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.

Lessons from the private finance initiative in the UK: benefits, problems and critical success factors

Purpose – This paper summarises the main research findings from a detailed, qualitative set of structured interviews and case studies of private finance initiative (PFI) schemes in the UK, which involve the construction of built facilities. The research, which was funded by the Foundation for the Built Environment, examines the emergence of PFI in the UK. Benefits and problems in the PFI process are investigated. Best practice, the key critical factors for success, and lessons for the future are also analysed. Design/methodology/approach – The research is based around 11 semi-structured interviews conducted with stakeholders in key PFI projects in the UK. Findings – The research demonstrates that value for money and risk transfer are key success criteria. High procurement and transaction costs are a feature of PFI projects, and the large-scale nature of PFI projects frequently acts as barrier to entry. Research limitations/implications – The research is based on a limited number of in-depth case study interviews. The paper also shows that further research is needed to find better ways to measure these concepts empirically. Practical implications – The paper is important in highlighting four main areas of practical improvement in the PFI process: value for money assessment; establishing end-user needs; developing competitive markets and developing appropriate skills in the public sector. Originality/value – The paper examines the drivers, barriers and critical success factors for PFI in the UK for the first time in detail and will be of value to property investors, financiers, and others involved in the PFI process.

Supporting multi-organisational collaborative groups in the public sector

In this paper, the issues that arise in multi-organisational collaborative groups (MOCGs) in the public sector are discussed and how a technology-based group support system (GSS) could assist individuals within these groups. MOCGs are commonly used in the public sector to find solutions to multifaceted social problems. Finding solutions for such problems is difficult because their scope is outside the boundary of a single government agency. The standard approach to solving such problems is collaborative involving a diverse range of stakeholders. Collaborative working can be advantageous but it also introduces its own pressures. Conflicts can arise due to the multiple contexts and goals of group members and the organisations that they represent. Trust, communication and a shared interface are crucial to making any significant progress. A GSS could support these elements.

Voices from the aid 'chain': The personal dynamics of care

This paper uses a simplified model of the aid 'chain' to explore some causes and consequences of breakdown in communication. Although the rhetoric of Northern-based donors is awash with words such as 'partnership' and 'inclusion' when dealing with their Southern-based partners, the situation in practice is different. Unequal power relationships sometimes result in donor imposition of Perspectives and values. It is our contention, based on a collective experience of fifty-four years in a Nigerian-based non-governmental development organization (NGDO), the Diocesan Development Services (DDS), that much of the driving force behind the successes and problems faced by the institution was founded on relationships that evolved between individuals. In order to understand why things happened the way they did it is necessary to begin with the human element that cannot be condensed into objects or categories. While injudicious donor interference bad damaging repercussions, our experience suggests that care and consideration flow throughout the aid chain and actions are not malevolent. Breakdowns can be attributed to a number of factors, with the over-riding one being pressures operating at the personal level that emanate from within the institution itself and the larger community. The paper analyses three experiences using institutional ethnography theory and methodologies as a basis. Examples taken address the influence key donor personnel had in the function of DDS, and how these changed with time. The mission, policies and even procedures of the donor did not change markedly over thirty-two years, but each changing desk officer had their own philosophy and approach and a different interpretation of their own institutional policies. Hence while the 'macro' has an influence it is mediated via individual interpretation. In our view, the importance of people-people relationships is particularly understated in development literature where emphasis gravitates towards the aggregate and global.

Moving towards a more mechanistic approach in the determination of soil heat flux from remote measurements - I. A universal approach to calculate thermal inertia

In this paper we pledge that physically based equations should be combined with remote sensing techniques to enable a more theoretically rigorous estimation of area-average soil heat flux, G. A standard physical equation (i.e. the analytical or exact method) for the estimation of G, in combination with a simple, but theoretically derived, equation for soil thermal inertia (F), provides the basis for a more transparent and readily interpretable method for the estimation of G; without the requirement for in situ instrumentation. Moreover, such an approach ensures a more universally applicable method than those derived from purely empirical studies (employing vegetation indices and albedo, for example). Hence, a new equation for the estimation of Gamma(for homogeneous soils) is discussed in this paper which only requires knowledge of soil type, which is readily obtainable from extant soil databases and surveys, in combination with a coarse estimate of moisture status. This approach can be used to obtain area-averaged estimates of Gamma(and thus G, as explained in paper II) which is important for large-scale energy balance studies that employ aircraft or satellite data. Furthermore, this method also relaxes the instrumental demand for studies at the plot and field scale (no requirement for in situ soil temperature sensors, soil heat flux plates and/or thermal conductivity sensors). In addition, this equation can be incorporated in soil-vegetation-atmosphere-transfer models that use the force restore method to update surface temperatures (such as the well-known ISBA model), to replace the thermal inertia coefficient.

Moving towards a more mechanistic approach in the determination of soil heat flux from remote measurements - II. Diurnal shape of soil heat flux

For vegetated surfaces, calculation of soil heat flux, G, with the Exact or Analytical method requires a harmonic analysis of below-canopy soil surface temperature, to obtain the shape of the diurnal course of G. When determining G with remote sensing methods, only composite (vegetation plus soil) radiometric brightness temperature is available. This paper presents a simple equation that relates the sum of the harmonic terms derived for the composite radiometric surface temperature to that of belowcanopy soil surface temperature. The thermal inertia, Gamma(,) for which a simple equation has been presented in a companion paper, paper I, is used to set the magnitude of G. To assess the success of the method proposed in this paper for the estimation of the diurnal shape of G, a comparison was made between 'remote' and in situ calculated values from described field sites. This indicated that the proposed method was suitable for the estimation of the shape of G for a variety of vegetation types and densities. The approach outlined in paper I, to obtain Gamma, was then combined with the estimated harmonic terms to predict estimates of G, which were compared to values predicted by empirical remote methods found in the literature. This indicated that the method proposed in the combination of papers I and II gave reliable estimates of G, which, in comparison to the other methods, resulted in more realistic predictions for vegetated surfaces. This set of equations can also be used for bare and sparsely vegetated soils, making it a universally applicable method. (C) 2007 Elsevier B.V. All rights reserved.

Predictive vegetation mapping in the Mediterranean context: Considerations and methodological issues

The need to map vegetation communities over large areas for nature conservation and to predict the impact of environmental change on vegetation distributions, has stimulated the development of techniques for predictive vegetation mapping. Predictive vegetation studies start with the development of a model relating vegetation units and mapped physical data, followed by the application of that model to a geographic database and over a wide range of spatial scales. This field is particularly important for identifying sites for rare and endangered species and locations of high biodiversity such as many areas of the Mediterranean Basin. The potential of the approach is illustrated with a mapping exercise in the alti-meditterranean zone of Lefka Ori in Crete. The study established the nature of the relationship between vegetation communities and physical data including altitude, slope and geomorphology. In this way the knowledge of community distribution was improved enabling a GIS-based model capable of predicting community distribution to be constructed. The paper describes the development of the spatial model and the methodological problems of predictive mapping for monitoring Mediterranean ecosystems. The paper concludes with a discussion of the role of predictive vegetation mapping and other spatial techniques, such as fuzzy mapping and geostatistics, for improving our understanding of the dynamics of Mediterranean ecosystems and for practical management in a region that is under increasing pressure from human impact.

An event-based approach to validating solar wind speed predictions: high-speed enhancements in the Wang-Sheeley-Arge model

One of the primary goals of the Center for Integrated Space Weather Modeling (CISM) effort is to assess and improve prediction of the solar wind conditions in near‐Earth space, arising from both quasi‐steady and transient structures. We compare 8 years of L1 in situ observations to predictions of the solar wind speed made by the Wang‐Sheeley‐Arge (WSA) empirical model. The mean‐square error (MSE) between the observed and model predictions is used to reach a number of useful conclusions: there is no systematic lag in the WSA predictions, the MSE is found to be highest at solar minimum and lowest during the rise to solar maximum, and the optimal lead time for 1 AU solar wind speed predictions is found to be 3 days. However, MSE is shown to frequently be an inadequate “figure of merit” for assessing solar wind speed predictions. A complementary, event‐based analysis technique is developed in which high‐speed enhancements (HSEs) are systematically selected and associated from observed and model time series. WSA model is validated using comparisons of the number of hit, missed, and false HSEs, along with the timing and speed magnitude errors between the forecasted and observed events. Morphological differences between the different HSE populations are investigated to aid interpretation of the results and improvements to the model. Finally, by defining discrete events in the time series, model predictions from above and below the ecliptic plane can be used to estimate an uncertainty in the predicted HSE arrival times.

Spectral analysis of the elliptic sine-Gordon equation in the quarter plane

We study the elliptic sine-Gordon equation in the quarter plane using a spectral transform approach. We determine the Riemann-Hilbert problem associated with well-posed boundary value problems in this domain and use it to derive a formal representation of the solution. Our analysis is based on a generalization of the usual inverse scattering transform recently introduced by Fokas for studying linear elliptic problems.

Design of a turn-linker-turn foldamer by incorporating meta-amino benzoic acid in the middle of a helix forming hexapeptide sequence: A helix breaking approach

Single crystal X-ray diffraction studies reveal that the incorporation of meta-amino benzoic acid in the middle of a helix forming hexapeptide sequence such as in peptide I Boc-Ile(1)-Aib(2)-Val(3)-m-ABA(4)-Ile(5)-Aib(6)-Leu(7)-OMe (Aib: alpha-amino isobutyric acid: m-ABA: meta-amino benzoic acid) breaks the helix propagation to produce a turn-linker-turn (T-L-T) foldamer in the solid state. In the crystalline state two conformational isomers of peptide I self-assemble in antiparallel fashion through intermolecular hydrogen bonds and aromatic pi-pi interactions to form a molecular duplex. The duplexes are further interconnected through intermolecular hydrogen bonds to form a layer of peptides. The layers are stacked one on top of the other through van der Waals interactions to form hydrophilic channels filled with solvent methanol. (C) 2009 Elsevier B.V. All rights reserved.