1,824 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
Expansions for the Bollobas-Riordan polynomial of separable ribbon graphs
We define 2-decompositions of ribbon graphs, which generalise 2-sums and
tensor products of graphs. We give formulae for the Bollobas-Riordan polynomial
of such a 2-decomposition, and derive the classical Brylawski formula for the
Tutte polynomial of a tensor product as a (very) special case. This study was
initially motivated from knot theory, and we include an application of our
formulae to mutation in knot diagrams.Comment: Version 2 has minor changes. To appear in Annals of Combinatoric
Measurement Of Quasiparticle Transport In Aluminum Films Using Tungsten Transition-Edge Sensors
We report new experimental studies to understand the physics of phonon
sensors which utilize quasiparticle diffusion in thin aluminum films into
tungsten transition-edge-sensors (TESs) operated at 35 mK. We show that basic
TES physics and a simple physical model of the overlap region between the W and
Al films in our devices enables us to accurately reproduce the experimentally
observed pulse shapes from x-rays absorbed in the Al films. We further estimate
quasiparticle loss in Al films using a simple diffusion equation approach.Comment: 5 pages, 6 figures, PRA
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 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.
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