Quantum Chromatic Numbers via Operator Systems

We define several new types of quantum chromatic numbers of a graph and characterize them in terms of operator system tensor products. We establish inequalities between these chromatic numbers and other parameters of graphs studied in the literature and exhibit a link between them and non-signalling correlation boxes.

Estimating quantum chromatic numbers

We develop further the new versions of quantum chromatic numbers of graphs introduced by the first and fourth authors. We prove that the problem of computation of the commuting quantum chromatic number of a graph is solvable by an SDP algorithm and describe an hierarchy of variants of the commuting quantum chromatic number which converge to it. We introduce the tracial rank of a graph, a parameter that gives a lower bound for the commuting quantum chromatic number and parallels the projective rank, and prove that it is multiplicative. We describe the tracial rank, the projective rank and the fractional chromatic numbers in a unified manner that clarifies their connection with the commuting quantum chromatic number, the quantum chromatic number and the classical chromatic number, respectively. Finally, we present a new SDP algorithm that yields a parameter larger than the Lovász number and is yet a lower bound for the tracial rank of the graph. We determine the precise value of the tracial rank of an odd cycle.

Experimental Investigation into the Free-Air Cooling of Air-Cooled Cylinders

This paper describes an experimental investigation into the surface heat transfer coefficient of finned metal cylinders in a free air stream. Eight cast aluminium alloy cylinders were tested with four different fin pitches and five different fin lengths. The cylinders and their fins were designed to be representative of those found on a motorcycle engine. Each electrically heated cylinder was mounted in a wind tunnel and subjected to a range of air speeds between 2 and 20 m/s. The surface heat transfer coefficient, h, was found primarily to be a function of the air speed and the fin separation, with fin length having a lesser effect. The coefficient increases with airspeed and as the fins are separated or shortened. It was also noted that a limiting value of coefficient exists, influenced only by airspeed. Above the limiting value the surface heat transfer could not be increased by further separation of the fins or reduction in their length.

Perspectives for quantum state engineering via high nonlinearity in a double-EIT regime

We analyse the possibilities for quantum state engineering offered by a model for Kerr-type nonlinearity enhanced by electromagnetically induced transparency (EIT), which was recently proposed by Petrosyan and Kurizki [2002, Phys. Rev. A, 65, 33833]. We go beyond the semiclassical treatment and derive a quantum version of the model with both a full Hamiltonian approach and an analysis in terms of dressed states. The preparation of an entangled coherent state via a cross-phase modulation effect is demonstrated. We briefly show that the violation of locality for such an entangled coherent state is robust against low detection efficiency. Finally, we investigate the possibility of a bi-chromatic photon blockade realized via the interaction of a low density beam of atoms with a bi-modal electromagnetic cavity which is externally driven. We show the effectiveness of the blockade effect even when more than a single atom is inside the cavity. The possibility to control two different cavity modes allows some insights into the generation of an entangled state of cavity modes.

A new look at the pulsating DB white dwarf GD 358: Line-of-sight velocity measurements and constraints on model atmospheres

We report on our findings of the bright, pulsating, helium atmosphere white dwarf GD 358, based on time-resolved optical spectrophotometry. We identify 5 real pulsation modes and at least 6 combination modes at frequencies consistent with those found in previous observations. The measured Doppler shifts from our spectra show variations with amplitudes of up to 5.5 km s-1 at the frequencies inferred from the flux variations. We conclude that these are variations in the line-of-sight velocities associated with the pulsational motion. We use the observed flux and velocity amplitudes and phases to test theoretical predictions within the convective driving framework, and compare these with similar observations of the hydrogen atmosphere white dwarf pulsators (DAVs). The wavelength dependence of the fractional pulsation amplitudes (chromatic amplitudes) allows us to conclude that all five real modes share the same spherical degree, most likely, l=1. This is consistent with previous identifications based solely on photometry. We find that a high signal-to-noise mean spectrum on its own is not enough to determine the atmospheric parameters and that there are small but significant discrepancies between the observations and model atmospheres. The source of these remains to be identified. While we infer Teff =24 kK and log g ~ 8.0 from the mean spectrum, the chromatic amplitudes, which are a measure of the derivative of the flux with respect to the temperature, unambiguously favour a higher effective temperature, 27 kK, which is more in line with independent determinations from ultra-violet spectra.

Experimental investigation into the temperature and heat transfer distribution around air-cooled cylinders

This paper describes an experimental investigation into the surface heat transfer coefficient of finned metal cylinders in a free air stream. Ten cylinders were tested with four different fin pitches and five different fin lengths. The cylinders and their fins were designed to be representative of those found on a motorcycle engine with an external cylinder diameter of 100 mm and fin lengths of 10 to 50 mm. The fins of each cylinder were gravity die cast in aluminum allow. Each cylinder was electrically heated and mounted in a wind tunnel which subjected it to a range of air speeds between 2 and 20 m/s. The surface heat transfer coefficient, h, was found primarily to be a function of the air speed and the fin separation, with fin length having a lesser effect. In addition to the determination of an overall heat transfer coefficient, the distribution of cooling around the circumference of each cylinder was also studied. Not surprisingly, the cooling was found to be greatest on the front of the cylinder, which was the side first impinged by the air stream. The cooling of the rear of the cylinder was better than might have been expected and this is quantified.

Development and validation of a fast monoclonal based disequilibrium enzyme-linked immunosorbent assay for the detection of triphenylmethane dyes and their metabolites in fish

Malachite Green (MG), Crystal Violet (CV) and Brilliant Green (BC) are antibacterial, antifungal and antiparasitic agents that have been used for treatment and prevention of diseases in fish. These dyes are metabolized into reduced leuco forms (LMG, LCV, LBG) that can be present in fish muscles for a long period. Due to the carcinogenic properties they are banned for use in fish for human consumption in many countries including the European Union and the United States. HPLC and LC-MS techniques are generally used for the detection of these compounds and their metabolites in fish. This study presents the development of a fast enzyme-linked immunosorbent assay (ELISA) method as an alternative for screening purposes. A first monoclonal cell line producing antibodies to MG was generated using a hybridoma technique. The antibody had good cross-reactivates with related chromatic forms of triphenylmethane dyes such as CV, BC, Methyl Green, Methyl Violet and Victoria Blue R. The monoclonal antibody (mAb) was used to develop a fast (20 min) disequilibrium ELISA screening method for the detection of triphenylmethanes in fish. By introducing an oxidation step with 2,3-dichloro-5,6-dicyano-1,4-benzoquinone (DDQ) during sample extraction the assay was also used to detect the presence of the reduced metabolites of triphenylmethanes. The detection capability of the assay was 1 ng g(-1) for MG, LMG, CV, LCV and BC which was below the minimum required performance limit (MRPL) for the detection method of total MG (sum of MG and LMG) set by the Commission Decision 2004/25/EC (2 ng g(-1)). The mean recoveries for fish samples spiked at 0.5 MRPL and MRPL levels with MG and LMG were between 74.9 and 117.0% and inter- and intra-assay coefficients of variation between 4.7 and 25.7%. The validated method allows the analysis of a batch of 20 samples in two to three hours. Additionally, this procedure is substantially faster than other ELISA methods developed for MG/LMG thus far. The stable and efficient monoclonal cell line obtained is an unlimited source of sensitive and specific antibody to MG and other triphenylmethanes. (C) 2011 Elsevier B.V. All rights reserved.

A puzzling periodicity in the pulsating DA white dwarf G 117-B15A

We present time-resolved optical spectrophotometry of the pulsating hydrogen atmosphere (DA) white dwarf G 117-B15A. We find three periodicities in the pulsation spectrum (215 s, 272 s, and 304 s) all of which have been found in earlier studies. By comparing the fractional wavelength dependence of the pulsation amplitudes ( chromatic amplitudes) with models, we confirm a previous report that the strongest mode, at 215 s, has l = 1. The chromatic amplitude for the 272 s mode is very puzzling, showing an increase in fractional amplitude with wavelength that cannot be reproduced by the models for any ` at optical wavelengths. Based on archival HST data, we show that while the behaviour of the 215 s mode at ultra-violet wavelengths is as expected from models, the weird behaviour of the 272 s periodicity is not restricted to optical wavelengths in that it fails to show the expected increase in fractional amplitude towards shorter wavelengths. We discuss possible causes for the discrepancies found for the 272 s variation, but find that all are lacking, and conclude that the nature of this periodicity remains unclear.

The hydrodynamics of small seabed mounted bottom hinged wave energy converters in shallow water:PhD thesis

This thesis investigates the hydrodynamics of a small, seabed mounted, bottom hinged, wave energy converter in shallow water. The Oscillating Wave Surge Converter is a pitching flap-type device which is located in 10-15m of water to take advantage of the amplification of horizontal water particle motion in shallow water. A conceptual model of the hydrodynamics of the device has been formulated and shows that, as the motion of the flap is highly constrained, the magnitude of the force applied to the flap by the wave is strongly linked to the power absorption.

An extensive set of experiments has been carried out in the wave tank at Queen’s University at both 40th and 20th scales. The experiments have included testing in realistic sea states to estimate device performance as well as fundamental tests using small amplitude monochromatic waves to determine the force applied to the flap by the waves. The results from the physical modelling programme have been used in conjunction with numerical data from WAMIT to validate the conceptual model.

The work finds that tuning the OWSC to the incident wave periods is problematic and only results in a marginal increase in power capture. It is also found that the addition of larger diameter rounds to the edges of the flap reduces viscous losses and has a greater effect on the performance of the device than tuning. As wave force is the primary driver of device performance it is shown that the flap should fill the water column and should pierce the water surface to reduce losses due to wave overtopping.

With the water depth fixed at approximately 10m it is shown that the width of the flap has the greatest impact on the magnitude of wave force, and thus device performance. An 18m wide flap is shown to have twice the absorption efficiency of a 6m wide flap and captures 6 times the power. However, the increase in power capture with device width is not limitless and a 24m wide flap is found to be affected by two-dimensional hydrodynamics which reduces its performance per unit width, especially in sea states with short periods. It is also shown that as the width increases the performance gains associated with the addition of the end effectors reduces. Furthermore, it is shown that as the flap width increases the natural pitching period of the flap increases, thus detuning the flap further from the wave periods of interest for wave energy conversion.

The effect of waves approaching the flap from an oblique angle is also investigated and the power capture is found to decrease with the cosine squared of the encounter angle. The characteristic of the damping applied by the power take off system is found to have a significant effect on the power capture of the device, with constant damping producing between 20% and 30% less power than quadratic damping. Furthermore, it is found that applying a higher level of damping, or a damping bias, to the flap as it pitches towards the beach increases the power capture by 10%.

A further set of experiments has been undertaken in a case study used to predict the power capture of a prototype of the OWSC concept. The device, called the Oyster Demonstrator, has been developed by Aquamarine Power Ltd. and is to be installed at the European Marine Energy Centre, Scotland, in 2009.

The work concludes that OWSC is a viable wave energy converter and absorption efficiencies of up 75% have been measured. It is found that to maximise power absorption the flap should be approximately 20m wide with large diameter rounded edges, having its pivot close to the seabed and its top edge piercing the water surface.

A compact broadband ion beam focusing device based on laser-driven megagauss thermoelectric magnetic fields

Ultra-intense lasers can nowadays routinely accelerate kiloampere ion beams. These unique sources of particle beams could impact many societal (e.g., proton-therapy or fuel recycling) and fundamental (e.g., neutron probing) domains. However, this requires overcoming the beam angular divergence at the source. This has been attempted, either with large-scale conventional setups or with compact plasma techniques that however have the restriction of short (<1 mm) focusing distances or a chromatic behavior. Here, we show that exploiting laser-triggered, long-lasting (>50 ps), thermoelectric multi-megagauss surface magnetic (B)-fields, compact capturing, and focusing of a diverging laser-driven multi-MeV ion beam can be achieved over a wide range of ion energies in the limit of a 5° acceptance angle.

Dynamic control of laser driven proton beams by exploiting self-generated, ultrashort electromagnetic pulses

As part of the ultrafast charge dynamics initiated by high intensity laser irradiations of solid targets,high amplitude EM pulses propagate away from the interaction point and are transported along anystalks and wires attached to the target. The propagation of these high amplitude pulses along a thinwire connected to a laser irradiated target was diagnosed via the proton radiography technique,measuring a pulse duration of 20 ps and a pulse velocity close to the speed of light. The strongelectric field associated with the EM pulse can be exploited for controlling dynamically the protonbeams produced from a laser-driven source. Chromatic divergence control of broadband laser drivenprotons (upto 75% reduction in divergence of >5 MeV protons) was obtained by winding the supportingwire around the proton beam axis to create a helical coil structure. In addition to providingfocussing and energy selection, the technique has the potential to post-accelerate the transiting protonsby the longitudinal component of the curved electric field lines produced by the helical coil lens.

LOTUS: A low cost, ultraviolet spectrograph

We describe the design, construction and commissioning of LOTUS; a simple, low-cost long-slit spectrograph for the Liverpool Telescope. The design is optimized for near-UV and visible wavelengths and uses all transmitting optics. It exploits the instrument focal plane field curvature to partially correct axial chromatic aberration. A stepped slit provides narrow (2.5x95 arcsec) and wide (5x25 arcsec) options that are optimized for spectral resolution and flux calibration respectively. On sky testing shows a wavelength range of 3200-6300 Angstroms with a peak system throughput (including detector quantum efficiency) of 15 per cent and wavelength dependant spectral resolution of R=225-430. By repeated observations of the symbiotic emission line star AG Peg we demonstrate the wavelength stability of the system is less than 2 Angstroms rms and is limited by the positioning of the object in the slit. The spectrograph is now in routine operation monitoring the activity of comet 67P/Churyumov-Gerasimenko during its current post-perihelion apparition.