Ribbon Graph Minors and Low-Genus Partial Duals

We give an excluded minor characterisation of the class of ribbon graphs that admit partial duals of Euler genus at most one

Unsigned state models for the Jones polynomial

It is well a known and fundamental result that the Jones polynomial can be expressed as Potts and vertex partition functions of signed plane graphs. Here we consider constructions of the Jones polynomial as state models of unsigned graphs and show that the Jones polynomial of any link can be expressed as a vertex model of an unsigned embedded graph. In the process of deriving this result, we show that for every diagram of a link in the 3-sphere there exists a diagram of an alternating link in a thickened surface (and an alternating virtual link) with the same Kauffman bracket. We also recover two recent results in the literature relating the Jones and Bollobas-Riordan polynomials and show they arise from two different interpretations of the same embedded graph.Comment: Minor corrections. To appear in Annals of Combinatoric

Direct Measurement of Effective Magnetic Diffusivity in Turbulent Flow of Liquid Sodium

The first direct measurements of effective magnetic diffusivity in turbulent flow of electro-conductive fluids (the so-called beta-effect) under magnetic Reynolds number Rm >> 1 are reported. The measurements are performed in a nonstationary turbulent flow of liquid sodium, generated in a closed toroidal channel. The peak level of the Reynolds number reached Re \approx 3 10^6, which corresponds to the magnetic Reynolds number Rm \approx 30. The magnetic diffusivity of the liquid metal was determined by measuring the phase shift between the induced and the applied magnetic fields. The maximal deviation of magnetic diffusivity from its basic (laminar) value reaches about 50% .Comment: 5 pages, 6 figuser, accepted in PR

Gauge vortex dynamics at finite mass of bosonic fields

The simple derivation of the string equation of motion adopted in the nonrelativistic case is presented, paying the special attention to the effects of finite masses of bosonic fields of an Abelian Higgs model. The role of the finite mass effects in the evaluation of various topological characteristics of the closed strings is discussed. The rate of the dissipationless helicity change is calculated. It is demonstrated how the conservation of the sum of the twisting and writhing numbers of the string is recovered despite the changing helicity.Comment: considerably revised to include errata to journal versio

A model of driven and decaying magnetic turbulence in a cylinder

Using mean-field theory, we compute the evolution of the magnetic field in a cylinder with outer perfectly conducting boundaries, an imposed axial magnetic and electric field. The thus injected magnetic helicity in the system can be redistributed by magnetic helicity fluxes down the gradient of the local current helicity of the small-scale magnetic field. A weak reversal of the axial magnetic field is found to be a consequence of the magnetic helicity flux in the system. Such fluxes are known to alleviate so-called catastrophic quenching of the {\alpha}-effect in astrophysical applications. Application to the reversed field pinch in plasma confinement devices is discussed.Comment: 7 pages, 4 figures, submitted to Phys. Rev.

A Spherical Plasma Dynamo Experiment

We propose a plasma experiment to be used to investigate fundamental properties of astrophysical dynamos. The highly conducting, fast-flowing plasma will allow experimenters to explore systems with magnetic Reynolds numbers an order of magnitude larger than those accessible with liquid-metal experiments. The plasma is confined using a ring-cusp strategy and subject to a toroidal differentially rotating outer boundary condition. As proof of principle, we present magnetohydrodynamic simulations of the proposed experiment. When a von K\'arm\'an-type boundary condition is specified, and the magnetic Reynolds number is large enough, dynamo action is observed. At different values of the magnetic Prandtl and Reynolds numbers the simulations demonstrate either laminar or turbulent dynamo action

General Relativistic Simulations of Slowly and Differentially Rotating Magnetized Neutron Stars

We present long-term (~10^4 M) axisymmetric simulations of differentially rotating, magnetized neutron stars in the slow-rotation, weak magnetic field limit using a perturbative metric evolution technique. Although this approach yields results comparable to those obtained via nonperturbative (BSSN) evolution techniques, simulations performed with the perturbative metric solver require about 1/4 the computational resources at a given resolution. This computational efficiency enables us to observe and analyze the effects of magnetic braking and the magnetorotational instability (MRI) at very high resolution. Our simulations demonstrate that (1) MRI is not observed unless the fastest-growing mode wavelength is resolved by more than about 10 gridpoints; (2) as resolution is improved, the MRI growth rate converges, but due to the small-scale turbulent nature of MRI, the maximum growth amplitude increases, but does not exhibit convergence, even at the highest resolution; and (3) independent of resolution, magnetic braking drives the star toward uniform rotation as energy is sapped from differential rotation by winding magnetic fields.Comment: 21 pages, 11 figures, published in Phys.Rev.

Shell to shell energy transfer in MHD, Part II: Kinematic dynamo

We study the transfer of energy between different scales for forced three-dimensional MHD turbulent flows in the kinematic dynamo regime. Two different forces are examined: a non-helical Taylor Green flow with magnetic Prandtl number P_M=0.4, and a helical ABC flow with P_M=1. This analysis allows us to examine which scales of the velocity flow are responsible for dynamo action, and identify which scales of the magnetic field receive energy directly from the velocity field and which scales receive magnetic energy through the cascade of the magnetic field from large to small scales. Our results show that the turbulent velocity fluctuations are responsible for the magnetic field amplification in the small scales (small scale dynamo) while the large scale field is amplified mostly due to the large scale flow. A direct cascade of the magnetic field energy from large to small scales is also present and is a complementary mechanism for the increase of the magnetic field in the small scales. Input of energy from the velocity field in the small magnetic scales dominates over the energy that is cascaded down from the large scales until the large-scale peak of the magnetic energy spectrum is reached. At even smaller scales, most of the magnetic energy input is from the cascading process.Comment: Submitted to PR