相关论文: Higher Helicity of Magnetic Lines and Arf-invarian…
Any smooth, closed oriented 4-manifold has a surface diagram of arbitrarily high genus g>2 that specifies it up to diffeomorphism. The goal of this paper is to prove the following statement: For any smooth, closed oriented 4-manifold M,…
We study the structure of invariant measures for continuous automorphisms of compact metrizable abelian groups satisfying the descending chain condition. We show that the finitely supported invariant measures are weak-* dense in the space…
We define a notion of finite type invariants for links with a fixed linking matrix. We show that Milnor's triple link homotopy invariant is a finite type invariant, of type 1, in this sense. We also generalize the approach to Milnor's…
Several classical knot invariants, such as the Alexander polynomial, the Levine-Tristram signature and the Blanchfield pairing, admit natural extensions from knots to links, and more generally, from oriented links to so-called colored…
The transverse magnetoresistance of a nodal line Dirac semi-metal InBi has been studied. It is found that the magnetoresistance is not quadratic. In the region of small magnetic fields $ B\lesssim 0.1$~T, it is characterized by high…
The dual symmetry between the electric and magnetic fields underlies Maxwell's electrodynamics. Due to this symmetry one can describe topological properties of an electromagnetic field in free space and obtain the conservation law of…
It is well known that an equivalence relation is invariant under the basic operations of an algebra if and only if it is invariant under the unary polynomials of the algebra. We show that a higher arity version of this property holds for a…
In this paper, we introduce a magneto-spectral invariant for finite graphs. This invariant vanishes on trees and is maximized by complete graphs. We compute this invariant for cycles, complete graphs, wheel graphs, hypercubes, complete…
We show that the set of ergodic invariant measures of a shift space with a safe symbol (this includes all hereditary shifts) is arcwise connected when endowed with the $d$-bar metric. As a consequence the set of ergodic measures of such a…
The paper considers dynamo generated by a shallow fluid layer in a celestial body (planet or star). This dynamo is based on the extra invariant for interacting magnetic Rossby waves. The magnetohydrodynamics (MHD) is linearized on the…
Magnetohydrodynamics (MHD) provides the simplest description of magnetic plasma turbulence in a variety of astrophysical and laboratory systems. MHD turbulence with nonzero cross helicity is often called imbalanced, as it implies that the…
To an ergodic, essentially free and measure-preserving action of a non-amenable Baumslag-Solitar group on a standard probability space, a flow is associated. The isomorphism class of the flow is shown to be an invariant of such actions of…
On an open, connected symplectic manifold $(M,\omega)$, the group of Hamiltonian diffeomorphisms forms an infinite-dimensional Fr\'echet Lie group with Lie algebra $C^{\infty}_c(M)$ and adjoint action given by pullbacks. We prove that this…
New heterotic modular invariants are found using the level-rank duality of affine Kac-Moody algebras. They provide strong evidence for the consistency of an infinite list of heterotic Wess-Zumino-Witten (WZW) conformal field theories. We…
Two kinds of invariance for geometrical objects under transformations are involved in this paper. With respect to these kinds, we obtained novel invariants for almost geodesic mappings of the third type of a non-symmetric affine connection…
In turbulence, for neutral or conducting fluids, a large ratio of scales is excited because of the possible occurrence of inverse cascades to large, global scales together with direct cascades to small, dissipative scales, as observed in…
We compare predictions of the mean-field theory of superconductivity for nearly antiferromagnetic and nearly ferromagnetic metals for cubic and tetragonal lattices. The calculations are based on the parametrization of an effective…
In our conventional understanding, large-scale magnetic fields are thought to originate from an inverse cascade in the presence of magnetic helicity, differential rotation, or a magneto-rotational instability. However, as recent simulations…
Helical magnetic background fields with adjustable pitch angle are imposed on a conducting fluid in a differentially rotating cylindrical container. The small-scale kinetic and current helicities are calculated for various field geometries,…
We theoretically describe a mechanism of low-field linear magnetoconductivity in helical magnetic metals. Two ingredients for the mechanism in three-dimensional metals are identified to be the spin-orbit coupling and momentum-dependent…