Accurate series solutions for gravity-driven Stokes waves

In the past, high order series expansion techniques have been used to study the nonlinear equations that govern the form of periodic Stokes waves moving steadily on the surface of an inviscid fluid. In the present study, two such series solutions are recomputed using exact arithmetic, eliminating any loss of accuracy due to accumulation of round-off error, allowing a much greater number of terms to be found with confidence. It is shown that higher order behaviour of series generated by the solution casts doubt over arguments that rely on estimating the series’ radius of convergence. Further, the exact nature of the series is used to shed light on the unusual nature of convergence of higher order Pade approximants near the highest wave. Finally, it is concluded that, provided exact values are used in the series, these Pade approximants prove very effective in successfully predicting three turning points in both the dispersion relation and the total energy.

The Eat Smart Study : a randomised controlled trial of a reduced carbohydrate versus a low fat diet for weight loss in obese adolescents

Background Despite the recognition of obesity in young people as a key health issue, there is limited evidence to inform health professionals regarding the most appropriate treatment options. The Eat Smart study aims to contribute to the knowledge base of effective dietary strategies for the clinical management of the obese adolescent and examine the cardiometablic effects of a reduced carbohydrate diet versus a low fat diet. Methods and design Eat Smart is a randomised controlled trial and aims to recruit 100 adolescents over a 2½ year period. Families will be invited to participate following referral by their health professional who has recommended weight management. Participants will be overweight as defined by a body mass index (BMI) greater than the 90th percentile, using CDC 2000 growth charts. An accredited 6-week psychological life skills program ‘FRIENDS for Life’, which is designed to provide behaviour change and coping skills will be undertaken prior to volunteers being randomised to group. The intervention arms include a structured reduced carbohydrate or a structured low fat dietary program based on an individualised energy prescription. The intervention will involve a series of dietetic appointments over 24 weeks. The control group will commence the dietary program of their choice after a 12 week period. Outcome measures will be assessed at baseline, week 12 and week 24. The primary outcome measure will be change in BMI z-score. A range of secondary outcome measures including body composition, lipid fractions, inflammatory markers, social and psychological measures will be measured. Discussion The chronic and difficult nature of treating the obese adolescent is increasingly recognised by clinicians and has highlighted the need for research aimed at providing effective intervention strategies, particularly for use in the tertiary setting. A structured reduced carbohydrate approach may provide a dietary pattern that some families will find more sustainable and effective than the conventional low fat dietary approach currently advocated. This study aims to investigate the acceptability and effectiveness of a structured reduced dietary carbohydrate intervention and will compare the outcomes of this approach with a structured low fat eating plan. Trial Registration: The protocol for this study is registered with the International Clinical Trials Registry (ISRCTN49438757).

Persons with age-related maculopathy risk genotypes and clinically normal eyes have reduced mesopic vision

PURPOSE: To determine if participants with normal visual acuity, no ophthalmoscopically signs of age-related maculopathy (ARM) in both eyes and who are carriers of the CFH, LOC387715 and HRTA1 high-risk genotypes (“gene-positive”) have impaired rod- and cone-mediated mesopic visual function compared to persons who do not carry the risk genotypes (“gene-negative”).---------- METHODS: Fifty-three Caucasian study participants (mean 55.8 ± 6.1) were genotyped for CFH, LOC387715/ARMS2 and HRTA1 polymorphisms. We genotyped single nucleotide polymorphisms (SNPs) in the CFH (rs380390), LOC387715/ARMS2 (rs10490924) and HTRA1 (rs11200638) genes using Applied Biosystems optimised TaqMan assays. We determined the critical fusion frequency (CFF) mediated by cones alone (Long, Middle and Short wavelength sensitive cones; LMS) and by the combined activities of cones and rods (LMSR). The stimuli were generated using a 4-primary photostimulator that provides independent control of the photoreceptor excitation under mesopic light levels. Visual function was further assessed using standard clinical tests, flicker perimetry and microperimetry.---------- RESULTS: The mesopic CFF mediated by rods and cones (LMSR) was significantly reduced in gene-positive compared to gene-negative participants after correction for age (p=0.03). Cone-mediated CFF (LMS) was not significantly different between gene-positive and -negative participants. There were no significant associations between flicker perimetry and microperimetry and genotype.---------- CONCLUSIONS: This is the first study to relate ARM risk genotypes with mesopic visual function in clinically normal persons. These preliminary results could become of clinical importance as mesopic vision may be used to document sub-clinical retinal changes in persons with risk genotypes and to determine whether those persons progress into manifest disease.

Free surface flow into a horizontal slot with zero gravity

The two-dimensional free surface flow of a finite-depth fluid into a horizontal slot is considered. For this study, the effects of viscosity and gravity are ignored. A generalised Schwarz-Christoffel mapping is used to formulate the problem in terms of a linear integral equation, which is solved exactly with the use of a Fourier transform. The resulting free surface profile is given explicitly in closed-form.

Effects of reduced contrast on the perception and control of speed when driving

Misperception of speed under low-contrast conditions has been identified as a possible contributor to motor vehicle crashes in fog. To test this hypothesis, we investigated the effects of reduced contrast on drivers’ perception and control of speed while driving under real-world conditions. Fourteen participants drove around a 2.85 km closed road course under three visual conditions: clear view and with two levels of reduced contrast created by diffusing filters on the windscreen and side windows. Three dependent measures were obtained, without view of the speedometer, on separate laps around the road course: verbal estimates of speed; adjustment of speed to instructed levels (25 to 70 km h-1); and estimation of minimum stopping distance. The results showed that drivers traveled more slowly under low-contrast conditions. Reduced contrast had little or no effect on either verbal judgments of speed or estimates of minimum stopping distance. Speed adjustments were significantly slower under low-contrast than clear conditions, indicating that, contrary to studies of object motion, drivers perceived themselves to be traveling faster under conditions of reduced contrast. Under real-world driving conditions, drivers’ ability to perceive and control their speed was not adversely affected by large variations in the contrast of their surroundings. These findings suggest that perceptions of self-motion and object motion involve neural processes that are differentially affected by variations in stimulus contrast as encountered in fog.

Higher-order spectral analysis of nonlinear ocean surface gravity waves

Higher-order spectral analysis is used to detect the presence of secondary and tertiary forced waves associated with the nonlinearity of energetic swell observed in 8- and 13-m water depths. Higher-order spectral analysis techniques are first described and then applied to the field data, followed by a summary of the results.