Fredholm determinants and pole-free solutions to the noncommutative Painleve' II equation

We extend the formalism of integrable operators a' la Its-Izergin-Korepin-Slavnov to matrix-valued convolution operators on a semi-infinite interval and to matrix integral operators with a kernel of the form E_1^T(x) E_2(y)/(x+y) thus proving that their resolvent operators can be expressed in terms of solutions of some specific Riemann-Hilbert problems. We also describe some applications, mainly to a noncommutative version of Painleve' II (recently introduced by Retakh and Rubtsov), a related noncommutative equation of Painleve' type. We construct a particular family of solutions of the noncommutative Painleve' II that are pole-free (for real values of the variables) and hence analogous to the Hastings-McLeod solution of (commutative) Painleve' II. Such a solution plays the same role as its commutative counterpart relative to the Tracy-Widom theorem, but for the computation of the Fredholm determinant of a matrix version of the Airy kernel.Comment: 46 pages, no figures (oddly

The Milky Way Bulge: Observed properties and a comparison to external galaxies

The Milky Way bulge offers a unique opportunity to investigate in detail the role that different processes such as dynamical instabilities, hierarchical merging, and dissipational collapse may have played in the history of the Galaxy formation and evolution based on its resolved stellar population properties. Large observation programmes and surveys of the bulge are providing for the first time a look into the global view of the Milky Way bulge that can be compared with the bulges of other galaxies, and be used as a template for detailed comparison with models. The Milky Way has been shown to have a box/peanut (B/P) bulge and recent evidence seems to suggest the presence of an additional spheroidal component. In this review we summarise the global chemical abundances, kinematics and structural properties that allow us to disentangle these multiple components and provide constraints to understand their origin. The investigation of both detailed and global properties of the bulge now provide us with the opportunity to characterise the bulge as observed in models, and to place the mixed component bulge scenario in the general context of external galaxies. When writing this review, we considered the perspectives of researchers working with the Milky Way and researchers working with external galaxies. It is an attempt to approach both communities for a fruitful exchange of ideas.Comment: Review article to appear in "Galactic Bulges", Editors: Laurikainen E., Peletier R., Gadotti D., Springer Publishing. 36 pages, 10 figure

Groundwater cooling at the Royal Festival Hall, London

A pumping and injection trial at the Royal Festival Hall simulated the operation of an open-loop ground sourced cooling system where all abstracted groundwater was returned to the originating aquifer. The trial used two existing boreholes (144 m apart) and existing heat input sources. The trial was conducted over a 4 week period in June–July 2007 and comprised step testing, a constant-rate abstraction–injection test and two tracer tests. The constant-rate test was undertaken over 29 days, at an average flow rate of 8.3 l s−1. The total heat input during the trial was approximately 194.1 MW h. The trial has provided an early indication that comparatively large (i.e. several hundred kilowatts and above) open-loop groundwater heating–cooling systems can be operated effectively in the Chalk aquifer without undue thermal interference, as defined by a measured thermal response in the abstraction borehole. Continued monitoring of water temperatures will confirm whether this remains the case over the longer term. The trial has shown that groundwater can be returned to the confined Chalk aquifer under gravity without undue complication. The trial method was developed in close consultation with the Environment Agency and may serve as a useful guide for subsequent trial

American College of Sports Medicine roundtable. The physiological and health effects of oral creatine supplementation

Creatine (Cr) supplementation has become a common practice among professional, elite, collegiate, amateur, and recreational athletes with the expectation of enhancing exercise performance. Research indicates that Cr supplementation can increase muscle phosphocreatine (PCr) content, but not in all individuals. A high dose of 20 g x d(-1) that is common to many research studies is not necessary, as 3 g x d(-1) will achieve the same increase in PCr given time. Coincident ingestion of carbohydrate with Cr may increase muscle uptake; however, the procedure requires a large amount of carbohydrate. Exercise performance involving short periods of extremely powerful activity can be enhanced, especially during repeated bouts of activity. This is in keeping with the theoretical importance of an elevated PCr content in skeletal muscle. Cr supplementation does not increase maximal isometric strength, the rate of maximal force production, nor aerobic exercise performance. Most of the evidence has been obtained from healthy young adult male subjects with mixed athletic ability and training status. Less research information is available related to the alterations due to age and gender. Cr supplementation leads to weight gain within the first few days, likely due to water retention related to Cr uptake in the muscle. Cr supplementation is associated with an enhanced accrual of strength in strength-training programs, a response not independent from the initial weight gain, but may be related to a greater volume and intensity of training that can be achieved. There is no definitive evidence that Cr supplementation causes gastrointestinal, renal, and/or muscle cramping complications. The potential acute effects of high-dose Cr supplementation on body fluid balance has not been fully investigated, and ingestion of Cr before or during exercise is not recommended. There is evidence that medical use of Cr supplementation is warranted in certain patients (e.g.. neuromuscular disease); future research may establish its potential usefulness in other medical applications. Although Cr supplementation exhibits small but significant physiological and performance changes, the increases in performance are realized during very specific exercise conditions. This suggests that the apparent high expectations for performance enhancement, evident by the extensive use of Cr supplementation, are inordinate

Large amplitude spatial fluctuations in the boundary region of the Bose-Einstein condensate in the Gross-Pitaevskii regime

The Gross-Pitaevskii regime of a Bose-Einstein condensate is investigated using a fully non-linear approach. The confining potential first adopted is that of a linear ramp. An infinite class of new analytical solutions of this linear ramp potential approximation to the Gross-Pitaevskii equation is found which are characterised by pronounced large-amplitude oscillations close to the boundary of the condensate. The limiting case within this class is a nodeless ground state which is known from recent investigations as an extension of the Thomas-Fermi approximation. We have found the energies of the oscillatory states to lie above the ground state energy but recent experimental work, especially on spatially confined superconductors, indicates that such states may be easily occupied and made manifest at finite temperatures. We have also investigated their stability using a Poincare section analysis as well as a linear perturbation approach. Both these techniques demonstrate stability against small perturbations. Finally, we have discussed the relevance of these quasi-one-dimensional solutions in the context of the fully three-dimensional condensates. This has been argued on the basis of numerical work and asymptotic approximations. (C) 2003 Elsevier Science B.V. All rights reserved