相关论文: Field line winding of braided vector fields in tub…

Models for astrophysical plasmas often have magnetic field lines that leave the boundary rather than closing within the computational domain. Thus, the relative magnetic helicity is frequently used in place of the usual magnetic helicity,…

We propose that at low energy four dimensional bosonic strings may form bound states where they become bundled together much like the filaments in a cable. We inspect the properties of these bundles in terms of their extrinsic geometry.…

We show that the torus knot topology is inherent in electromagnetic and gravitational radiation by constructing spin-$N$ fields based on this topology from the elementary states of twistor theory. The twistor functions corresponding to the…

The purpose of this paper is to put into a noncommutative context basic notions related to vector fields from classical differential geometry. The manner of exposition is an attempt to make the material as accessible as possible to…

We consider the dynamics of vector fields on three-manifolds which are constrained to lie within a plane field, such as occurs in nonholonomic dynamics. On compact manifolds, such vector fields force dynamics beyond that of a gradient flow,…

We study constructions of vector fields with properties which are characteristic to Reeb vector fields of contact forms. In particular, we prove that all closed oriented odd-dimensional manifold have geodesible vector fields.

New examples of harmonic unit vector fields on hyperbolic 3-space are constructed by exploiting the reduction of symmetry arising from the foliation by horospheres. This is compared and contrasted with the analogous construction in…

We characterize the convexity of functions and the monotonicity of vector fields on metric measure spaces with Riemannian Ricci curvature bounded from below. Our result offers a new approach to deal with some rigidity theorems such as…

There are few explicit examples in the literature of vector fields exhibiting complex dynamics that may be proved analytically. We construct explicitly a {two parameter family of vector fields} on the three-dimensional sphere $\EU^3$, whose…

In this paper, we investigate the localization of a five-dimensional vector field on a pure geometrical thick brane. In previous work, it was shown that a free massless vector field cannot be localized on such thick brane. Hence we…

Two-band Hamiltonians provide a typical description of topological band structures, in which the eigenfunctions can be characterized by a %Bloch vector field whose winding number that defines an integer topological invariant. This winding…

We present a simple method to efficiently compute a lower limit of the topological entropy and its spatial distribution for two-dimensional mappings. These mappings could represent either two-dimensional time-periodic fluid flows or…

This paper shows that the topological structures of particle orbits generated by a generic class of vector fields on spherical surfaces, called {\it the flow of finite type}, are in one-to-one correspondence with discrete structures such as…

In the time evolution of fluids, the topologies of fluids can be changed by the creations and annihilations of singular points and by switching combinatorial structures of separatrices. In this paper, to describe the possible generic time…

Orbifolds in field theory are potentially singular objects for at their fixed points the curvature becomes infinite, therefore one may wonder whether field theory calculations near orbifold singularities can be trusted. String theory is…

Recently many methods have been proposed to create the vector fields, due to the academic interest and a variety of attractive applications such as for particle acceleration, optical trapping, particle manipulation, and fluorescence…

The interaction of magnetic fields and stratified convection was studied in the context of the solar and late type stellar dynamos by using numerical 3D MHD simulations. The topology of stratified asymmetric and over-turning convection…

Twistor string models have been known for more than a decade now but have come back under the spotlight recently with the advent of the scattering equation formalism which has greatly generalized the scope of these models. A striking…

We consider a class of foliations on the complex projective plane that are determined by a quadratic vector field in a fixed affine neighborhood. Such foliations, as a rule, have an invariant line at infinity. Two foliations with…

Context. Magnetic helicity is an important quantity in studies of magnetized plasmas as it provides a measure of the geometrical complexity of the magnetic field in a given volume. A more detailed description of the spatial distribution of…