An analytical solution to electromagnetically coupled duct flow in MHD

The flow of an electrically conducting fluid in an array of square ducts, separated by arbitrary thickness conducting walls, subject to an applied magnetic field is studied. The analytical solution presented here is valid for thick walls and is based on the homogeneous solution obtained by Shercliff (Math. Proc. Camb. Phil. Soc., vol. 49 (01), 1953, pp. 136-144). Arrangements of ducts arise in a number of applications, most notably in fusion blankets, where liquid metal is used both as coolant and for tritium generation purposes. Analytical solutions, such as those presented here, provide insight into the physics and important benchmarking and validation data for computational magnetohydrodynamics (MHD), as well as providing approximate flow parameters for 1D systems codes. It is well known that arrays of such ducts with conducting walls exhibit varying degrees of coupling, significantly affecting the flow. An important practical example is the so-called Madarame problem (Madarame et al., Fusion Technol., vol. 8, 1985, pp. 264-269). In this work analytical results are derived for the relevant hydrodynamic and magnetic parameters for a single duct with thick walls analogous to the Hunt II case. These results are then extended to an array of such ducts stacked in the direction of the applied magnetic field. It is seen that there is a significant coupling affect, resulting in modifications to pressure drop and velocity profile. In certain circumstances, counter-current flow can occur as a result of the MHD effects, even to the point where the mean flow is reversed. Such phenomena are likely to have significant detrimental effects on both heat and mass transfer in fusion applications. The dependence of this coupling on parameters such as conductivities, wall thickness and Hartmann number is studied

Systematic review and meta-analysis of the growth and rupture rates of small abdominal aortic aneurysms: implications for surveillance intervals and their cost-effectiveness.

BACKGROUND: Small abdominal aortic aneurysms (AAAs; 3.0-5.4 cm in diameter) are usually asymptomatic and managed by regular ultrasound surveillance until they grow to a diameter threshold (commonly 5.5 cm) at which surgical intervention is considered. The choice of appropriate surveillance intervals is governed by the growth and rupture rates of small AAAs, as well as their relative cost-effectiveness. OBJECTIVES: The aim of this series of studies was to inform the evidence base for small AAA surveillance strategies. This was achieved by literature review, collation and analysis of individual patient data, a focus group and health economic modelling. DATA SOURCES: We undertook systematic literature reviews of growth rates and rupture rates of small AAAs. The databases MEDLINE, EMBASE on OvidSP, Cochrane Central Register of Controlled Trials 2009 Issue 4, ClinicalTrials.gov, and controlled-trials.com were searched from inception up until the end of 2009. We also obtained individual data on 15,475 patients from 18 surveillance studies. REVIEW METHODS: Systematic reviews of publications identified 15 studies providing small AAA growth rates, and 14 studies with small AAA rupture rates, up to December 2009 (later updated to September 2012). We developed statistical methods to analyse individual surveillance data, including the effects of patient characteristics, to inform the choice of surveillance intervals and provide inputs for health economic modelling. We updated an existing health economic model of AAA screening to address the cost-effectiveness of different surveillance intervals. RESULTS: In the literature reviews, the mean growth rate was 2.3 mm/year and the reported rupture rates varied between 0 and 1.6 ruptures per 100 person-years. Growth rates increased markedly with aneurysm diameter, but insufficient detail was available to guide surveillance intervals. Based on individual surveillance data, for each 0.5-cm increase in AAA diameter, growth rates increased by about 0.5 mm/year and rupture rates doubled. To control the risk of exceeding 5.5 cm to below 10% in men, on average a 7-year surveillance interval is sufficient for a 3.0-cm aneurysm, whereas an 8-month interval is necessary for a 5.0-cm aneurysm. To control the risk of rupture to below 1%, the corresponding estimated surveillance intervals are 9 years and 17 months. Average growth rates were higher in smokers (by 0.35 mm/year) and lower in patients with diabetes (by 0.51 mm/year). Rupture rates were almost fourfold higher in women than men, doubled in current smokers and increased with higher blood pressure. Increasing the surveillance interval from 1 to 2 years for the smallest aneurysms (3.0-4.4 cm) decreased costs and led to a positive net benefit. For the larger aneurysms (4.5-5.4 cm), increasing surveillance intervals from 3 to 6 months led to equivalent cost-effectiveness. LIMITATIONS: There were no clear reasons why the growth rates varied substantially between studies. Uniform diagnostic criteria for rupture were not available. The long-term cost-effectiveness results may be susceptible to the modelling assumptions made. CONCLUSIONS: Surveillance intervals of several years are clinically acceptable for men with AAAs in the range 3.0-4.0 cm. Intervals of around 1 year are suitable for 4.0-4.9-cm AAAs, whereas intervals of 6 months would be acceptable for 5.0-5.4-cm AAAs. These intervals are longer than those currently employed in the UK AAA screening programmes. Lengthening surveillance intervals for the smallest aneurysms was also shown to be cost-effective. Future work should focus on optimising surveillance intervals for women, studying whether or not the threshold for surgery should depend on patient characteristics, evaluating the usefulness of surveillance for those with aortic diameters of 2.5-2.9 cm, and developing interventions that may reduce the growth or rupture rates of small AAAs. FUNDING: The National Institute for Health Research Health Technology Assessment programme

Four-Dimensional String/String Duality

We present supersymmetric soliton solutions of the four-dimensional heterotic string corresponding to monopoles, strings and domain walls. These solutions admit the $D=10$ interpretation of a fivebrane wrapped around $5$, $4$ or $3$ of the $6$ toroidally compactified dimensions and are arguably exact to all orders in $\alpha'$. The solitonic string solution exhibits an $SL(2,Z)$ {\it strong/weak coupling} duality which however corresponds to an $SL(2,Z)$ {\it target space} duality of the fundamental string.Comment: 14 page

The effect of ethnicity on the vascular responses to cold exposure of the extremities

This is an accepted manuscript of an article published by Springer in European Journal of Applied Physiology on 01/08/2014, available online: https://doi.org/10.1007/s00421-014-2962-2 The accepted version of the publication may differ from the final published version.© 2014, Springer-Verlag Berlin Heidelberg. Purpose: Cold injuries are more prevalent in individuals of African descent (AFD). Therefore, we investigated the effect of extremity cooling on skin blood flow (SkBF) and temperature (Tsk) between ethnic groups.Methods: Thirty males [10 Caucasian (CAU), 10 Asian (ASN), 10 AFD] undertook three tests in 30 °C air whilst digit Tsk and SkBF were measured: (i) vasomotor threshold (VT) test—arm immersed in 35 °C water progressively cooled to 10 °C and rewarmed to 35 °C to identify vasoconstriction and vasodilatation; (ii) cold-induced vasodilatation (CIVD) test—hand immersed in 8 °C water for 30 min followed by spontaneous warming; (iii) cold sensitivity (CS) test—foot immersed in 15 °C water for 2 min followed by spontaneous warming. Cold sensory thresholds of the forearm and finger were also assessed.Results: In the VT test, vasoconstriction and vasodilatation occurred at a warmer finger Tsk in AFD during cooling [21.2 (4.4) vs. 17.0 (3.1) °C, P = 0.034] and warming [22.0 (7.9) vs. 12.1 (4.1) °C, P = 0.002] compared with CAU. In the CIVD test, average SkBF during immersion was greater in CAU [42 (24) %] than ASN [25 (8) %, P = 0.036] and AFD [24 (13) %, P = 0.023]. Following immersion, SkBF was higher and rewarming faster in CAU [3.2 (0.4) °C min−1] compared with AFD [2.5 (0.7) °C min−1, P = 0.037], but neither group differed from ASN [3.0 (0.6) °C min−1]. Responses to the CS test and cold sensory thresholds were similar between groups.Conclusion: AFD experienced a more intense protracted finger vasoconstriction than CAU during hand immersion, whilst ASN experienced an intermediate response. This greater sensitivity to cold may explain why AFD are more susceptible to cold injuries.Published versio

Practical applications of small-angle neutron scattering.

Recent improvements in beam-line accessibility and technology have led to small-angle neutron scattering (SANS) becoming more frequently applied to materials problems. SANS has been used to study the assembly, dispersion, alignment and mixing of nanoscale condensed matter, as well as to characterise the internal structure of organic thin films, porous structures and inclusions within steel. Using time-resolved SANS, growth mechanisms in materials systems and soft matter phase transitions can also be explored. This review is intended for newcomers to SANS as well as experts. Therefore, the basic knowledge required for its use is first summarised. After this introduction, various examples are given of the types of soft and hard matter that have been studied by SANS. The information that can be extracted from the data is highlighted, alongside the methods used to obtain it. In addition to presenting the findings, explanations are provided on how the SANS measurements were optimised, such as the use of contrast variation to highlight specific parts of a structure. Emphasis is placed on the use of complementary techniques to improve data quality (e.g. using other scattering methods) and the accuracy of data analysis (e.g. using microscopy to separately determine shape and size). This is done with a view to providing guidance on how best to design and analyse future SANS measurements on materials not listed below

Role of cyclooxygenase in the vascular response to locally delivered acetylcholine in Caucasian and African descent individuals

This is an accepted manuscript of an article published by Elsevier in Microvascular Research on 17/01/2017, available online: https://doi.org/10.1016/j.mvr.2017.01.005 The accepted version of the publication may differ from the final published version.© 2017 Elsevier Inc. Introduction Individuals of African descent (AFD) are more susceptible to non-freezing cold injury (NFCI) compared with Caucasian individuals (CAU). Vasodilatation to acetylcholine (ACh) is lower in AFD compared with CAU in the non-glabrous foot and finger skin sites; the reason for this is unknown. Prostanoids are responsible, in part, for the vasodilator response to ACh, however it is not known whether the contribution differs between ethnicities. Methods 12 CAU and 12 AFD males received iontophoresis of ACh (1 w/v%) on non-glabrous foot and finger skin sites following placebo and then aspirin (600 mg, single blinded). Aspirin was utilised to inhibit prostanoid production by inhibiting the cyclooxygenase (COX) enzyme. Laser Doppler flowmetry was utilised to measure changes in skin blood flow. Results Not all participants could receive iontophoresis charge due to high skin resistance; these participants were therefore excluded from the analyses. Foot: ACh elicited greater maximal vasodilatation in CAU than AFD following placebo (P = 0.003) and COX inhibition (COXib) (P < 0.001). COXib did not affect blood flow responses in AFD, but caused a reduction in the area under the curve for CAU (P = 0.031). Finger: ACh elicited a greater maximal vasodilatation in CAU than AFD following placebo (P = 0.013) and COXib (P = 0.001). COXib tended to reduce the area under the curve in AFD (P = 0.053), but did not affect CAU. Conclusions CAU have a greater endothelial reactivity than AFD in both foot and finger skin sites irrespective of COXib. It is concluded that the lower ACh-induced vasodilatation in AFD is not due to a compromised COX pathway.Published versio

Cannon-Thurston Maps,i-bounded Geometry and a theorem of McMullen

The notion of i-bounded geometry generalises simultaneously bounded geometry and the geometry of punctured torus Kleinian groups. We show that the limit set of a surface Kleinian group of i-bounded geometry is locally connected by constructing a natural Cannon-Thurston map. This is an exposition of a special case of the main result of arXiv:math/0607509.Comment: v3: 32 pages 3 figure