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.

Decadal predictability of the Atlantic Ocean in a coupled GCM: forecast skill and optimal perturbations using Linear Inverse Modelling

The decadal predictability of three-dimensional Atlantic Ocean anomalies is examined in a coupled global climate model (HadCM3) using a Linear Inverse Modelling (LIM) approach. It is found that the evolution of temperature and salinity in the Atlantic, and the strength of the meridional overturning circulation (MOC), can be effectively described by a linear dynamical system forced by white noise. The forecasts produced using this linear model are more skillful than other reference forecasts for several decades. Furthermore, significant non-normal amplification is found under several different norms. The regions from which this growth occurs are found to be fairly shallow and located in the far North Atlantic. Initially, anomalies in the Nordic Seas impact the MOC, and the anomalies then grow to fill the entire Atlantic basin, especially at depth, over one to three decades. It is found that the structure of the optimal initial condition for amplification is sensitive to the norm employed, but the initial growth seems to be dominated by MOC-related basin scale changes, irrespective of the choice of norm. The consistent identification of the far North Atlantic as the most sensitive region for small perturbations suggests that additional observations in this region would be optimal for constraining decadal climate predictions.

The influence of time on lead toxicity and bioaccumulation determined by the OECD earthworm toxicity test

Internationally agreed standard protocols for assessing chemical toxicity of contaminants in soil to worms assume that the test soil does not need to equilibrate with the chemical to be tested prior to the addition of the test organisms and that the chemical will exert any toxic effect upon the test organism within 28 days. Three experiments were carried out to investigate these assumptions. The first experiment was a standard toxicity test where lead nitrate was added to a soil in solution to give a range of concentrations. The mortality of the worms and the concentration of lead in the survivors were determined. The LC(50)s for 14 and 28 days were 5311 and 5395 mug(Pb) g(soil)(-1) respectively. The second experiment was a timed lead accumulation study with worms cultivated in soil containing either 3000 or 5000 mug(Pb) g(soil)(-1). The concentration of lead in the worms was determined at various sampling times. Uptake at so' Sol both concentrations was linear with time. Worms in the 5000 mug g(-1) soil accumulated lead at a faster rate (3.16 mug Pb g(tissue)(-1) day(-1)) tiss than those in the 3000 mug g(-1) soil (2.21 mug Pb-tissue g(-1) day(-1)). The third experiment was a timed experiment with worms cultivated in tiss soil containing 7000 mugPb g(soil)(-1). Soil and lead nitrate solution were mixed and stored at 20 degreesC. Worms were added at various times over a 35-day period. The time to death increased from 23 h, when worms were added directly after the lead was added to the soil, to 67 It when worms were added after the soil had equilibrated with the lead for 35 days. In artificially Pb-amended soils the worms accumulate Pb over the duration of their exposure to the Pb. Thus time limited toxicity tests may be terminated before worm body load has reached a toxic level. This could result in under-estimates of the toxicity of Pb to worms. As the equilibration time of artificially amended Pb-bearing soils increases the bioavailability of Pb decreases. Thus addition of worms shortly after addition of Pb to soils may result in the over-estimate of Pb toxicity to worms. The current OECD acute worm toxicity test fails to take these two phenomena into account thereby reducing the environmental relevance of the contaminant toxicities it is used to calculate. (C) 2002 Elsevier Science Ltd. All rights reserved.

Analysis of water-level response to rainfall and implications for recharge pathways in the Chalk aquifer, SE England

Water table response to rainfall was investigated at six sites in the Upper, Middle and Lower Chalk of southern England. Daily time series of rainfall and borehole water level were cross-corretated to investigate seasonal variations in groundwater-level response times, based on periods of 3-month duration. The time tags (in days) yielding significant correlations were compared with the average unsaturated zone thickness during each 3-month period. In general, for cases when the unsaturated zone was greater than 18 m thick, the time tag for a significant water-level response increased rapidly once the depth to the water table exceeded a critical value, which varied from site to site. For shallower water tables, a linear relationship between the depth to the water table and the water-level response time was evident. The observed variations in response time can only be partially accounted for using a diffusive model for propagation through the unsaturated matrix, suggesting that some fissure flow was occurring. The majority of rapid responses were observed during the winter/spring recharge period, when the unsaturated zone is thinnest and the unsaturated zone moisture content is highest, and were more likely to occur when the rainfall intensity exceeded 5 mm/day. At some sites, a very rapid response within 24 h of rainfall was observed in addition to the longer term responses even when the unsaturated zone was up to 64 m thick. This response was generally associated with the autumn period. The results of the cross-correlation analysis provide statistical support for the presence of fissure flow and for the contribution of multiple pathways through the unsaturated zone to groundwater recharge. (c) 2006 Elsevier B.V. All rights reserved.

A record of Holocene climate change from lake geochemical analyses in southeastern Arabia

Lacustrine sediments from southeastern Arabia reveal variations in lake level corresponding to changes in the strength and duration of Indian Ocean Monsoon (IOM) summer rainfall and winter cyclonic rainfall. The late glacial/Holocene transition of the region was characterised by the development of mega-linear dunes. These dunes became stabilised and vegetated during the early Holocene and interdunal lakes formed in response to the incursion of the IOM at approximately 8500 cal yr BP with the development of C3 dominated savanna grasslands. The IOM weakened ca. 6000 cal yr BP with the onset of regional aridity, aeolian sedimentation and dune reactivation and accretion. Despite this reduction in precipitation, the take was maintained by winter dominated rainfall. There was a shift to drier adapted C4 grasslands across the dune field. Lake sediment geochemical analyses record precipitation minima at 8200, 5000 and 4200 cal yr BP that coincide with Bond events in the North Atlantic. A number of these events correspond with changes in cultural periods, suggesting that climate was a key mechanism affecting human occupation and exploitation of this region. (c) 2006 University of Washington. All rights reserved.

The impact of contract duration on the cost of cash retention

Cash retention is a common means of protecting an employer from a contractor's insolvency as well as ensuring that contractors finish the work that they start. Similarly, contractors withhold part of payments due to their sub-contractors. Larger contracts tend to be subjected to smaller rates of retention. By calculating the cost of retention as an amount per year of a contract, it is shown that retention is far more expensive for firms whose work consists of short contracts. The extra cost is multiplied when the final payment is delayed, as it often is for those whose work takes place at the beginning of a project. This may explain why it is that main contractors are a lot less interested than sub-contractors in alternatives to cash retention, such as retention bonds

Linear Contributions of Different Time Scales to Teleconnectivity

The contributions of different time scales to extratropical teleconnections are examined. By applying empirical orthogonal functions and correlation analyses to reanalysis data, it is shown that eddies with periods shorter than 10 days have no linear contribution to teleconnectivity. Instead, synoptic variability follows wavelike patterns along the storm tracks, interpreted as propagating baroclinic disturbances. In agreement with preceding studies, it is found that teleconnections such as the North Atlantic Oscillation (NAO) and the Pacific–North America (PNA) pattern occur only at low frequencies, typically for periods more than 20 days. Low-frequency potential vorticity variability is shown to follow patterns analogous to known teleconnections but with shapes that differ considerably from them. It is concluded that the role, if any, of synoptic eddies in determining and forcing teleconnections needs to be sought in nonlinear interactions with the slower transients. The present results demonstrate that daily variability of teleconnection indices cannot be interpreted in terms of the teleconnection patterns, only the slow part of the variability.

Linear and nonlinear generalized Fourier transforms

This article presents an overview of a transform method for solving linear and integrable nonlinear partial differential equations. This new transform method, proposed by Fokas, yields a generalization and unification of various fundamental mathematical techniques and, in particular, it yields an extension of the Fourier transform method.