The supercuspidal representations of p-adic classical groups

Let G be a unitary, symplectic or special orthogonal group over a locally compact non-archimedean local field of odd residual characteristic. We construct many new supercuspidal representations of G, and Bushnell-Kutzko types for these representations. Moreover, we prove that every irreducible supercuspidal representation of G arises from our constructions.Comment: 55 pages -- minor changes from 1st version (mostly in sections 2.2, 4.2 and 6.2). To appear in Inventiones mathematicae, 2008 (DOI is not yet active as at 12 Nov 2007

Quantum interest in two dimensions

The quantum interest conjecture of Ford and Roman asserts that any negative-energy pulse must necessarily be followed by an over-compensating positive-energy one within a certain maximum time delay. Furthermore, the minimum amount of over-compensation increases with the separation between the pulses. In this paper, we first study the case of a negative-energy square pulse followed by a positive-energy one for a minimally coupled, massless scalar field in two-dimensional Minkowski space. We obtain explicit expressions for the maximum time delay and the amount of over-compensation needed, using a previously developed eigenvalue approach. These results are then used to give a proof of the quantum interest conjecture for massless scalar fields in two dimensions, valid for general energy distributions.Comment: 17 pages, 4 figures; final version to appear in PR

A neural network approach for determining spatial and geometry dependent Green's functions for thermal stress approximation in power plant header components

The trend in power generation to operate plant with a greater frequency of on/partial/off load conditions creates several concerns for the long term structural integrity of many high temperature components. The Green's function method has been used for many years to estimate the thermal stresses in components such as steam headers by attempting to solve the un-coupled thermal stress problem for a unit temperature step. Once a Green's function for a unit temperature step has been determined, realistic or actual component temperature profiles can be discretised and the time dependent stress profile reconstructed using Duhamel's theorem. Stress fluctuations can therefore be estimated and damage due to fatigue mechanisms can be quantified. A potential difficulty with this method is that Green's function approximations are determined for a single analysis point in a structure. This is because Green's functions are approximated by fitting a trial function to the results of finite element (FE) simulations. While a user can make some judgement on which point in a structure will give the “worst case” (or life limiting) conditions, it is foreseeable that points of interest will be dependent on the specific analysis conditions, such as the stub penetration geometry and the loading condition considered. The neural network approach described in this paper provides a means where transient thermal stress models of complex components (here taken to be steam headers) can be generated relatively quickly and used pro-actively to assess and modify plant operation. A range of header geometries have been considered to make the network applicable over an industry relevant envelope. Coefficients of determination (R2) are typically above 0.92 when reconstructed (from neural network results) unit temperature step stress profiles are compared against “true” FEA results. Mean errors in the stress profiles are, for the majority of cases, less than 10%. Suggestions are also made on possible future improvements to the method through the use of additional constraints on the reconstructed stress profiles

Quantum inequalities in two dimensional curved spacetimes

We generalize a result of Vollick constraining the possible behaviors of the renormalized expected stress-energy tensor of a free massless scalar field in two dimensional spacetimes that are globally conformal to Minkowski spacetime. Vollick derived a lower bound for the energy density measured by a static observer in a static spacetime, averaged with respect to the observers proper time by integrating against a smearing function. Here we extend the result to arbitrary curves in non-static spacetimes. The proof, like Vollick's proof, is based on conformal transformations and the use of our earlier optimal bound in flat Minkowski spacetime. The existence of such a quantum inequality was previously established by Fewster.Comment: revtex 4, 5 pages, no figures, submitted to Phys. Rev. D. Minor correction

Spatial governance in Beijing: informality, illegality and the displacement of the “low-end population”

Asian Studie

Quantum inequalities for the free Rarita-Schwinger fields in flat spacetime

Using the methods developed by Fewster and colleagues, we derive a quantum inequality for the free massive spin-${3\over 2}$ Rarita-Schwinger fields in the four dimensional Minkowski spacetime. Our quantum inequality bound for the Rarita-Schwinger fields is weaker, by a factor of 2, than that for the spin-${1\over 2}$ Dirac fields. This fact along with other quantum inequalities obtained by various other authors for the fields of integer spin (bosonic fields) using similar methods lead us to conjecture that, in the flat spacetime, separately for bosonic and fermionic fields, the quantum inequality bound gets weaker as the the number of degrees of freedom of the field increases. A plausible physical reason might be that the more the number of field degrees of freedom, the more freedom one has to create negative energy, therefore, the weaker the quantum inequality bound.Comment: Revtex, 11 pages, to appear in PR

The E-ELT Multi-Object Spectrograph: latest news from MOSAIC

There are 8000 galaxies, including 1600 at z larger than 1.6, which could be simultaneously observed in an E-ELT field of view of 40 sq. arcmin. A considerable fraction of astrophysical discoveries require large statistical samples, which can only be obtained with multi-object spectrographs (MOS). MOSAIC will provide a vast discovery space, enabled by a multiplex of 200 and spectral resolving powers of R=5000 and 20000. MOSAIC will also offer the unique capability of more than 10 "high-definition" (multi-object adaptive optics, MOAO) integral-field units, optimised to investigate the physics of the sources of reionization. The combination of these modes will make MOSAIC the world-leading MOS facility, contributing to all fields of contemporary astronomy, from extra-solar planets, to the study of the halo of the Milky Way and its satellites, and from resolved stellar populations in nearby galaxies out to observations of the earliest "first-light" structures in the Universe. It will also study the distribution of the dark and ordinary matter at all scales and epochs of the Universe. Recent studies of critical technical issues such as sky-background subtraction and MOAO have demonstrated that such a MOS is feasible with state-of-the-art technology and techniques. Current studies of the MOSAIC team include further trade-offs on the wavelength coverage, a solution for compensating for the non-telecentric new design of the telescope, and tests of the saturation of skylines especially in the near-IR bands. In the 2020s the E-ELT will become the world's largest optical/IR telescope, and we argue that it has to be equipped as soon as possible with a MOS to provide the most efficient, and likely the best way to follow-up on James Webb Space Telescope (JWST) observations.Comment: 10 pages, 3 Figures, in Ground-based and Airborne Instrumentation for Astronomy VI, 2016, Proc. SPI

Spatially Averaged Quantum Inequalities Do Not Exist in Four-Dimensional Spacetime

We construct a particular class of quantum states for a massless, minimally coupled free scalar field which are of the form of a superposition of the vacuum and multi-mode two-particle states. These states can exhibit local negative energy densities. Furthermore, they can produce an arbitrarily large amount of negative energy in a given region of space at a fixed time. This class of states thus provides an explicit counterexample to the existence of a spatially averaged quantum inequality in four-dimensional spacetime.Comment: 13 pages, 1 figure, minor corrections and added comment

A Glasgow tipple-transjugular intrahepatic portosystemic shunt insertion prior to Whipple resection

Abdominal surgery performed in patients with significant liver disease and portal hypertension is associated with high mortality rates, with even poorer outcomes associated with complex pancreaticobiliary operations. We report on a patient requiring portal decompression via transjugular intrahepatic portosystemic shunt (TIPS) prior to a pancreaticoduodenectomy. The 49-year-old patient presented with pain, jaundice and weight loss. At ERCP an edematous ampulla was biopsied, revealing high-grade dysplasia within a distal bile duct adenoma. Liver biopsy was performed to investigate portal hypertension, confirming congenital hepatic fibrosis (CHF). A TIPS was performed to enable a pancreaticoduodenectomy. Prophylactic TIPS can be performed for preoperative portal decompression for patients requiring pancreatic resection. A potentially curative resection was performed when abdominal surgery was initially thought impossible. Notably, CHF has been associated with the development of cholangiocarcinoma in only four previous instances, with this case being only the second reported distal bile duct cholangiocarcinoma

The Quantum Interest Conjecture

Although quantum field theory allows local negative energy densities and fluxes, it also places severe restrictions upon the magnitude and extent of the negative energy. The restrictions take the form of quantum inequalities. These inequalities imply that a pulse of negative energy must not only be followed by a compensating pulse of positive energy, but that the temporal separation between the pulses is inversely proportional to their amplitude. In an earlier paper we conjectured that there is a further constraint upon a negative and positive energy delta-function pulse pair. This conjecture (the quantum interest conjecture) states that a positive energy pulse must overcompensate the negative energy pulse by an amount which is a monotonically increasing function of the pulse separation. In the present paper we prove the conjecture for massless quantized scalar fields in two and four-dimensional flat spacetime, and show that it is implied by the quantum inequalities.Comment: 17 pages, Latex, 3 figures, uses eps