Oriented vehicles travelling in spherical space

This paper tackles the path planning problem for oriented vehicles travelling in the non-Euclidean 3-Dimensional space; spherical space S3. For such problem, the orientation of the vehicle is naturally represented by orthonormal frame bundle; the rotation group SO(4). Orthonormal frame bundles of space forms coincide with their isometry groups and therefore the focus shifts to control systems defined on Lie groups. The oriented vehicles, in this case, are constrained to travel at constant speed in a forward direction and their angular velocities directly controlled. In this paper we identify controls that induce steady motions of these oriented vehicles and yield closed form parametric expressions for these motions. The paths these vehicles trace are defined explicitly in terms of the controls and therefore invariant with respect to the coordinate system used to describe the motion.

Optimal steady motions for oriented vehicles

Motivated by the motion planning problem for oriented vehicles travelling in a 3-Dimensional space; Euclidean space E3, the sphere S3 and Hyperboloid H3. For such problems the orientation of the vehicle is naturally represented by an orthonormal frame over a point in the underlying manifold. The orthonormal frame bundles of the space forms R3,S3 and H3 correspond with their isometry groups and are the Euclidean group of motion SE(3), the rotation group SO(4) and the Lorentzian group SO(1; 3) respectively. Orthonormal frame bundles of space forms coincide with their isometry groups and therefore the focus shifts to left-invariant control systems defined on Lie groups. In this paper a method for integrating these systems is given where the controls are time-independent. For constant twist motions or helical motions, the corresponding curves g(t) 2 SE(3) are given in closed form by using the well known Rodrigues’ formula. However, this formula is only applicable to the Euclidean case. This paper gives a method for computing the non-Euclidean screw/helical motions in closed form. This involves decoupling the system into two lower dimensional systems using the double cover properties of Lie groups, then the lower dimensional systems are solved explicitly in closed form.

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

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.

Remaking place and securitising space: Urban regeneration and the strategies, tactics and practices of policing in the UK

Urban regeneration programmes in the UK over the past 20 years have increasingly focused on attracting investors, middle-class shoppers and visitors by transforming places and creating new consumption spaces. Ensuring that places are safe and are seen to be safe has taken on greater salience as these flows of income are easily disrupted by changing perceptions of fear and the threat of crime. At the same time, new technologies and policing strategies and tactics have been adopted in a number of regeneration areas which seek to establish control over these new urban spaces. Policing space is increasingly about controlling human actions through design, surveillance technologies and codes of conduct and enforcement. Regeneration agencies and the police now work in partnerships to develop their strategies. At its most extreme, this can lead to the creation of zero-tolerance, or what Smith terms 'revanchist', measures aimed at particular social groups in an effort to sanitise space in the interests of capital accumulation. This paper, drawing on an examination of regeneration practices and processes in one of the UK's fastest-growing urban areas, Reading in Berkshire, assesses policing strategies and tactics in the wake of a major regeneration programme. It documents and discusses the discourses of regeneration that have developed in the town and the ways in which new urban spaces have been secured. It argues that, whilst security concerns have become embedded in institutional discourses and practices, the implementation of security measures has been mediated, in part, by the local socio-political relations in and through which they have been developed.

Ensemble-based data assimilation and the localisation problem

The “butterfly effect” is a popularly known paradigm; commonly it is said that when a butterfly flaps its wings in Brazil, it may cause a tornado in Texas. This essentially describes how weather forecasts can be extremely senstive to small changes in the given atmospheric data, or initial conditions, used in computer model simulations. In 1961 Edward Lorenz found, when running a weather model, that small changes in the initial conditions given to the model can, over time, lead to entriely different forecasts (Lorenz, 1963). This discovery highlights one of the major challenges in modern weather forecasting; that is to provide the computer model with the most accurately specified initial conditions possible. A process known as data assimilation seeks to minimize the errors in the given initial conditions and was, in 1911, described by Bjerkness as “the ultimate problem in meteorology” (Bjerkness, 1911).

A wavenumber independent boundary element method for an acoustic scattering problem

In this paper we consider the impedance boundary value problem for the Helmholtz equation in a half-plane with piecewise constant boundary data, a problem which models, for example, outdoor sound propagation over inhomogeneous. at terrain. To achieve good approximation at high frequencies with a relatively low number of degrees of freedom, we propose a novel Galerkin boundary element method, using a graded mesh with smaller elements adjacent to discontinuities in impedance and a special set of basis functions so that, on each element, the approximation space contains polynomials ( of degree.) multiplied by traces of plane waves on the boundary. We prove stability and convergence and show that the error in computing the total acoustic field is O( N-(v+1) log(1/2) N), where the number of degrees of freedom is proportional to N logN. This error estimate is independent of the wavenumber, and thus the number of degrees of freedom required to achieve a prescribed level of accuracy does not increase as the wavenumber tends to infinity.