Related papers: Obstructions to topological relaxation for generic…
A magnetic helicity integral is proposed which can be applied to domains which are not magnetically closed, i.e. have a non-vanishing normal component of the magnetic field on the boundary. In contrast to the relative helicity integral,…
We study the topology associated with physical vector and scalar fields. A mathematical object, e.g., a ball, can be continuously deformed, without tearing or gluing, to make other topologically equivalent objects, e.g., a cube or a solid…
Gravitational properties of a hedge-hog type topological defect in two extra dimensions are considered in General Relativity employing a vector as the order parameter. The developed macroscopic theory of phase transitions with spontaneous…
In this paper we study a nonlinear magneto-static model on a general domain which is multiply-connected and has $m$ holes, and under a nonlinear relation between magnetic induction $\bold B$ and magnetic field $\bold H$. The equation…
Nonintegrable dynamical systems have complex structures in their phase space. Motion of a test charged particle in a dipole magnetic field can be reduced to a 2 degree-of-freedom (2 d.o.f.) nonintegrable Hamiltonian system. We carried out a…
Let $\Omega \subset \mathbb{C}^n$ be a domain whose Bergman space contains all holomorphic monomials. We derive sufficient conditions for $\Omega$ to be Reinhardt, complete Reinhardt, circular or Hartogs in terms of the orthogonality…
This paper is devoted to the analysis of a singular perturbation problem for a $2$-D incompressible MHD system with density variations and Coriolis force, in the limit of small Rossby numbers. Two regimes are considered. The first one is…
This paper establishes an explicit obstruction to constructing algebraic cycles from automorphic cohomology classes on Shimura varieties. We produce a rational Hodge class $\Omega_E$ in the intersection cohomology of the Baily-Borel…
For $C^2$ vector fields, we study regular ergodic measures whose supports admit singular dominated splittings with one of the bundles having dimension $1$. For such a measure $\mu$, we prove that if any periodic orbit within the support of…
We study the magnetic braking and viscous damping of differential rotation in incompressible, uniform density stars in general relativity. Differentially rotating stars can support significantly more mass in equilibrium than nonrotating or…
We show that there is an hierarchy of intersection rigidity properties of sets in a closed symplectic manifold: some sets cannot be displaced by symplectomorphisms from more sets than the others. We also find new examples of rigidity of…
We derive general equations for axisymmetric Newtonian MHD and use these as the basis of a code for calculating equilibrium configurations of rotating magnetised neutron stars in a stationary state. We investigate the field configurations…
We show that holography poses non-trivial restrictions on various couplings of an interacting field. For a vector boson in the AdS Reissner-Nordstrom background, the dual boundary theory is pathological unless its electromagnetic and…
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…
Tetrahedral frame fields have applications to certain classes of nematic liquid crystals and frustrated media. We consider the problem of constructing a tetrahedral frame field in three dimensional domains in which the boundary normal…
We study the Yang-Mills-Higgs system within the framework of general relativity. In the static situation, using Bogomol'nyi type analysis, we derive a positive-definite energy functional which has a lower bound. Specializing to the gauge…
A general formula for the average vector potential of bulk periodic systems is proposed and shown to set the boundary conditions at magnetic interfaces. For antiferromagnetic materials, the study reveals a unique relation between the…
At high densities fluids of strongly dipolar spherical particles exhibit spontaneous long-ranged orientational order. Typically, due to demagnetization effects induced by the long range of the dipolar interactions, the magnetization…
Topological magnetoelectric effect (TME) is a hallmark response of the topological field theory, which provides a paradigm shift in the study of emergent topological phenomena. However, its direct observation is yet to be realized due to…
Magnetic fields are an important component of the interstellar medium (ISM) and exhibit strongly varying field strengths and a non-trivial correlation with the gas density. Its dynamical impact varies between individual regions of the ISM…