Exponential asymptotics and gravity waves

The problem of irrotational inviscid incompressible free-surface flow is examined in the limit of small Froude number. Since this is a singular perturbation, singularities in the flow field (or its analytic continuation) such as stagnation points, or corners in submerged objects or on rough beds, lead to a divergent asymptotic expansion, with associated Stokes lines. Recent techniques in exponential asymptotics are employed to observe the switching on of exponentially small gravity waves across these Stokes lines. As a concrete example, the flow over a step is considered. It is found that there are three possible parameter regimes, depending on whether the dimensionless step height is small, of the same order, or large compared to the square of the Froude number. Asymptotic results are derived in each case, and compared with numerical simulations of the full nonlinear problem. The agreement is remarkably good, even at relatively large Froude number. This is in contrast to the alternative analytical theory of small step height, which is accurate only for very small steps

Large-amplitude capillary waves in electrified fluid sheets

Large-amplitude capillary waves on fluid sheets are computed in the presence of a uniform electric field acting in a direction parallel to the undisturbed configuration. The fluid is taken to be inviscid, incompressible and non-conducting. Travelling waves of arbitrary amplitudes and wavelengths are calculated and the effect of the electric field is studied. The solutions found generalize the exact symmetric solutions of Kinnersley (1976) to include electric fields, for which no exact solutions have been found. Long-wave nonlinear waves are also constructed using asymptotic methods. The asymptotic solutions are compared with the full computations as the wavelength increases, and agreement is found to be excellent

Trapped waves between submerged obstacles

Free-surface flows past submerged obstacles in a channel are considered. The fluid is assumed to be inviscid and incompressible and the flow to be irrotational. In previous work involving a single obstacle (Dias & Vanden-Broeck 2002), new solutions called ‘generalized hydraulic falls’ were found. These solutions are characterized by a supercritical flow on one side of the obstacle and a train of waves on the other. However, in the case of a single submerged object, the generalized hydraulic falls are unphysical because the waves do not satisfy the radiation condition. In this paper new solutions for the flow past two obstacles of arbitrary shape are computed. These solutions are characterized by a train of waves ‘trapped’ between the obstacles. The generalized hydraulic falls are shown to describe locally the flow over one of the two obstacles when the distance between the two obstacles is large

Some Remarks on IBNR Evaluation Techniques

In this short paper we discuss a new methodology for estimating reserves for IBNR (incurred but not reported) claims.

High Redshift HCN Emission: Dense Star-Forming Molecular Gas in IRAS F10214+4724

Hydrogen cyanide emission in the J=1-0 transition has been detected at redshift z=2.2858 in IRAS F10214+4724 using the Green Bank Telescope . This is the second detection of HCN emission at high redshift. The large HCN line luminosity in F10214 is similar to that in the Cloverleaf (z=2.6) and the ultra-luminous infrared galaxies Mrk231 and Arp220. This is also true of the ratio of HCN to CO luminosities. The ratio of far-infrared luminosity to HCN luminosity, an indicator of the star formation rate per solar mass of dense gas, follows the correlation found for normal spirals and infrared luminous starburst galaxies. F10214 clearly contains a starburst that contributes, together with its embedded quasar, to its overall infrared luminosity. A new technique for removing spectral baselines in the search for weak, broad emission lines is presented.Comment: 9 pages, 2 figures; accepted ApJ(Letters

Biodiversity's big wet secret: the global distribution of marine biological records reveals chronic under-exploration of the deep pelagic ocean

Background: Understanding the distribution of marine biodiversity is a crucial first step towards the effective and sustainable management of marine ecosystems. Recent efforts to collate location records from marine surveys enable us to assemble a global picture of recorded marine biodiversity. They also effectively highlight gaps in our knowledge of particular marine regions. In particular, the deep pelagic ocean - the largest biome on Earth - is chronically under-represented in global databases of marine biodiversity. Methodology/Principal Findings: We use data from the Ocean Biogeographic Information System to plot the position in the water column of ca 7 million records of marine species occurrences. Records from relatively shallow waters dominate this global picture of recorded marine biodiversity. In addition, standardising the number of records from regions of the ocean differing in depth reveals that regardless of ocean depth, most records come either from surface waters or the sea bed. Midwater biodiversity is drastically under-represented. Conclusions/Significance: The deep pelagic ocean is the largest habitat by volume on Earth, yet it remains biodiversity's big wet secret, as it is hugely under-represented in global databases of marine biological records. Given both its value in the provision of a range of ecosystem services, and its vulnerability to threats including overfishing and climate change, there is a pressing need to increase our knowledge of Earth's largest ecosystem

Long-term use of motion-based video games in care home settings

Recent research suggests that motion-based video games have the potential to provide both mental and physical stimulation for older adults in residential care. However, little research has explored the practical challenges and opportunities that arise from integrating these games within existing schedules of activities in these contexts. In our work, we report on a qualitative enquiry that was conducted over a three month period at two long-term care facilities. Findings suggest that older adults enjoyed playing video games, and that games can be a valuable means of re-introducing challenge in late life, but that the impact of age-related changes and impairment can influence people’s ability to engage with games in a group setting. We outline core challenges in the design for care context and discuss implications of our work regarding the suitability of games as a self-directed leisure activity