Completed cohomology of Shimura curves and a p-adic Jacquet-Langlands correspondence

We study indefinite quaternion algebras over totally real fields F, and give an example of a cohomological construction of p-adic Jacquet-Langlands functoriality using completed cohomology. We also study the (tame) levels of p-adic automorphic forms on these quaternion algebras and give an analogue of Mazur's `level lowering' principle.Comment: Updated version. Contains some minor corrections compared to the published versio

Condition matters: pupil voices on the design and condition of secondary schools

This research was produced by Sheffield Hallam University. The project aimed to inform the creation of a national schools Facilities Management network and an ongoing programme to research and benchmark the impact of school condition and design on pupils

What is the most useful approach for forecasting hydrological extremes during El Niño?

In the past, efforts to prepare for the impacts of El Niño-driven flood and drought hazards have often relied on seasonal precipitation forecasts as a proxy for hydrological extremes, due to a lack of hydrologically relevant information. However, precipitation forecasts are not the best indicator of hydrological extremes. Now, two different global scale hydro-meteorological approaches for predicting river flow extremes are available to support flood and drought preparedness. These approaches are statistical forecasts based on large-scale climate variability and teleconnections, and resource-intensive dynamical forecasts using coupled ocean-atmosphere general circulation models. Both have the potential to provide early warning information, and both are used to prepare for El Niño impacts, but which approach provides the most useful forecasts? This study uses river flow observations to assess and compare the ability of two recently-developed forecasts to predict high and low river flow during El Niño: statistical historical probabilities of ENSO-driven hydrological extremes, and the dynamical seasonal river flow outlook of the Global Flood Awareness System (GloFAS-Seasonal). Our findings highlight regions of the globe where each forecast is (or is not) skilful compared to a forecast of climatology, and the advantages and disadvantages of each forecasting approach. We conclude that in regions where extreme river flow is predominantly driven by El Niño, or in regions where GloFAS-Seasonal currently lacks skill, the historical probabilities generally provide a more useful forecast. In areas where other teleconnections also impact river flow, with the effect of strengthening, mitigating or even reversing the influence of El Niño, GloFAS-Seasonal forecasts are typically more useful

Kinematic alignment in total knee arthroplasty

Kinematic alignment (KA) is an alternative philosophy for aligning a total knee replacement (TKR) which aims to restore all three kinematic axes of the native knee. Many of the studies on KA have actually described non-KA techniques, which has led to much confusion about what actually fits the definition of KA. Alignment should only be measured using three-dimensional cross-sectional imaging. Many of the studies looking at the influence of implants/limb alignment on total knee arthroplasty outcomes are of limited value because of the use of two-dimensional imaging to measure alignment, potentially leading to inaccuracy. No studies have shown KA to be associated with higher complication rates or with worse implant survival; and the clinical outcomes following KA tend to be at least as good as mechanical alignment. Further high-quality multi-centre randomized controlled trials are needed to establish whether KA provides better function and without adversely impacting implant survival

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

Shear-Induced Isotropic-to-Lamellar Transition in a Lattice-Gas Model of Ternary Amphiphilic Fluids

Although shear-induced isotropic-to-lamellar transitions in ternary systems of oil, water and surfactant have been observed experimentally and predicted theoretically by simple models for some time now, their numerical simulation has not been achieved so far. In this work we demonstrate that a recently introduced hydrodynamic lattice-gas model of amphiphilic fluids is well suited for this purpose: the two-dimensional version of this model does indeed exhibit a shear-induced isotropic-to-lamellar phase transition.Comment: 17 pages, LaTeX with epsf and REVTeX, PostScript and EPS illustrations included. To appear in J. Phys. Cond. Ma

Breakdown of scale-invariance in the coarsening of phase-separating binary fluids

We present evidence, based on lattice Boltzmann simulations, to show that the coarsening of the domains in phase separating binary fluids is not a scale-invariant process. Moreover we emphasise that the pathway by which phase separation occurs depends strongly on the relation between diffusive and hydrodynamic time scales.Comment: 4 pages, Latex, 4 eps Figures included. (higher quality Figures can be obtained from [email protected]

Three dimensional hysdrodynamic lattice-gas simulations of binary immiscible and ternary amphiphilic flow through porous media

We report the results of a study of multiphase flow in porous media. A Darcy's law for steady multiphase flow was investigated for both binary and ternary amphiphilic flow. Linear flux-forcing relationships satisfying Onsager reciprocity were shown to be a good approximation of the simulation data. The dependence of the relative permeability coefficients on water saturation was investigated and showed good qualitative agreement with experimental data. Non-steady state invasion flows were investigated, with particular interest in the asymptotic residual oil saturation. The addition of surfactant to the invasive fluid was shown to significantly reduce the residual oil saturation.Comment: To appear in Phys. Rev.

Lattice Boltzmann simulations of lamellar and droplet phases

Lattice Boltzmann simulations are used to investigate spinodal decomposition in a two-dimensional binary fluid with equilibrium lamellar and droplet phases. We emphasise the importance of hydrodynamic flow to the phase separation kinetics. For mixtures slightly asymmetric in composition the fluid phase separates into bulk and lamellar phases with the lamellae forming distinctive spiral structures to minimise their elastic energy.Comment: 19 pages, 5 figure