A Simple Method for Computing Singular or Nearly Singular Integrals on Closed Surfaces

We present a simple, accurate method for computing singular or nearly singular integrals on a smooth, closed surface, such as layer potentials for harmonic functions evaluated at points on or near the surface. The integral is computed with a regularized kernel and corrections are added for regularization and discretization, which are found from analysis near the singular point. The surface integrals are computed from a new quadrature rule using surface points which project onto grid points in coordinate planes. The method does not require coordinate charts on the surface or special treatment of the singularity other than the corrections. The accuracy is about $O(h^3)$, where $h$ is the spacing in the background grid, uniformly with respect to the point of evaluation, on or near the surface. Improved accuracy is obtained for points on the surface. The treecode of Duan and Krasny for Ewald summation is used to perform sums. Numerical examples are presented with a variety of surfaces.Comment: to appear in Commun. Comput. Phy

A Qualitative Investigation Into the Impact of the Basketball Learning Intervention Programme (BLIP) on Disengaged Secondary School Students in the United Kingdom

This paper will evaluate the longitudinal effects of a basketball based intervention programme that targeted ten disengaged male secondary school students at a school in the Kent, England. The programme aimed to improve the behaviour and academic performance of the participants through a weekly intervention carried out by an external basketball player and coach providing academic support, mentoring and specially designed basketball sessions. Sports interventions have been deemed to provide a positive short-term impact on young people. However, researchers have identified the need for a longitudinal approach in order to examine the effects of such interventions post involvement as supported. This study involved five former Basketball Learning Intervention Programme (BLIP) members (with a mean age of 16.4 SD± 0.55 years) that were interviewed using semi-structured interview approach, 12 months after completing the intervention. Interpretative Phenomenological Analysis (IPA) revealed four superordinate and eleven subordinate themes. The four superordinate themes were; ‘baseline behaviours pre-intervention’, ‘immediate outcomes of the BLIP’, ‘impact of the coach’ and ‘long standing transferable outcomes’. The results revealed an immediate impact in comparison to the baseline behaviours of the participants pre-intervention. The data suggested that one of the most effective aspects of the programme was the positive impact of the coach on the participants. More importantly, this is the only study to report long-term improvements amongst the participants in terms of behaviour and academics as a result of engagement in a sports based intervention

Hot methane line lists for exoplanet and brown dwarf atmospheres

We present comprehensive experimental line lists of methane (CH4) at high temperatures obtained by recording Fourier transform infrared emission spectra. Calibrated line lists are presented for the temperatures 300 - 1400 degC at twelve 100 degC intervals spanning the 960 - 5000 cm-1 (2.0 - 10.4 microns) region of the infrared. This range encompasses the dyad, pentad and octad regions, i.e., all fundamental vibrational modes along with a number of combination, overtone and hot bands. Using our CH4 spectra, we have estimated empirical lower state energies (Elow in cm-1) and our values have been incorporated into the line lists along with line positions (cm-1) and calibrated line intensities (S' in cm molecule-1). We expect our hot CH4 line lists to find direct application in the modeling of planetary atmospheres and brown dwarfs.Comment: Supplementary material is provided via the Astrophysical Journal referenc

Nerve excitability changes in critical illness polyneuropathy

Patients in intensive care units frequently suffer muscle weakness and atrophy due to critical illness polyneuropathy (CIP), an axonal neuropathy associated with systemic inflammatory response syndrome and multiple organ failure. CIP is a frequent and serious complication of intensive care that delays weaning from mechanical ventilation and increases mortality. The pathogenesis of CIP is not well understood and no specific therapy is available. The aim of this project was to use nerve excitability testing to investigate the changes in axonal membrane properties occurring in CIP. Ten patients (aged 37-76 years; 7 males, 3 females) were studied with electrophysiologically proven CIP. The median nerve was stimulated at the wrist and compound action potentials were recorded from abductor pollicis brevis muscle. Strength-duration time constant, threshold electrotonus, current-threshold relationship and recovery cycle (refractoriness, superexcitability and late subexcitability) were recorded using a recently described protocol. In eight patients a follow-up investigation was performed. All patients underwent clinical examination and laboratory investigations. Compared with age-matched normal controls (20 subjects; aged 38-79 years; 7 males, 13 females), CIP patients exhibited reduced superexcitability at 7 ms, from −22.3 ± 1.6% to −7.6 ± 3.1% (mean ± SE, P ≈ 0.0001) and increased accommodation to depolarizing (P < 0.01) and hyperpolarizing currents (P < 0.01), indicating membrane depolarization. Superexcitability was reduced both in patients with renal failure and without renal failure. In the former, superexcitability correlated with serum potassium (R = 0.88), and late subexcitability was also reduced (as also occurs owing to hyperkalaemia in patients with chronic renal failure). In patients without renal failure, late subexcitability was normal, and the signs of membrane depolarization correlated with raised serum bicarbonate and base excess, indicating compensated respiratory acidosis. It is inferred that motor axons in these CIP patients are depolarized, in part because of raised extracellular potassium, and in part because of hypoperfusion. The chronic membrane depolarization may contribute to the development of neuropath

On the global well-posedness of a class of Boussinesq- Navier-Stokes systems

In this paper we consider the following 2D Boussinesq-Navier-Stokes systems \partial_{t}u+u\cdot\nabla u+\nabla p+ |D|^{\alpha}u &= \theta e_{2} \partial_{t}\theta+u\cdot\nabla \theta+ |D|^{\beta}\theta &=0 \quad with $\textrm{div} u=0$ and $0<\beta<\alpha<1$. When $\frac{6-\sqrt{6}}{4}<\alpha< 1$, $1-\alpha<\beta\leq f(\alpha)$, where $f(\alpha)$ is an explicit function as a technical bound, we prove global well-posedness results for rough initial data.Comment: 23page

Controlling magnetic order and quantum disorder in molecule-based magnets.

We investigate the structural and magnetic properties of two molecule-based magnets synthesized from the same starting components. Their different structural motifs promote contrasting exchange pathways and consequently lead to markedly different magnetic ground states. Through examination of their structural and magnetic properties we show that [Cu(pyz)(H 2 O)(gly) 2 ](ClO 4 ) 2 may be considered a quasi-one-dimensional quantum Heisenberg antiferromagnet whereas the related compound [Cu(pyz)(gly)](ClO 4 ) , which is formed from dimers of antiferromagnetically interacting Cu 2+ spins, remains disordered down to at least 0.03 K in zero field but shows a field-temperature phase diagram reminiscent of that seen in materials showing a Bose-Einstein condensation of magnons