1,538 research outputs found
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
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
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
Evolution of the Leading-Edge Vortex over an Accelerating Rotating Wing
AbstractThe flow field over an accelerating rotating wing model at Reynolds numbers Re ranging from 250 to 2000 is investigated using particle image velocimetry, and compared with the flow obtained by three-dimensional time-dependent Navier-Stokes simulations. It is shown that the coherent leading-edge vortex that characterises the flow field at Re~200-300 transforms to a laminar separation bubble as Re is increased. It is further shown that the ratio of the instantaneous circulation of the leading-edge vortex in the accel-eration phase to that over a wing rotating steadily at the same Re decreases monotonically with increasing Re. We conclude that the traditional approach based on steady wing rotation is inadequate for the prediction of the aerodynamic performance of flapping wings at Re above about 1000
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
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
Measurements of the magnetic field induced by a turbulent flow of liquid metal
Initial results from the Madison Dynamo Experiment provide details of the
inductive response of a turbulent flow of liquid sodium to an applied magnetic
field. The magnetic field structure is reconstructed from both internal and
external measurements. A mean toroidal magnetic field is induced by the flow
when an axial field is applied, thereby demonstrating the omega effect.
Poloidal magnetic flux is expelled from the fluid by the poloidal flow.
Small-scale magnetic field structures are generated by turbulence in the flow.
The resulting magnetic power spectrum exhibits a power-law scaling consistent
with the equipartition of the magnetic field with a turbulent velocity field.
The magnetic power spectrum has an apparent knee at the resistive dissipation
scale. Large-scale eddies in the flow cause significant changes to the
instantaneous flow profile resulting in intermittent bursts of non-axisymmetric
magnetic fields, demonstrating that the transition to a dynamo is not smooth
for a turbulent flow.Comment: 9 pages, 11 figures, invited talk by C. B. Forest at 2005 APS DPP
meeting, resubmitted to Physics of Plasma
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