Approximate solution of second kind integral equations on infinite cylindrical surfaces

The paper considers second kind integral equations of the form $\phi (x) = g(x) + \int_S {k(x,y)} \phi (y)ds(y)$ (abbreviated $\phi = g + K\phi $), in which S is an infinite cylindrical surface of arbitrary smooth cross section. The “truncated equation” (abbreviated $\phi _a = E_a g + K_a \phi _a $), obtained by replacing S by $S_a $, a closed bounded surface of class $C^2 $, the boundary of a section of the interior of S of length $2a$, is also discussed. Conditions on k are obtained (in particular, implying that K commutes with the operation of translation in the direction of the cylinder axis) which ensure that $I - K$ is invertible, that $I - K_a $ is invertible and $(I - K_a )^{ - 1} $ is uniformly bounded for all sufficiently large a, and that $\phi _a $ converges to $\phi $ in an appropriate sense as $a \to \infty $. Uniform stability and convergence results for a piecewise constant boundary element collocation method for the truncated equations are also obtained. A boundary integral equation, which models three-dimensional acoustic scattering from an infinite rigid cylinder, illustrates the application of the above results to prove existence of solution (of the integral equation and the corresponding boundary value problem) and convergence of a particular collocation method.

Investigating the value dairy farmers place on a reduction of lameness in their herds using a willingness to pay approach

A survey was conducted to elicit dairy farmers’ willingness to pay (WTP) to reduce the prevalence of lameness in their herds. A choice experiment questionnaire was administered using face-to-face interviews of 163 farmers in England and Wales. Whole herd lameness assessments by trained researchers recorded a mean lameness prevalence of nearly 24% which was substantially higher than that estimated by farmers. Farmers’ responses to a series of attitudinal questions showed that they strongly agreed that cows can suffer a lot of pain from lameness and believed that they could reduce lameness in their herds. Farmers’ mean WTP to avoid lameness amounted to UK£411 per lame cow but with considerable variation across the sample. Median WTP of UK£249 per lame cow was considered a better measure of central tendency for the sample. In addition, the survey found that farmers had a substantial WTP to avoid the inconvenience associated with lameness control (a median value of UK£97 per lame cow) but that they were generally prepared to incur greater inconvenience if it reduced lameness. The study findings suggest that farmers need a better understanding of the scale and costs of lameness in their herds and the benefits of control. To encourage action, farmers need to be convinced that lameness control measures perceived as inconvenient will be cost effective.

What does “retrofit” mean, and how can we scale up action in the UK sector?

Purpose – Progress in retrofitting the UK's commercial properties continues to be slow and fragmented. New research from the UK and USA suggests that radical changes are needed to drive large-scale retrofitting, and that new and innovative models of financing can create new opportunities. The purpose of this paper is to offer insights into the terminology of retrofit and the changes in UK policy and practice that are needed to scale up activity in the sector. Design/methodology/approach – The paper reviews and synthesises key published research into commercial property retrofitting in the UK and USA and also draws on policy and practice from the EU and Australia. Findings – The paper provides a definition of “retrofit”, and compares and contrasts this with “refurbishment” and “renovation” in an international context. The paper summarises key findings from recent research and suggests that there are a number of policy and practice measures which need to be implemented in the UK for commercial retrofitting to succeed at scale. These include improved funding vehicles for retrofit; better transparency in actual energy performance; and consistency in measurement, verification and assessment standards. Practical implications – Policy and practice in the UK needs to change if large-scale commercial property retrofit is to be rolled out successfully. This requires mandatory legislation underpinned by incentives and penalties for non-compliance. Originality/value – This paper synthesises recent research to provide a set of policy and practice recommendations which draw on international experience, and can assist on implementation in the UK.

Curl free pressure gradients over orography in a solution of the fully compressible Euler equations with implicit treatment of acoustic and gravity waves

Steep orography can cause noisy solutions and instability in models of the atmosphere. A new technique for modelling flow over orography is introduced which guarantees curl free gradients on arbitrary grids, implying that the pressure gradient term is not a spurious source of vorticity. This mimetic property leads to better hydrostatic balance and better energy conservation on test cases using terrain following grids. Curl-free gradients are achieved by using the co-variant components of velocity over orography rather than the usual horizontal and vertical components. In addition, gravity and acoustic waves are treated implicitly without the need for mean and perturbation variables or a hydrostatic reference profile. This enables a straightforward description of the implicit treatment of gravity waves. Results are presented of a resting atmosphere over orography and the curl-free pressure gradient formulation is advantageous. Results of gravity waves over orography are insensitive to the placement of terrain-following layers. The model with implicit gravity waves is stable in strongly stratified conditions, with N∆t up to at least 10 (where N is the Brunt-V ̈ais ̈al ̈a frequency). A warm bubble rising over orography is simulated and the curl free pressure gradient formulation gives much more accurate results for this test case than a model without this mimetic property.

Does more detailed information mean better performance? An experiment in information explicitness

Purpose – Investors are now able to analyse more noise-free news to inform their trading decisions than ever before. Their expectation that more information means better performance is not supported by previous psychological experiments which argue that too much information actually impairs performance. The purpose of this paper is to examine whether the degree of information explicitness improves stock market performance. Design/methodology/approach – An experiment is conducted in a computer laboratory to examine a trading simulation manipulated from a real market-shock. Participants’ performance efficiency and effectiveness are measured separately. Findings – The results indicate that the explicitness of information neither improves nor impairs participants’ performance effectiveness from the perspectives of returns, share and cash positions, and trading volumes. However, participants’ performance efficiency is significantly affected by information explicitness. Originality/value – The novel approach and findings of this research add to the knowledge of the impact of information explicitness on the quality of decision making in a financial market environment.

Advances in the study of boundary value problems for nonlinear integrable PDEs

In this review I summarise some of the most significant advances of the last decade in the analysis and solution of boundary value problems for integrable partial differential equations in two independent variables. These equations arise widely in mathematical physics, and in order to model realistic applications, it is essential to consider bounded domain and inhomogeneous boundary conditions. I focus specifically on a general and widely applicable approach, usually referred to as the Unified Transform or Fokas Transform, that provides a substantial generalisation of the classical Inverse Scattering Transform. This approach preserves the conceptual efficiency and aesthetic appeal of the more classical transform approaches, but presents a distinctive and important difference. While the Inverse Scattering Transform follows the "separation of variables" philosophy, albeit in a nonlinear setting, the Unified Transform is a based on the idea of synthesis, rather than separation, of variables. I will outline the main ideas in the case of linear evolution equations, and then illustrate their generalisation to certain nonlinear cases of particular significance.

A semantic solution to the problem with aesthetic testimony

There is something peculiar about aesthetic testimony. It seems more difficult to gain knowledge of aesthetic properties based solely upon testimony than it is in the case of other types of property. In this paper, I argue that we can provide an adequate explanation at the level of the semantics of aesthetic language, without defending any substantive thesis in epistemology or about aesthetic value/judgement. If aesthetic predicates are given a non-invariantist semantics, we can explain the supposed peculiar difficulty with aesthetic testimony.

Recent progress in understanding and projecting regional and global mean sea-level change

Considerable progress has been made in understanding the present and future regional and global sea level in the 2 years since the publication of the Fifth Assessment Report (AR5) of the Intergovernmental Panel on Climate Change. Here, we evaluate how the new results affect the AR5’s assessment of (i) historical sea level rise, including attribution of that rise and implications for the sea level budget, (ii) projections of the components and of total global mean sea level (GMSL), and (iii) projections of regional variability and emergence of the anthropogenic signal. In each of these cases, new work largely provides additional evidence in support of the AR5 assessment, providing greater confidence in those findings. Recent analyses confirm the twentieth century sea level rise, with some analyses showing a slightly smaller rate before 1990 and some a slightly larger value than reported in the AR5. There is now more evidence of an acceleration in the rate of rise. Ongoing ocean heat uptake and associated thermal expansion have continued since 2000, and are consistent with ocean thermal expansion reported in the AR5. A significant amount of heat is being stored deeper in the water column, with a larger rate of heat uptake since 2000 compared to the previous decades and with the largest storage in the Southern Ocean. The first formal detection studies for ocean thermal expansion and glacier mass loss since the AR5 have confirmed the AR5 finding of a significant anthropogenic contribution to sea level rise over the last 50 years. New projections of glacier loss from two regions suggest smaller contributions to GMSL rise from these regions than in studies assessed by the AR5; additional regional studies are required to further assess whether there are broader implications of these results. Mass loss from the Greenland Ice Sheet, primarily as a result of increased surface melting, and from the Antarctic Ice Sheet, primarily as a result of increased ice discharge, has accelerated. The largest estimates of acceleration in mass loss from the two ice sheets for 2003–2013 equal or exceed the acceleration of GMSL rise calculated from the satellite altimeter sea level record over the longer period of 1993–2014. However, when increased mass gain in land water storage and parts of East Antarctica, and decreased mass loss from glaciers in Alaska and some other regions are taken into account, the net acceleration in the ocean mass gain is consistent with the satellite altimeter record. New studies suggest that a marine ice sheet instability (MISI) may have been initiated in parts of the West Antarctic Ice Sheet (WAIS), but that it will affect only a limited number of ice streams in the twenty-first century. New projections of mass loss from the Greenland and Antarctic Ice Sheets by 2100, including a contribution from parts of WAIS undergoing unstable retreat, suggest a contribution that falls largely within the likely range (i.e., two thirds probability) of the AR5. These new results increase confidence in the AR5 likely range, indicating that there is a greater probability that sea level rise by 2100 will lie in this range with a corresponding decrease in the likelihood of an additional contribution of several tens of centimeters above the likely range. In view of the comparatively limited state of knowledge and understanding of rapid ice sheet dynamics, we continue to think that it is not yet possible to make reliable quantitative estimates of future GMSL rise outside the likely range. Projections of twenty-first century GMSL rise published since the AR5 depend on results from expert elicitation, but we have low confidence in conclusions based on these approaches. New work on regional projections and emergence of the anthropogenic signal suggests that the two commonly predicted features of future regional sea level change (the increasing tilt across the Antarctic Circumpolar Current and the dipole in the North Atlantic) are related to regional changes in wind stress and surface heat flux. Moreover, it is expected that sea level change in response to anthropogenic forcing, particularly in regions of relatively low unforced variability such as the low-latitude Atlantic, will be detectable over most of the ocean by 2040. The east-west contrast of sea level trends in the Pacific observed since the early 1990s cannot be satisfactorily accounted for by climate models, nor yet definitively attributed either to unforced variability or forced climate change.