicity and measures the entanglement of magnetic field lines. Like magnetic helicity, magnetic winding is also an invariant of ideal magnetohydrodynamics. In…
The 2D Parker's mean-field dynamo equations with a various distributions of the $\alpha$- and $\omega$-effects are considered. We show that smooth profiles of $\alpha$ and $\omega$ can produce dipole configuration of the magnetic field with…
We computed flat rotation curves from scalar-tensor theories in their weak field limit. Our model, by construction, fits a flat rotation profile for velocities of stars. As a result, the form of the scalar field potential and DM…
A symplectic rational cuspidal curve with positive self-intersection number admits a concave neighborhood, and thus a corresponding contact manifold on the boundary. In this article, we study symplectic fillings of such contact manifolds,…
A convection-driven MHD dynamo in a rotating spherical shell, with clearly defined structural elements in the flow and magnetic field, is simulated numerically. Such dynamos can be called deterministic, in contrast to those explicitly…
In this article, we classify (non-compact) $3$-manifolds with uniformly positive scalar curvature. Precisely, we show that an oriented $3$-manifold has a complete metric with uniformly positive scalar curvature if and only if it is…
In this paper we study slant null curves with respect to the original parameter on 3-dimensional normal almost contact B-metric manifolds with parallel Reeb vector field. We prove that for non-geodesic such curves there exists a unique…
It is shown that C-flows in Riemannian three-dimensional compact manifold can be naturally considered as generalized dynamo Arnold's metric in compact manifolds, the so-called cat map dynamo. The generalized solution of self-induction…
In this survey article, we summarise the known results towards the conjecture: elliptic curves over totally real number fields are modular. For understanding these recent results in the literature, we present some necessary background along…
We characterize the orientation of polar plumes as a tracer of the large-scale coronal magnetic field configuration. We monitor in particular the north and south magnetic pole locations and the magnetic opening during 2007-2008 and provide…
In this article we study $p$-biharmonic curves as a natural generalization of biharmonic curves. In contrast to biharmonic curves $p$-biharmonic curves do not need to have constant geodesic curvature if $p=\frac{1}{2}$ in which case their…
Curved magnetic architectures are key enablers of the prospective magnetic devices with respect to size, functionality and speed. By exploring geometry-governed magnetic interactions, curvilinear magnetism offers a number of intriguing…