Wave trapping in a two-dimensional sound-soft or sound-hard acoustic waveguide of slowly-varying width

In this paper we derive novel approximations to trapped waves in a two-dimensional acoustic waveguide whose walls vary slowly along the guide, and at which either Dirichlet (sound-soft) or Neumann (sound-hard) conditions are imposed. The guide contains a single smoothly bulging region of arbitrary amplitude, but is otherwise straight, and the modes are trapped within this localised increase in width. Using a similar approach to that in Rienstra (2003), a WKBJ-type expansion yields an approximate expression for the modes which can be present, which display either propagating or evanescent behaviour; matched asymptotic expansions are then used to derive connection formulae which bridge the gap across the cut-off between propagating and evanescent solutions in a tapering waveguide. A uniform expansion is then determined, and it is shown that appropriate zeros of this expansion correspond to trapped mode wavenumbers; the trapped modes themselves are then approximated by the uniform expansion. Numerical results determined via a standard iterative method are then compared to results of the full linear problem calculated using a spectral method, and the two are shown to be in excellent agreement, even when $\epsilon$, the parameter characterising the slow variations of the guide’s walls, is relatively large.

The interaction of flexural-gravity waves with periodic geometries

A periodic structure of finite extent is embedded within an otherwise uniform two-dimensional system consisting of finite-depth fluid covered by a thin elastic plate. An incident harmonic flexural-gravity wave is scattered by the structure. By using an approximation to the corresponding linearised boundary value problem that is based on a slowly varying structure in conjunction with a transfer matrix formulation, a method is developed that generates the whole solution from that for just one cycle of the structure, providing both computational savings and insight into the scattering process. Numerical results show that variations in the plate produce strong resonances about the ‘Bragg frequencies’ for relatively few periods. We find that certain geometrical variations in the plate generate these resonances above the Bragg value, whereas other geometries produce the resonance below the Bragg value. The familiar resonances due to periodic bed undulations tend to be damped by the plate.

Valuation and arbitrage

The use of discounted cash flow (DCF) methods in investment valuation and appraisal is argued by many academics as being rational and more rigorous than the traditional capitalisation model. However those advocates of DCF should be cautious in their claims for rationality. The various DCF models all rely upon an all-encompassing equated yield (IRR) within the calculation. This paper will argue that this is a simplification of the risk perception which the investor places on the income profile from property. In determining the long term capital value of a property an 'average' DCF method will produce the 'correct' price, however, the individual short term values of each cash-flow may differ significantly. In the UK property market today, where we are facing a period in which prices are not expected to rise generally at the same rate or with such persistence as hitherto, investors and tenants are increasingly concerned with the down side implications of rental growth and investors may indeed be interested in trading property over a shorter investment horizon than they had originally planned. The purpose of this paper is therefore to bring to the analysis a rigorous framework which can be used to analyse the constituent cash flows within the freehold valuation. We show that the arbitrage analysis lends itself to segregating the capital value of the cash flows in a way which is more appropriate for financial investors

Statistical monitoring of student performance: an early warning system

Weekly monitoring of profiles of student performances on formative and summative coursework throughout the year can be used to quickly identify those who need additional help, possibly due to acute and sudden-onset problems. Such an early-warning system can help retention, but also assist students in overcoming problems early on, thus helping them fulfil their potential in the long run. We have developed a simple approach for the automatic monitoring of student mark profiles for individual modules, which we intend to trial in the near future. Its ease of implementation means that it can be used for very large cohorts with little additional effort when marks are already collected and recorded on a spreadsheet.

Architecture, sedentism, and social complexity at Pre-Pottery Neolithic A WF16, Southern Jordan

Recent excavations at Pre-Pottery Neolithic A (PPNA) WF16 in southern Jordan have revealed remarkable evidence of architectural developments in the early Neolithic. This sheds light on both special purpose structures and “domestic” settlement, allowing fresh insights into the development of increasingly sedentary communities and the social systems they supported. The development of sedentary communities is a central part of the Neolithic process in Southwest Asia. Architecture and ideas of homes and households have been important to the debate, although there has also been considerable discussion on the role of communal buildings and the organization of early sedentarizing communities since the discovery of the tower at Jericho. Recently, the focus has been on either northern Levantine PPNA sites, such as Jerf el Ahmar, or the emergence of ritual buildings in the Pre-Pottery Neolithic B of the southern Levant. Much of the debate revolves around a division between what is interpreted as domestic space, contrasted with “special purpose” buildings. Our recent evidence allows a fresh examination of the nature of early Neolithic communities.

Lighting energy saving due to the use of direct sunlight

This paper describe a simulation program, which uses Trengenza’s average room illuminance method in conjunction with hourly solar irradiance and luminous efficacy, to predict the potential lighting energy saving for a side-lit room. Two lighting control algorithms of photoelectric switching (on/off) and photoelectric dimming (top-up) have been coded in the program. A simulation for a typical UK office room has been conducted and the results show that energy saving due to the sunlight dependent on the various factors such as orientation, control methods, building depth, glazing area and shading types, etc. This simple tool can be used for estimating the potential lighting energy saving of the windows with various shading devices at the early design stage.

Cuckoos at Wicken Fen, snow, and radiocarbon dating

This week in the Planet Earth Podcast: the cunning tricks the cuckoo uses to get another bird to do the parenting, why researchers are studying snow in Sweden, and how an improved radiocarbon dating technique may put a few scientists' noses out of joint.

Acidity controls on dissolved organic carbon mobility in organic soils

Dissolved organic carbon (DOC) concentrations in surface waters have increased across much of Europe and North America, with implications for the terrestrial carbon balance, aquatic ecosystem functioning, water treatment costs and human health. Over the past decade, many hypotheses have been put forward to explain this phenomenon, from changing climate and land-management to eutrophication and acid deposition. Resolution of this debate has been hindered by a reliance on correlative analyses of time-series data, and a lack of robust experimental testing of proposed mechanisms. In a four-year, four-site replicated field experiment involving both acidifying and de-acidifying treatments, we tested the hypothesis that DOC leaching was previously suppressed by high levels of soil acidity in peat and organo-mineral soils, and therefore that observed DOC increases a consequence of decreasing soil acidity. We observed a consistent, positive relationship between DOC and acidity change at all sites. Responses were described by similar hyperbolic relationships between standardised changes in DOC and hydrogen ion concentrations at all sites, suggesting potentially general applicability. These relationships explained a substantial proportion of observed changes in peak DOC concentrations in nearby monitoring streams, and application to a UK-wide upland soil pH dataset suggests that recovery from acidification alone could have led to soil solution DOC increases in the range 46-126% by habitat type since 1978. Our findings raise the possibility that changing soil acidity may have wider impacts on ecosystem carbon balances. Decreasing sulphur deposition may be accelerating terrestrial carbon loss, and returning surface waters to a natural, high-DOC condition.