Homfly Polynomials of Generalized Hopf Links

Following the recent work by T.-H. Chan in [HOMFLY polynomial of some generalized Hopf links, J. Knot Theory Ramif. 9 (2000) 865--883] on reverse string parallels of the Hopf link we give an alternative approach to finding the Homfly polynomials of these links, based on the Homfly skein of the annulus. We establish that two natural skein maps have distinct eigenvalues, answering a question raised by Chan, and use this result to calculate the Homfly polynomial of some more general reverse string satellites of the Hopf link.Comment: Published by Algebraic and Geometric Topology at http://www.maths.warwick.ac.uk/agt/AGTVol2/agt-2-2.abs.htm

Model fitting of kink waves in the solar atmosphere: Gaussian damping and time-dependence

{Observations of the solar atmosphere have shown that magnetohydrodynamic waves are ubiquitous throughout. Improvements in instrumentation and the techniques used for measurement of the waves now enables subtleties of competing theoretical models to be compared with the observed waves behaviour. Some studies have already begun to undertake this process. However, the techniques employed for model comparison have generally been unsuitable and can lead to erroneous conclusions about the best model. The aim here is to introduce some robust statistical techniques for model comparison to the solar waves community, drawing on the experiences from other areas of astrophysics. In the process, we also aim to investigate the physics of coronal loop oscillations. } {The methodology exploits least-squares fitting to compare models to observational data. We demonstrate that the residuals between the model and observations contain significant information about the ability for the model to describe the observations, and show how they can be assessed using various statistical tests. In particular we discuss the Kolmogorov-Smirnoff one and two sample tests, as well as the runs test. We also highlight the importance of including any observational trend line in the model-fitting process.} {To demonstrate the methodology, an observation of an oscillating coronal loop undergoing standing kink motion is used. The model comparison techniques provide evidence that a Gaussian damping profile provides a better description of the observed wave attenuation than the often used exponential profile. This supports previous analysis from Pascoe et al. (2016). Further, we use the model comparison to provide evidence of time-dependent wave properties of a kink oscillation, attributing the behaviour to the thermodynamic evolution of the local plasma.}Comment: Accepted in Astronomy & Astrophysics http://dx.doi.org/10.1051/0004-6361/20162861

Mutants and SU(3)_q invariants

Details of quantum knot invariant calculations using a specific SU(3)_q-module are given which distinguish the Conway and Kinoshita-Teresaka pair of mutant knots. Features of Kuperberg's skein-theoretic techniques for SU(3)_q invariants in the context of mutant knots are also discussed.Comment: 17 pages. Published copy, also available at http://www.maths.warwick.ac.uk/gt/GTMon1/paper18.abs.htm

Dynamics of internetwork chromospheric fibrils: Basic properties and MHD kink waves

Using the spectroscopic imaging capabilities of the Swedish Solar Telescope, we aim to provide the first investigation on the nature and dynamics of elongated absorption features (fibrils) observed in H$\alpha$ in the internetwork. We observe and identify a number of internetwork fibrils, which form away from the kilogauss, network magnetic flux, and we provide a synoptic view on their behaviour. The internetwork fibrils are found to support wave-like behaviour, which we interpret as Magnetohydrodynamic (MHD) kink waves. The properties of these waves, that is, amplitude, period, and propagation speed, are measured from time-distance diagrams and we attempt to exploit them via magneto-seismology in order to probe the variation of plasma properties along the wave-guides. We found that the Internetwork (IN) fibrils appear, disappear, and re-appear on timescales of tens of minutes, suggesting that they are subject to repeated heating. No clear photospheric footpoints for the fibrils are found in photospheric magnetograms or H$\alpha$ wing images. However, we suggest that they are magnetised features as the majority of them show evidence of supporting propagating MHD kink waves, with a modal period of $120$~s. Additionally, one IN fibril is seen to support a flow directed along its elongated axis, suggesting a guiding field. The wave motions are found to propagate at speeds significantly greater than estimates for typical chromospheric sound speeds. Through their interpretation as kink waves, the measured speeds provide an estimate for local average Alfv\'en speeds. Furthermore, the amplitudes of the waves are also found to vary as a function of distance along the fibrils, which can be interpreted as evidence of stratification of the plasma in the neighbourhood of the IN fibril.Comment: Accepted Astronomy & Astrophysic

Pressure and velocity measurements in a three-dimensional wall jet

The effects on the flow fields of varying the ratio of the velocity at the exit plane of the nozzle to the outer tunnel flow are reported. The pressure-velocity correlations are taken and some trends are discussed. Emphasis is placed on comparing the coherence between the fluctuating pressure and velocity fields at various locations in the different flow configurations

An experimental investigation of an axisymmetric jet in a coflowing airstream

The flow development of an axisymmetric jet exhausting into a moving airstream has been studied. The jet has a Reynolds number of 22,600, and the ratio of the jet velocity to the wind tunnel velocity is 5.1 to 1. The flow field of the axisymmetric jet was examined at locations varying from approximately zero to eight diameters downstream of the orifice. Of primary concern at each downstream location was the mapping of the one point statistical properties of the flow, including mean velocity, turbulent intensity, and intermittency. Autocorrelations and power spectral density curves were determined for both the fluctuating velocity field and the concentration signal at various distances from the jet's center line for different downstream locations. A laser Doppler velocimeter, using a phase locked loop processor, was used to make the desired velocity field measurements which were compared with hot wire anemometer and pressure probe data

Spin-dependent recombination in Czochralski silicon containing oxide precipitates

Electrically detected magnetic resonance is used to identify recombination centers in a set of Czochralski grown silicon samples processed to contain strained oxide precipitates with a wide range of densities (~ 1e9 cm-3 to ~ 7e10 cm-3). Measurements reveal that photo-excited charge carriers recombine through Pb0 and Pb1 dangling bonds and comparison to precipitate-free material indicates that these are present at both the sample surface and the oxide precipitates. The electronic recombination rates vary approximately linearly with precipitate density. Additional resonance lines arising from iron-boron and interstitial iron are observed and discussed. Our observations are inconsistent with bolometric heating and interpreted in terms of spin-dependent recombination. Electrically detected magnetic resonance is thus a very powerful and sensitive spectroscopic technique to selectively probe recombination centers in modern photovoltaic device materials.Comment: 8 pages, 8 figure

Deligne-Beilinson cohomology and abelian link invariants: torsion case

For the abelian Chern-Simons field theory, we consider the quantum functional integration over the Deligne-Beilinson cohomology classes and present an explicit path-integral non-perturbative computation of the Chern-Simons link invariants in $SO(3)\simeq\mathbb{R}P^3$, a toy example of 3-manifold with torsion

Hi-C and AIA observations of transverse magnetohydrodynamic waves in active regions

The recent launch of the High resolution Coronal imager (Hi-C) provided a unique opportunity of studying the EUV corona with unprecedented spatial resolution. We utilize these observations to investigate the properties of low-frequency (50−200 s) active region transverse waves, whose omnipresence had been suggested previously. The five-fold improvement in spatial resolution over SDO/AIA reveals coronal loops with widths 150−310 km and that these loops support transverse waves with displacement amplitudes <50 km. However, the results suggest that wave activity in the coronal loops is of low energy, with typical velocity amplitudes <3 km s-1. An extended time-series of SDO data suggests that low-energy wave behaviour is typical of the coronal structures both before and after the Hi-C observations