Related papers: Magnetic Curves in $C$-manifolds
Topological textures in magnetically ordered materials are important case studies for fundamental research with promising applications in data science. They can also serve as photonic elements to mold electromagnetic fields endowing them…
Early-type B stars with strong magnetic fields and rapid rotation form centrifugal magnetospheres (CMs), as the relatively weak stellar wind becomes magnetically confined and centrifugally supported above the Kepler co-rotation radius. CM…
Curves in ${\mathbb R}^n$ for which the ratios between two consecutive curvatures are constant are characterized by the fact that their tangent indicatrix is a geodesic in a flat torus. For $n= 3,4$, spherical curves of this kind are also…
Detailed magneto-transport data on dense wires of $MgB_2$ are reported for applied magnetic fields up to 18 T. The temperature and field dependencies of the electrical resistivity are consistent with $MgB_2$ behaving like a simple metal and…
We classify compact manifolds of dimension three equipped with a path structure and a fixed contact form (which we refer to as a strict path structure) under the hypothesis that their automorphism group is non-compact. We use a Cartan…
This article studies families of curves with monotonic curvature function (MC-curves) and their applications in geometric modelling and aesthetic design. Aesthetic analysis and assessment of the structure and plastic qualities of…
A natural connection with totally skew-symmetric torsion on almost contact manifolds with B-metric is constructed. The class of these manifolds, where the considered connection exists, is determined. Some curvature properties for this…
Quasi-periodic oscillations have been seen in the light curves following several magnetar giant flares. These oscillations are of great interest as they probably provide our first ever view of the normal modes of oscillation of neutron…
Let $(M, \alpha)$ be a $2n+1$-dimensional connected compact contact toric manifold of Reeb type. Suppose the contact form $\alpha$ is regular, we find conditions under which $M$ is homeomorphic to $S^{2n+1}$.
We study the electron motion near magnetic field steps at which the strength and/or sign of the magnetic field changes. The energy spectrum for such systems is found and the electron states (bound and scattered) are compared with their…
The magnetization curves M(H) for ideal type-II superconductors and the maximum, minimum, and saddle point magnetic fields of the vortex lattice are calculated from Ginzburg-Landau theory for the entire ranges of applied magnetic fields Hc1…
To any metric spaces there is an associated metric profile. The rectifiability of the metric profile gives a good notion of curvature of a sub-Riemannian space. We shall say that a curvature class is the rectifiability class of the metric…
It is generally believed that the radiation of relativistic particles in a curved magnetic field proceeds in either the synchrotron or the curvature radiation modes. In this paper we show that in strong curved magnetic fields a significant…
We discuss 1-Ahlfors-regular connected sets in a general metric space and prove that such sets are `flat' on most scales and in most locations. Our result is quantitative, and when combined with work of I. Hahlomaa, gives a characterization…
The semiclassical Laplacian with discontinuous magnetic field is considered in two dimensions. The magnetic field is sign changing with exactly two distinct values and is discontinuous along a smooth closed curve, thereby producing an…
We introduce a topological flux function to quantify the topology of magnetic braids: non-zero, line-tied magnetic fields whose field lines all connect between two boundaries. This scalar function is an ideal invariant defined on a…
In this paper we deal with polarizations on a nodal curve $C$ with smooth components. Our aim is to study and characterize a class of polarizations, which we call "good", for which depth one sheaves on $C$ reflect some properties that hold…
We prove that certain non-exact magnetic Hamiltonian systems on products of closed hyperbolic surfaces and with a potential function of large oscillation admit non-constant contractible periodic solutions of energy below the Ma\~n\'e…
This is an overview article. After an introduction to convenient calculus in infinite dimensions, the foundational material for manifolds of mappings is presented. The central character is the smooth convenient manifold $C^{\infty}(M,N)$ of…
We show that smooth curves with prescribed curvature satisfy a $C^1$-dense $h$-principle in the space of immersed curves in Euclidean space. More precisely, every $C^{\alpha \geq 2}$ curve with nonvanishing curvature in $R^{n\geq 3}$ can be…