Cohomology of Banach algebras of operators and geometry of Banach spaces.

In the paper we give an exposition of the major results concerning the relation between first order cohomology of Banach algebras of operators on a Banach space with coefficients in specified modules and the geometry of the underlying Banach space. In particular we shall compare the properties weak amenability and amenability for Banach algebras A(X), the approximable operators on a Banach space X. Whereas amenability is a local property of the Banach space X, weak amenability is often the consequence of properties of large scale geometry.

Modelling the Geometry of the Repeat Unit Cell of Three-Dimensional Weave Architectures,

The three-dimensional (3D) weaving process offers the ability to tailor the mechanical properties via design of the weave architecture. One repeat of the 3D woven fabric is represented by the unit cell. The model accepts basic weaver and material manufacturer data as inputs in order to calculate the geometric characteristics of the 3D woven unit cell. The specific weave architecture manufactured and subsequently modelled had an angle interlock type binding configuration. The modelled result was shown to have a close approximation compared to the experimentally measured values and highlighted the importance of the representation of the binder tow path.

Dependence of spatial coherence of 23.2-23.6-nm radiation on the geometry of a multielement germanium x-ray laser target

The spatial coherence of a nanosecond pulsed germanium collisionally excited x-ray laser is measured experimentally for three target configurations. The diagnostic is based on Young's slit interference fringes with a dispersing element to resolve the 23.2- and 23.6-nm spectral lines. Target configurations include a double-slab target, known as the injector, and geometries in which the injector image is image relayed to seed either an additional single-slab target or a second double-slab target. A special feature of this study is the observation of the change in the apparent source size with angle of refraction across the diverging laser beam. Source sizes derived with a Gaussian source model decrease from 44 mu m for the injector target by a variable factor of as much as 2, according to target configuration, for beams leaving the additional amplifiers after strong refraction in the plasma. (C) 1998 Optical Society of America [S0740-3224(98)00810-8].

The geometry of unstented and stented pig common carotid artery bypass grafts

The long-term success of arterial bypass grafting with autologous saphenous veins is limited by neointimal hyperplasia (NIH), which seemingly develops preferentially at sites where hydrodynamic wall shear is low. Placement of a loose-fitting, porous stent around end-to-end, or end-to-side, autologous saphenous vein grafts on the porcine common carotid artery has been found significantly to reduce NIH, but the mechanism is unclear. In a preliminary study, we implanted autologous saphenous vein grafts bilaterally on the common carotid arteries of pigs, placing a stent around one graft and leaving the contralateral graft unstented. At sacrifice 1 month post implantation, the grafts were pressure fixed in situ and resin casts were made. Unstented graft geometry was highly irregular, with non-uniform dilatation, substantial axial lengthening, curvature, kinking, and possible long-pitch helical distortion. In contrast, stented grafts showed no major dilatation, lengthening or curvature, but there was commonly fine corrugation, occasional slight kinking or narrowing of segments, and possible long-pitch helical distortion. Axial growth of grafts against effectively tethered anastomoses could account for these changes. CFD studies are planned, using 3D MR reconstructions, on the effects of graft geometry on the flow. Abnormality of the flow could favour the development of vascular pathology, including NIH.

Diabetes in the young - a global view and worldwide estimates of numbers of children with type 1 diabetes

This paper describes the methodology, results and limitations of the 2013 International Diabetes Federation (IDF) Atlas (6th edition) estimates of the worldwide numbers of prevalent cases of type 1 diabetes in children (<15 years). The majority of relevant information in the published literature is in the form of incidence rates derived from registers of newly diagnosed cases. Studies were graded on quality criteria and, if no information was available in the published literature, extrapolation was used to assign a country the rate from an adjacent country with similar characteristics. Prevalence rates were then derived from these incidence rates and applied to United Nations 2012 Revision population estimates for 2013 for each country to obtain estimates of the number of prevalent cases. Data availability was highest for the countries in Europe (76%) and lowest for the countries in sub-Saharan Africa (8%). The prevalence estimates indicate that there are almost 500,000 children aged under 15 years with type 1 diabetes worldwide, the largest numbers being in Europe (129,000) and North America (108,700). Countries with the highest estimated numbers of new cases annually were the United States (13,000), India (10,900) and Brazil (5000). Compared with the prevalence estimates made in previous editions of the IDF Diabetes Atlas, the numbers have increased in most of the IDF Regions, often reflecting the incidence rate increases that have been well-documented in many countries. Monogenic diabetes is increasingly being recognised among those with clinical features of type 1 or type 2 diabetes as genetic studies become available, but population-based data on incidence and prevalence show wide variation due to lack of standardisation in the studies. Similarly, studies on type 2 diabetes in childhood suggest increased incidence and prevalence in many countries, especially in Indigenous peoples and ethnic minorities, but detailed population-based studies remain limited.

Self-consistent geometry in the computation of the vibrational spectra of molecules

An exact and general approach to study molecular vibrations is provided by the Watson Hamiltonian. Within this framework, it is customary to omit the contribution of the terms with the vibrational angular momentum and the Watson term, especially for the study of large systems. We discover that this omission leads to results which depend on the choice of the reference structure. The self-consistent solution proposed here yields a geometry that coincides with the quantum averaged geometry of the Watson Hamiltonian and appears to be a promising way for the computation of the vibrational spectra of strongly anharmonic systems.

Design of a thick-walled screen for flow equalization in microstructured reactors

A systematic computational fluid dynamics (CFD) approach has been applied to design the geometry of the channels of a three-dimensional (thick-walled) screen comprising upstream and downstream sets of elongated channels positioned at an angle of 90 degrees with respect to each other. Such a geometry of the thick-wall screen can effectively drop the ratio of the maximum flow velocity to mean flow velocity below 1.005 in a downstream microstructured reactor at low Reynolds numbers. In this approach the problem of flow equalization reduces to that of flow equalization in the first and second downstream channels of the thick-walled screen. In turn, this requires flow equalization in the corresponding cross-sections of the upstream channels. The validity of the proposed design method was assessed through a case study. The effect of different design parameters on the flow non-uniformity in the downstream channels has been established. The design equation is proposed to calculate the optimum values of the screen parameters. The CFD results on flow distribution were experimentally validated by Laser Doppler Anemometry measurements in the range of Reynolds numbers from 6 to 113. The measured flow non-uniformity in the separate reactor channels was below 2%.

A numerical study of trailing edge geometry for low inertia automotive mixed flow turbines

Abstract. Mixed flow turbines can offer improvements over typical radial turbines used in automotive turbochargers, with respect to transient performance and low velocity ratio efficiency. Turbine rotor mass dominates the rotating inertia of the turbocharger’s rotating assembly, and any reductions of mass in the outer radii of the wheel, including the rotor back-disk, can significantly reduce this inertia and improve the acceleration of the assembly. Off-design, low velocity ratio conditions are typified by highly tangential flow at the rotor inlet and a non-zero inlet blade angle is desirable for such operating conditions. This is achievable in a Mixed Flow Turbine without increasing bending stresses within the rotor blade, which is beneficial in high speed and high inlet temperature turbine designs.
This study considers the meridional geometry of Mixed Flow Turbines using a multi-disciplinary study to assess both the structural and aerodynamic performance of each rotor, incorporating both CFD and FEA. Variations of rotor trailing edge were investigated at different operating conditions representing both on- and off-design operation within the constraints of existing hardware geometries. In all cases, the performance is benchmarked against an existing state-of-the-art radial turbocharger turbine with consideration of rotor inertia and its benefit for engine transient performance. The results indicate the influence of these parameters and this report details their benefits with respect to turbocharging a downsized, automotive engine.

A numerical study of automotive turbocharger mixed flow turbine inlet geometry for off design performance

Mixed flow turbines represent a potential solution to the increasing requirement for high pressure, low velocity ratio operation in turbocharger applications. While literature exists for the use of these turbines at such operating conditions, there is a lack of detailed design guidance for defining the basic geometry of the turbine, in particular, the cone angle – the angle at which the inlet of the mixed flow turbine is inclined to the axis. This investigates the effect and interaction of such mixed flow turbine design parameters.
Computational Fluids Dynamics was initially used to investigate the performance of a modern radial turbine to create a baseline for subsequent mixed flow designs. Existing experimental data was used to validate this model.
Using the CFD model, a number of mixed flow turbine designs were investigated. These included studies varying the cone angle and the associated inlet blade angle.
The results of this analysis provide insight into the performance of a mixed flow turbine with respect to cone and inlet blade angle.

Discovery of relict subglacial lakes and their geometry and mechanism of drainage

Recent proxy measurements reveal that subglacial lakes beneath modern ice sheets periodically store and release large volumes of water, providing an important but poorly understood influence on contemporary ice dynamics and mass balance. This is because direct observations of how lake drainage initiates and proceeds are lacking. Here we present physical evidence of the mechanism and geometry of lake drainage from the discovery of relict subglacial lakes formed during the last glaciation in Canada. These palaeo-subglacial lakes comprised shallow (<10 m) lenses of water perched behind ridges orientated transverse to ice flow. We show that lakes periodically drained through channels incised into bed substrate (canals). Canals sometimes trend into eskers that represent the depositional imprint of the last high-magnitude lake outburst. The subglacial lakes and channels are preserved on top of glacial lineations, indicating long-term re-organization of the subglacial drainage system and coupling to ice flow.

Searching for the IRA 'disappeared': Ground-penetrating radar investigation of a churchyard burial site, Northern Ireland

A search for the body of a victim of terrorist abduction and murder was made in a graveyard on the periphery of a major conurbation in Northern Ireland. The area is politically sensitive and the case of high profile. This required non-invasive, completely non-destructive and rapid assessment of the scene. A MALA RAMAC ground-penetrating radar system was used to achieve these objectives. Unprocessed and processed 400MHz data shows the presence of a collapse feature above and around a known 1970s burial with no similar collapse above the suspect location. In the saturated, clay-rich sediments of the site, 200MHz data offered no advantage over 400MHz data. Unprocessed 100MHz data shows a series of multiples in the known burial with no similar features in the suspect location. Processed 100MHz lines defined the shape of the collapse around the known burial to 2m depth, together with the geometry of the platform (1m depth) the gravedigger used in the 1970s to construct the site. In addition, processed 100MHz data showed both the dielectric contrast in and internal reflection geometry of the soil imported above the known grave. Thus the sequence, geometry, difference in infill and infill direction of the grave was reconstructed 30 years after burial. The suspect site showed no evidence of shallow or deep inhumation. Subsequently, the missing person������¢���¯���¿���½���¯���¿���½s body was found some distance from this site, vindicating the results and interpretation from ground-penetrating radar. The acquisition, processing, collapse feature and sequence stratigraphic interpretation of the known burial and empty (suspect) burial site may be useful proxies for other, similar investigations. GPR was used to evaluate this site within 3 hours of the survey commencing, using unprocessed data. An additional day of processing established that the suspect body did not reside here, which was counter to police and community intelligence.

The extreme-ultraviolet structure and properties of a newly emerged active region

The structure and properties of a newly emerged solar active region (NOAA Active Region 7985) are discussed using the Coronal Diagnostic Spectrometer (CDS) and the Extreme- Ultraviolet Imaging Telescope (EIT) on board the Solar and Heliospheric Observatory. CDS obtained high-resolution EUV spectra in the 308-381 Angstrom and 513-633 Angstrom wavelength ranges, while EIT recorded full-disk EUV images in the He II (304 Angstrom), Fe IX/X (171 Angstrom), Fe xii (195 Angstrom), and Fe XV (284 Angstrom) bandpasses. Electron density measurements from Si rx, Si X, Fe xii, Fe XIII, and Fe xiv line ratios indicate that the region consists of a central high- density core with peak densities of the order of 1.2 x 10(10) cm(-3), which decrease monotonically to similar to5.0 X 10(8) cm(-3) at the active region boundary. The derived electron densities also vary systematically with temperature. Electron pressures as a function of both active region position and temperature were estimated using the derived electron densities and ion formation temperatures, and the constant pressure assumption was found to be an unrealistic simplification. Indeed, the active region is found to have a high-pressure core (1.3 x 10(16) cm(-3) K) that falls to 6.0 x 10(14) cm(-3) K just outside the region. CDS line ratios from different ionization stages of iron, specifically Fe xvi (335.4 Angstrom) and Fe xiv (334.4 Angstrom), were used to diagnose plasma temperatures within the active region. Using this method, peak temperatures of 2.1 x 10(6) K were identified. This is in good agreement with electron temperatures derived using EIT filter ratios and the two-temperature model of Zhang et al. The high- temperature emission is confined to the active region core, while emission from cooler (1-1.6) x 10(6) K lines originates in a system of loops visible in EIT 171 and 195 X images. Finally, the three-dimensional geometry of the active region is investigated using potential field extrapolations from a Kitt Peak magnetogram. The combination of EUV and magnetic field extrapolations extends the "core-halo" picture of active region structure to one in which the core is composed of a number of compact coronal loops that confine the hot, dense, high- pressure core plasma while the halo emission emerges from a system of cooler and more extended loops.