X-point collapse and saturation in the nonlinear tearing mode reconnection

We study the nonlinear evolution of the resistive tearing mode in slab geometry in two dimensions. We show that, in the strongly driven regime (large Delta'), a collapse of the X-point occurs once the island width exceeds a certain critical value ~1/Delta'. A current sheet is formed and the reconnection is exponential in time with a growth rate ~eta^1/2, where eta is the resistivity. If the aspect ratio of the current sheet is sufficiently large, the sheet can itself become tearing-mode unstable, giving rise to secondary islands, which then coalesce with the original island. The saturated state depends on the value of Delta'. For small Delta', the saturation amplitude is ~Delta' and quantitatively agrees with the theoretical prediction. If Delta' is large enough for the X-point collapse to have occured, the saturation amplitude increases noticeably and becomes independent of Delta'.Comment: revtex4, 4 pages, 18 figure

Auto-calibration of ultrasonic lubricant-film thickness measurements

The measurement of oil film thickness in a lubricated component is essential information for performance monitoring and design. It is well established that such measurements can be made ultrasonically if the lubricant film is modelled as a collection of small springs. The ultrasonic method requires that component faces are separated and a reference reflection recorded in order to obtain a reflection coefficient value from which film thickness is calculated. The novel and practically useful approach put forward in this paper and validated experimentally allows reflection coefficient measurement without the requirement for a reference. This involves simultaneously measuring the amplitude and phase of an ultrasonic pulse reflected from a layer. Provided that the acoustic properties of the substrate are known, the theoretical relationship between the two can be fitted to the data in order to yield reflection coefficient amplitude and phase for an infinitely thick layer. This is equivalent to measuring a reference signal directly, but importantly does not require the materials to be separated. The further valuable aspect of this approach, which is demonstrated experimentally, is its ability to be used as a self-calibrating routine, inherently compensating for temperature effects. This is due to the relationship between the amplitude and phase being unaffected by changes in temperature which cause unwanted changes to the incident pulse. Finally, error analysis is performed showing how the accuracy of the results can be optimized. A finding of particular significance is the strong dependence of the accuracy of the technique on the amplitude of reflection coefficient input data used. This places some limitations on the applicability of the technique. © 2008 IOP Publishing Ltd

The classification of irreducible admissible mod p representations of a p-adic GL_n

Let F be a finite extension of Q_p. Using the mod p Satake transform, we define what it means for an irreducible admissible smooth representation of an F-split p-adic reductive group over \bar F_p to be supersingular. We then give the classification of irreducible admissible smooth GL_n(F)-representations over \bar F_p in terms of supersingular representations. As a consequence we deduce that supersingular is the same as supercuspidal. These results generalise the work of Barthel-Livne for n = 2. For general split reductive groups we obtain similar results under stronger hypotheses.Comment: 55 pages, to appear in Inventiones Mathematica

Shapley Optical Survey. I: Luminosity Functions in the Supercluster Environment

We present the Shapley Optical Survey, a photometric study covering a 2 deg^2 region of the Shapley Supercluster core at z ~ 0.05 in two bands (B and R). The galaxy sample is complete to B=22.5 (>M^*+6, N_{gal}=16588), and R=22.0 (>M^*+7, N_{gal}=28008). The galaxy luminosity function cannot be described by a single Schechter function due to dips apparent at B ~ 17.5 (M_B ~ -19.3) and R ~ 17.0 (M_R ~ -19.8) and the clear upturn in the counts for galaxies fainter than B and R ~18 mag. We find, instead, that the sum of a Gaussian and a Schechter function, for bright and faint galaxies respectively, is a suitable representation of the data. We study the effects of the environment on the photometric properties of galaxies, deriving the galaxy luminosity functions in three regions selected according to the local galaxy density, and find a marked luminosity segregation, in the sense that the LF faint-end is different at more than 3sigma confidence level in regions with different densities. In addition, the luminosity functions of red and blue galaxy populations show very different behaviours: while red sequence counts are very similar to those obtained for the global galaxy population, the blue galaxy luminosity functions are well described by a single Schechter function and do not vary with the density. Such large environmentally-dependent deviations from a single Schechter function are difficult to produce solely within galaxy merging or suffocation scenarios. Instead the data support the idea that mechanisms related to the cluster environment, such as galaxy harassment or ram-pressure stripping, shape the galaxy LFs by terminating star-formation and producing mass loss in galaxies at \~M^*+2, a magnitude range where blue late-type spirals used to dominate cluster populations, but are now absent.Comment: 23 pages, 13 figures, MNRAS accepte

Assessment of Current Global and Regional Mean Sea Level Estimates Based on the TOPEX/Poseidon Jason-1 and 2 Climate Data Record

Recent developments in Precise Orbit Determinations (POD) due to in particular to revisions to the terrestrial reference frame realization and the time variable gravity (TVG) continues to provide improvements to the accuracy and stability of the PO directly affecting mean sea level (MSL) estimates. Long-term credible MSL estimates require the development and continued maintenance of a stable reference frame, along with vigilant monitoring of the performance of the independent tracking systems used to calculate the orbits for altimeter spacecrafts. The stringent MSL accuracy requirements of a few tenths of an mm/yr are particularly essential for mass budget closure analysis over the relative short time period of Jason-l &2, GRACE, and Argo coincident measurements. In an effort to adhere to cross mission consistency, we have generated a full time series of experimental orbits (GSFC stdlllO) for TOPEX/Poseidon (TP), Jason-I, and OSTM based on an improved terrestrial reference frame (TRF) realization (ITRF2008), revised static (GGM03s), and time variable gravity field (Eigen6s). In this presentation we assess the impact of the revised precision orbits on inter-mission bias estimates, and resultant global and regional MSL trends. Tide gauge verification results are shown to assess the current stability of the Jason-2 sea surface height time series that suggests a possible discontinuity initiated in early 2010. Although the Jason-2 time series is relatively short (approximately 3 years), a thorough review of the entire suite of geophysical and environmental range corrections is warranted and is underway to maintain the fidelity of the record

Semiclassical energy formulas for power-law and log potentials in quantum mechanics

We study a single particle which obeys non-relativistic quantum mechanics in R^N and has Hamiltonian H = -Delta + V(r), where V(r) = sgn(q)r^q. If N \geq 2, then q > -2, and if N = 1, then q > -1. The discrete eigenvalues E_{n\ell} may be represented exactly by the semiclassical expression E_{n\ell}(q) = min_{r>0}\{P_{n\ell}(q)^2/r^2+ V(r)}. The case q = 0 corresponds to V(r) = ln(r). By writing one power as a smooth transformation of another, and using envelope theory, it has earlier been proved that the P_{n\ell}(q) functions are monotone increasing. Recent refinements to the comparison theorem of QM in which comparison potentials can cross over, allow us to prove for n = 1 that Q(q)=Z(q)P(q) is monotone increasing, even though the factor Z(q)=(1+q/N)^{1/q} is monotone decreasing. Thus P(q) cannot increase too slowly. This result yields some sharper estimates for power-potential eigenvlaues at the bottom of each angular-momentum subspace.Comment: 20 pages, 5 figure

A new modality of treatment for non-united fracture of the humerus in a patient with osteopetrosis: a case report

<p>Abstract</p> <p>Introduction</p> <p>Osteopetrosis introduces technical limitations to the traditional treatment of fracture management that may be minimised with specific pre-operative planning. Extreme care and caution are required when drilling, reaming, or inserting implants in patients with osteopetrosis. Caution must be exercised throughout the postoperative course when these patients are at greatest risk for device failure or further injury.</p> <p>Case presentation</p> <p>We present our experience of treating such a fracture where a patient presented with a non-united fracture of the humerus. The bone was already osteoporotic. We successfully used a new technique which has not been described in the literature before. This included the use of a high-speed drill to prepare the bone for screw fixation. Bone healing was augmented with bone morphogenic protein.</p> <p>Conclusion</p> <p>This technique can give invaluable experience to surgeons who are involved in treating these types of fracture.</p

Towards seasonal Arctic shipping route predictions

The continuing decline in Arctic sea-ice will likely lead to increased human activity and opportunities for shipping in the region, suggesting that seasonal predictions of route openings will become ever more important. Here we present results from a set of 'perfect model' experiments to assess the predictability characteristics of the opening of Arctic sea routes. We find skilful predictions of the upcoming summer shipping season can be made from as early as January, although typically forecasts show lower skill before a May 'predictability barrier'. We demonstrate that in forecasts started from January, predictions of route opening date are twice as uncertain as predicting the closing date and that the Arctic shipping season is becoming longer due to climate change, with later closing dates mostly responsible. We find that predictive skill is state dependent with predictions for high or low ice years exhibiting greater skill than medium ice years. Forecasting the fastest open water route through the Arctic is accurate to within 200 km when predicted from July, a six-fold increase in accuracy compared to forecasts initialised from the previous November, which are typically no better than climatology. Finally we find that initialisation of accurate summer sea-ice thickness information is crucial to obtain skilful forecasts, further motivating investment into sea-ice thickness observations, climate models, and assimilation systems