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

Boundary value problems for third-order linear PDEs in time-dependent domains

We present the extension of a methodology to solve moving boundary value problems from the second-order case to the case of the third-order linear evolution PDE qt + qxxx = 0. This extension is the crucial step needed to generalize this methodology to PDEs of arbitrary order. The methodology is based on the derivation of inversion formulae for a class of integral transforms that generalize the Fourier transform and on the analysis of the global relation associated with the PDE. The study of this relation and its inversion using the appropriate generalized transform are the main elements of the proof of our results.

Methods and resources for climate impacts research: achieving synergy

The prediction of climate variability and change requires the use of a range of simulation models. Multiple climate model simulations are needed to sample the inherent uncertainties in seasonal to centennial prediction. Because climate models are computationally expensive, there is a tradeoff between complexity, spatial resolution, simulation length, and ensemble size. The methods used to assess climate impacts are examined in the context of this trade-off. An emphasis on complexity allows simulation of coupled mechanisms, such as the carbon cycle and feedbacks between agricultural land management and climate. In addition to improving skill, greater spatial resolution increases relevance to regional planning. Greater ensemble size improves the sampling of probabilities. Research from major international projects is used to show the importance of synergistic research efforts. The primary climate impact examined is crop yield, although many of the issues discussed are relevant to hydrology and health modeling. Methods used to bridge the scale gap between climate and crop models are reviewed. Recent advances include large-area crop modeling, quantification of uncertainty in crop yield, and fully integrated crop–climate modeling. The implications of trends in computer power, including supercomputers, are also discussed.

An interpretation of baroclinic initial value problems: results for simple basic states with nonzero interior PV gradients

In the Eady model, where the meridional potential vorticity (PV) gradient is zero, perturbation energy growth can be partitioned cleanly into three mechanisms: (i) shear instability, (ii) resonance, and (iii) the Orr mechanism. Shear instability involves two-way interaction between Rossby edge waves on the ground and lid, resonance occurs as interior PV anomalies excite the edge waves, and the Orr mechanism involves only interior PV anomalies. These mechanisms have distinct implications for the structural and temporal linear evolution of perturbations. Here, a new framework is developed in which the same mechanisms can be distinguished for growth on basic states with nonzero interior PV gradients. It is further shown that the evolution from quite general initial conditions can be accurately described (peak error in perturbation total energy typically less than 10%) by a reduced system that involves only three Rossby wave components. Two of these are counterpropagating Rossby waves—that is, generalizations of the Rossby edge waves when the interior PV gradient is nonzero—whereas the other component depends on the structure of the initial condition and its PV is advected passively with the shear flow. In the cases considered, the three-component model outperforms approximate solutions based on truncating a modal or singular vector basis.

Living up to the value agenda: the empirical realities of through-life value creation in construction

Current research agendas are increasingly encouraging the construction industry to operate on the basis of 'added value'. Such debates echo the established concept of 'high value manufacturing' and associated trends towards servitization. Within construction, the so-called 'value agenda' draws heavily from the notion of integrated solutions. This is held to be especially appropriate in the context of PFI projects. Also relevant is the concept of service-led projects whereby the project rationale is driven by the client's objectives for delivering an enhanced service to its own customers. Such ideas are contextualized by a consideration of broader trends of privatization and outsourcing within and across the construction industry's client base. The current emphasis on integrated solutions reflects long-term trends within privatized client organizations towards the outsourcing of asset management capabilities. However, such trends are by no means uniform or consistent. An in-depth case study of three operating divisions within a major construction company illustrates that firms are unlikely to reorientate their business in response to the 'value agenda'. In the case of PFI, the tendency has been to establish specialist units for the purposes of winning work. Meanwhile, institutionally embedded operating routines within the rest of the business remain broadly unaffected.

Does changing the taxonomical resolution alter the value of soil macroinvertebrates as bioindicators of metal pollution?

Ecological indicators are taxa that are affected by, and indicate effects of, anthropogenic environmental stress or disturbance on ecosystems. There is evidence that some species of soil macrofauna (i.e. diameter > 2 min) constitute valuable biological indicators of certain types of soil perturbations. This study aims to determine which level of taxonomic resolution, (species, family or ecological group) is the best to identify indicator of soil disturbance. Macrofauna were sampled in a set of sites encompassing different land-use systems (e.g. forests, pastures, crops) and different levels of pollution. Indicator taxa were sought using the IndVal index proposed by Dufrene and Legendre [Dufrene, M., Legendre, P., 1997. Species assemblages and indicator species: the need for a flexible asymetrical approach. Ecological Monographs 67, 345-3661. This approach is based on a hierarchical typology of sites. The index value changes along the typology and decreases (increases) for generalist (specialist) faunal units (species, families or ecological groups). Of the 327 morphospecies recorded, 19 were significantly associated with a site type or a group of sites (5.8%). Similarly, species were aggregated to form 59 families among which 17 (28.8%) displayed a significant indicator value. Gathering species into 28 broad ecological assemblages led to 14 indicator groups (50%). Beyond the simple proportion of units having significant association with a given level of the site typology, the proportion of specialist and generalist groups changed dramatically when the level of taxonomic resolution was altered. At the species level 84% of the indicator units were specialist, whereas this proportion decreased to 70 and 43% when families and ecological groups were considered. Because specialist groups are the most interesting type of indicators either in terms of conservation or for management purposes we come to the conclusion that the species level is the most accurate taxonomic level in bioindication studies although it requires a high amount of labour and operator knowledge and is time-consuming. (c) 2005 Published by Elsevier Ltd.

Unification of the probe and singular sources methods for the inverse boundary value problem by the no-response test

In this article, we use the no-response test idea, introduced in Luke and Potthast (2003) and Potthast (Preprint) and the inverse obstacle problem, to identify the interface of the discontinuity of the coefficient gamma of the equation del (.) gamma(x)del + c(x) with piecewise regular gamma and bounded function c(x). We use infinitely many Cauchy data as measurement and give a reconstructive method to localize the interface. We will base this multiwave version of the no-response test on two different proofs. The first one contains a pointwise estimate as used by the singular sources method. The second one is built on an energy (or an integral) estimate which is the basis of the probe method. As a conclusion of this, the probe and the singular sources methods are equivalent regarding their convergence and the no-response test can be seen as a unified framework for these methods. As a further contribution, we provide a formula to reconstruct the values of the jump of gamma(x), x is an element of partial derivative D at the boundary. A second consequence of this formula is that the blow-up rate of the indicator functions of the probe and singular sources methods at the interface is given by the order of the singularity of the fundamental solution.