An integral equation method for a boundary value problem arising in unsteady water wave problems

In this paper we consider the 2D Dirichlet boundary value problem for Laplace’s equation in a non-locally perturbed half-plane, with data in the space of bounded and continuous functions. We show uniqueness of solution, using standard Phragmen-Lindelof arguments. The main result is to propose a boundary integral equation formulation, to prove equivalence with the boundary value problem, and to show that the integral equation is well posed by applying a recent partial generalisation of the Fredholm alternative in Arens et al [J. Int. Equ. Appl. 15 (2003) pp. 1-35]. This then leads to an existence proof for the boundary value problem. Keywords. Boundary integral equation method, Water waves, Laplace’s

Rational modification of the hierarchy of intermolecular interactions in molecular crystal structures by using tunable halogen bonds

A family of 16 isomolecular salts (3-XpyH)(2)[MX'(4)] (3-XpyH=3-halopyridinium; M=Co, Zn; X=(F), Cl, Br, (I); X'=Cl, Br, I) each containing rigid organic cations and tetrahedral halometallate anions has been prepared and characterized by X-ray single crystal and/or powder diffraction. Their crystal structures reflect the competition and cooperation between non-covalent interactions: N-H center dot center dot center dot X'-M hydrogen bonds, C-X center dot center dot center dot X'-M halogen bonds and pi-pi stacking. The latter are essentially unchanged in strength across the series, but both halogen bonds and hydrogen bonds are modified in strength upon changing the halogens involved. Changing the organic halogen (X) from F to I strengthens the C-X center dot center dot center dot X'-M halogen bonds, whereas an analogous change of the inorganic halogen (X') weakens both halogen bonds and N-H center dot center dot center dot X'-M hydrogen bonds. By so tuning the strength of the putative halogen bonds from repulsive to weak to moderately strong attractive interactions, the hierarchy of the interactions has been modified rationally leading to systematic changes in crystal packing. Three classes of crystal structure are obtained. In type A (C-F center dot center dot center dot X'-M) halogen bonds are absent. The structure is directed by N-H center dot center dot center dot X'-M hydrogen bonds and pi-stacking interactions. In type B structures, involving small organic halogens (X) and large inorganic halogens (X'), long (weak) C-X center dot center dot center dot X'-M interactions are observed with type I halogen-halogen interaction geometries (C-X center dot center dot center dot X' approximate to X center dot center dot center dot X'-M approximate to 155 degrees), but hydrogen bonds still dominate. Thus, minor but quite significant perturbations from the type A structure arise. In type C, involving larger organic halogens (X) and smaller inorganic halogens (X'), stronger halogen bonds are formed with a type II halogen-halogen interaction geometry (C-X center dot center dot center dot X' approximate to 180 degrees; X center dot center dot center dot X'-M approximate to 110 degrees) that is electrostatically attractive. The halogen bonds play a major role alongside hydrogen bonds in directing the type C structures, which as a result are quite different from type A and B.

Problem structuring methods: theorizing the benefits of deconstructing sustainable development projects

Problem structuring methods or PSMs are widely applied across a range of variable but generally small-scale organizational contexts. However, it has been argued that they are seen and experienced less often in areas of wide ranging and highly complex human activity-specifically those relating to sustainability, environment, democracy and conflict (or SEDC). In an attempt to plan, track and influence human activity in SEDC contexts, the authors in this paper make the theoretical case for a PSM, derived from various existing approaches. They show how it could make a contribution in a specific practical context-within sustainable coastal development projects around the Mediterranean which have utilized systemic and prospective sustainability analysis or, as it is now known, Imagine. The latter is itself a PSM but one which is 'bounded' within the limits of the project to help deliver the required 'deliverables' set out in the project blueprint. The authors argue that sustainable development projects would benefit from a deconstruction of process by those engaged in the project and suggest one approach that could be taken-a breakout from a project-bounded PSM to an analysis that embraces the project itself. The paper begins with an introduction to the sustainable development context and literature and then goes on to illustrate the issues by grounding the debate within a set of projects facilitated by Blue Plan for Mediterranean coastal zones. The paper goes on to show how the analytical framework could be applied and what insights might be generated.

Putting the pieces back together again: an illustration of the problem of interpreting development indicators using an African case study

Indicators are commonly recommended as tools for assessing the attainment of development, and the current vogue is for aggregating a number of indicators together into a single index. It is claimed that such indices of development help facilitate maximum impact in policy terms by appealing to those who may not necessarily have technical expertise in data collection, analysis and interpretation. In order to help counter criticisms of over-simplification, those advocating such indices also suggest that the raw data be provided so as to allow disaggregation into component parts and hence facilitate a more subtle interpretation if a reader so desires. This paper examines the problems involved with interpreting indices of development by focusing on the United Nations Development Programmes (UNDP) Human Development Index (HDI) published each year in the Human Development Reports (HDRs). The HDI was intended to provide an alternative to the more economic based indices, such as GDP, commonly used within neo-liberal development agendas. The paper explores the use of the HDI as a gauge of human development by making comparisons between two major political and economic communities in Africa (ECOWAS and SADC). While the HDI did help highlight important changes in human development as expressed by the HDI over 10 years, it is concluded that the HDI and its components are difficult to interpret as methodologies have changed significantly and the 'averaging' nature of the HDI could hide information unless care is taken. The paper discusses the applicability of alternative models to the HDI such as the more neo-populist centred methods commonly advocated for indicators of sustainable development. (C) 2003 Elsevier Ltd. All rights reserved.

Making 'dirty' nations look clean? The nation state and the problem of selecting and weighting indices as tools for measuring progress towards sustainability

Pressing global environmental problems highlight the need to develop tools to measure progress towards "sustainability." However, some argue that any such attempt inevitably reflects the views of those creating such tools and only produce highly contested notions of "reality." To explore this tension, we critically assesses the Environmental Sustainability Index (ESI), a well-publicized product of the World Economic Forum that is designed to measure 'sustainability' by ranking nations on league tables based on extensive databases of environmental indicators. By recreating this index, and then using statistical tools (principal components analysis) to test relations between various components of the index, we challenge ways in which countries are ranked in the ESI. Based on this analysis, we suggest (1) that the approach taken to aggregate, interpret and present the ESI creates a misleading impression that Western countries are more sustainable than the developing world; (2) that unaccounted methodological biases allowed the authors of the ESI to over-generalize the relative 'sustainability' of different countries; and, (3) that this has resulted in simplistic conclusions on the relation between economic growth and environmental sustainability. This criticism should not be interpreted as a call for the abandonment of efforts to create standardized comparable data. Instead, this paper proposes that indicator selection and data collection should draw on a range of voices, including local stakeholders as well as international experts. We also propose that aggregating data into final league ranking tables is too prone to error and creates the illusion of absolute and categorical interpretations. (c) 2004 Elsevier Ltd. All rights reserved.

The basic ingredients of the North Atlantic storm track. Part I: land-sea contrast and orography

Understanding and predicting changes in storm tracks over longer time scales is a challenging problem, particularly in the North Atlantic. This is due in part to the complex range of forcings (land–sea contrast, orography, sea surface temperatures, etc.) that combine to produce the structure of the storm track. The impact of land–sea contrast and midlatitude orography on the North Atlantic storm track is investigated through a hierarchy of GCM simulations using idealized and “semirealistic” boundary conditions in a high-resolution version of the Hadley Centre atmosphere model (HadAM3). This framework captures the large-scale essence of features such as the North and South American continents, Eurasia, and the Rocky Mountains, enabling the results to be applied more directly to realistic modeling situations than was possible with previous idealized studies. The physical processes by which the forcing mechanisms impact the large-scale flow and the midlatitude storm tracks are discussed. The characteristics of the North American continent are found to be very important in generating the structure of the North Atlantic storm track. In particular, the southwest–northeast tilt in the upper tropospheric jet produced by southward deflection of the westerly flow incident on the Rocky Mountains leads to enhanced storm development along an axis close to that of the continent’s eastern coastline. The approximately triangular shape of North America also enables a cold pool of air to develop in the northeast, intensifying the surface temperature contrast across the eastern coastline, consistent with further enhancements of baroclinicity and storm growth along the same axis.