Related papers: Obstructions to topological relaxation for generic…
In [15], V. Jimenez and J. Llibre characterized, up to homeomorphism, the omega limit sets of analytic vector fields on the sphere and the projective plane. The authors also studied the same problem for open subsets of these surfaces.…
In a bounded domain $\mathcal{O}\subset\mathbb{R}^3$ of class $C^{1,1}$, we consider a stationary Maxwell system with the boundary conditions of perfect conductivity. It is assumed that the magnetic permeability is given by a constant…
In this paper we use the gradient flow equation introduced in [10] to construct a Morse complex for the Hamiltonian action $\mathbb A_H$ on a mixed regularity space of loops in the cotangent bundle $T^*M$ of a closed manifold $M$.…
We study persistence of periodic and homoclinic orbits, first integrals and commutative vector fields in dynamical systems depending on a small parameter $\varepsilon>0$ and give several necessary conditions for their persistence. Here we…
From new neutron powder diffraction experiments on the chiral cubic ($P2{_1}3$) magnet manganese germanide MnGe, we analyse all of the possible crystal symmetry-allowed magnetic superstructures that are determined successfully from the…
We find topological defect solutions to the equations of motion of a generalised Higgs model with antisymmetric tensor fields. These solutions are direct higher dimensional analogues of the Nielsen-Olesen vortex solution for a gauge field…
Building on the first variational formula of the calculus of variations, one can derive the energy-momentum conservation laws from the condition of the Lie derivative of gravitation Lagrangians along vector fields corresponding to…
We study cohomological obstructions to the existence of global conserved quantities. In particular, we show that, if a given local variational problem is supposed to admit global solutions, certain cohomology classes cannot appear as…
This work studies the symmetries, the associated momentum map, and relative equilibria of a mechanical system consisting of a small axisymmetric magnetic body-dipole in an also axisymmetric external magnetic field that additionally exhibits…
We present new aspects of the electromagnetic field by introducting the natural potentials. These natural potentials are suitable for constructing the first order distortions of the metric tensor of Complex Relativity - the theory combining…
Astrophysical objects with negligible resistivity are often threaded by large scale magnetic fields. The generation of these fields is somewhat mysterious, since a magnetic field in a perfectly conducting fluid cannot change the flux…
The topological superfluid 3He-B provides many examples of the interplay of symmetry and topology. Here we consider the effect of magnetic field on topological properties of 3He-B. Magnetic field violates the time reversal symmetry. As a…
A quasisymmetry is a special symmetry that enhances the ability of a magnetic field to trap charged particles. Quasisymmetric magnetic fields may allow the realization of next generation fusion reactors (stellarators) with superior…
We employ partitioning methods, in the spirit of Montiel--Ros but here recast for general actions of compact Lie groups, to prove effective lower bounds on the Morse index of certain families of closed minimal hypersurfaces in the round…
In this work, we find novel static and spherically symmetric wormhole geometries using a three-form field. By solving the gravitational field equations, we find a variety of analytical and numerical solutions and show that it is possible…
A direct construction of equilibrium magnetic fields with toroidal topology at arbitrary order in the distance from the magnetic axis is carried out, yielding an analytical framework able to explore the landscape of possible magnetic flux…
Earlier, Chicone, Latushkin and Montgomery-Smith [Comm Math Phys (1997)] have proved the existence of a fast dynamo operator, in compact two-dimensional manifold, as long as its Riemannian curvature be constant and negative. More recently…
We study the stability of static, spherically symmetric, traversable wormholes existing due to conformal continuations in a class of scalar-tensor theories with zero scalar field potential (so that Fisher's well-known scalar-vacuum solution…
We reformulate the construction of wormhole solutions as perturbations around near-horizon geometries of near-extremal Reissner-Nordstr\"{o}m black holes in four dimensions and equal-angular-momenta Myers-Perry black holes in five…
For any compact oriented manifold $M$, we show that that the top degree multi-vector fields transverse to the zero section of $\wedge^{\text{top}}TM$ are classified, up to orientation preserving diffeomorphism, in terms of the topology of…