Acoustic trapped modes in a three-dimensional waveguide of slowly varying cross section

In this paper we develop an asymptotic scheme to approximate the trapped mode solutions to the time harmonic wave equation in a three-dimensional waveguide with a smooth but otherwise arbitrarily shaped cross section and a single, slowly varying `bulge', symmetric in the longitudinal direction. Extending the work in Biggs (2012), we first employ a WKBJ-type ansatz to identify the possible quasi-mode solutions which propagate only in the thicker region, and hence find a finite cut-on region of oscillatory behaviour and asymptotic decay elsewhere. The WKBJ expansions are used to identify a turning point between the cut-on and cut-on regions. We note that the expansions are nonuniform in an interior layer centred on this point, and we use the method of matched asymptotic expansions to connect the cut-on and cut-on regions within this layer. The behaviour of the expansions within the interior layer then motivates the construction of a uniformly valid asymptotic expansion. Finally, we use this expansion and the symmetry of the waveguide around the longitudinal centre, x = 0, to extract trapped mode wavenumbers, which are compared with those found using a numerical scheme and seen to be extremely accurate, even to relatively large values of the small parameter.

The value premium and time-varying volatility

Numerous studies have documented the failure of the static and conditional capital asset pricing models to explain the difference in returns between value and growth stocks. This paper examines the post-1963 value premium by employing a model that captures the time-varying total risk of the value-minus-growth portfolios. Our results show that the time-series of value premia is strongly and positively correlated with its volatility. This conclusion is robust to the criterion used to sort stocks into value and growth portfolios and to the country under review (the US and the UK). Our paper is consistent with evidence on the possible role of idiosyncratic risk in explaining equity returns, and also with a separate strand of literature concerning the relative lack of reversibility of value firms' investment decisions.

Postprandial lipid and hormone responses to meals of varying fat contents: modulatory role of lipoprotein lipase?

OBJECTIVE: Substrate and hormone responses to meals of differing fat content were evaluated in normal subjects in order to investigate mechanisms underlying the regulation of postprandial lipoprotein concentration. DESIGN: A randomised cross-over study with three different meals on three occasions. SETTING: Free-living subjects associated with Surrey University. SUBJECTS: Ten male volunteers (aged 18-23 years) were recruited. INTERVENTIONS: Three test meals containing 20, 40 or 80 g fat but identical carbohydrate and protein content were randomly allocated to volunteers. MAJOR OUTCOME MEASURES: Pre- and postprandial blood samples were taken for the analysis of plasma triacylglycerol, non-esterified fatty acids, glucose, immunoreactive insulin and glucose-dependent insulinotrophic polypeptide levels and postheparin lipoprotein lipase activity measurements. RESULTS: Peak triacylglycerol concentrations and lipoprotein lipase activity measurements were significantly higher following the 80 g than the 20 g fat meal (P = 0.009 and P = 0.049 respectively). Areas under the glucose-dependent insulinotrophic polypeptide time-response concentration curves were significantly higher following the 80 g compared with the 20 g fat meal (P = 0.04), but no differences in insulin response to the meals were seen. The 30-360 min decrease in the non-esterified fatty acid concentration was less following the 80 g than the 20 g meal (P = 0.001). CONCLUSIONS: The results suggest that glucose-dependent insulinotrophic polypeptide may mediate increased lipoprotein lipase activity in response to fat-containing meals and may play a role in circulating lipoprotein homeostasis. This mechanism may be overloaded with high fat meals with adverse consequences on circulating triacylglycerol and NEFA concentrations.

Interaction of visual and haptic information in simulated environments: texture perception

This paper describes experiments relating to the perception of the roughness of simulated surfaces via the haptic and visual senses. Subjects used a magnitude estimation technique to judge the roughness of “virtual gratings” presented via a PHANToM haptic interface device, and a standard visual display unit. It was shown that under haptic perception, subjects tended to perceive roughness as decreasing with increased grating period, though this relationship was not always statistically significant. Under visual exploration, the exact relationship between spatial period and perceived roughness was less well defined, though linear regressions provided a reliable approximation to individual subjects’ estimates.

Distortion in distributed virtual environments

This paper proposes a solution to the problems associated with network latency within distributed virtual environments. It begins by discussing the advantages and disadvantages of synchronous and asynchronous distributed models, in the areas of user and object representation and user-to-user interaction. By introducing a hybrid solution, which utilises the concept of a causal surface, the advantages of both synchronous and asynchronous models are combined. Object distortion is a characteristic feature of the hybrid system, and this is proposed as a solution which facilitates dynamic real-time user collaboration. The final section covers implementation details, with reference to a prototype system available from the Internet.