Boundary integral methods in high frequency scattering

In this article we review recent progress on the design, analysis and implementation of numerical-asymptotic boundary integral methods for the computation of frequency-domain acoustic scattering in a homogeneous unbounded medium by a bounded obstacle. The main aim of the methods is to allow computation of scattering at arbitrarily high frequency with finite computational resources.

Mean climate and transience in the tropics of the UGAMP GCM - sensitivity to convective parametrization

The sensitivity of the UK Universities Global Atmospheric Modelling Programme (UGAMP) General Circulation Model (UGCM) to two very different approaches to convective parametrization is described. Comparison is made between a Kuo scheme, which is constrained by large-scale moisture convergence, and a convective-adjustment scheme, which relaxes to observed thermodynamic states. Results from 360-day integrations with perpetual January conditions are used to describe the model's tropical time-mean climate and its variability. Both convection schemes give reasonable simulations of the time-mean climate, but the representation of the main modes of tropical variability is markedly different. The Kuo scheme has much weaker variance, confined to synoptic frequencies near 4 days, and a poor simulation of intraseasonal variability. In contrast, the convective-adjustment scheme has much more transient activity at all time-scales. The various aspects of the two schemes which might explain this difference are discussed. The particular closure on moisture convergence used in this version of the Kuo scheme is identified as being inappropriate.

The PML for rough surface scattering

In this paper we investigate the use of the perfectly matched layer (PML) to truncate a time harmonic rough surface scattering problem in the direction away from the scatterer. We prove existence and uniqueness of the solution of the truncated problem as well as an error estimate depending on the thickness and composition of the layer. This global error estimate predicts a linear rate of convergence (under some conditions on the relative size of the real and imaginary parts of the PML function) rather than the usual exponential rate. We then consider scattering by a half-space and show that the solution of the PML truncated problem converges globally at most quadratically (up to logarithmic factors), providing support for our general theory. However we also prove exponential convergence on compact subsets. We continue by proposing an iterative correction method for the PML truncated problem and, using our estimate for the PML approximation, prove convergence of this method. Finally we provide some numerical results in 2D.(C) 2008 IMACS. Published by Elsevier B.V. All rights reserved.

Boundary integral equations on unbounded rough surfaces: Fredholmness and the finite section method

We consider a class of boundary integral equations that arise in the study of strongly elliptic BVPs in unbounded domains of the form $D = \{(x, z)\in \mathbb{R}^{n+1} : x\in \mathbb{R}^n, z > f(x)\}$ where $f : \mathbb{R}^n \to\mathbb{R}$ is a sufficiently smooth bounded and continuous function. A number of specific problems of this type, for example acoustic scattering problems, problems involving elastic waves, and problems in potential theory, have been reformulated as second kind integral equations $u+Ku = v$ in the space $BC$ of bounded, continuous functions. Having recourse to the so-called limit operator method, we address two questions for the operator $A = I + K$ under consideration, with an emphasis on the function space setting $BC$. Firstly, under which conditions is $A$ a Fredholm operator, and, secondly, when is the finite section method applicable to $A$?

Condition number estimates for combined potential boundary integral operators in acoustic scattering

We study the classical combined field integral equation formulations for time-harmonic acoustic scattering by a sound soft bounded obstacle, namely the indirect formulation due to Brakhage-Werner/Leis/Panic, and the direct formulation associated with the names of Burton and Miller. We obtain lower and upper bounds on the condition numbers for these formulations, emphasising dependence on the frequency, the geometry of the scatterer, and the coupling parameter. Of independent interest we also obtain upper and lower bounds on the norms of two oscillatory integral operators, namely the classical acoustic single- and double-layer potential operators.

Periodic Reordering

For many networks in nature, science and technology, it is possible to order the nodes so that most links are short-range, connecting near-neighbours, and relatively few long-range links, or shortcuts, are present. Given a network as a set of observed links (interactions), the task of finding an ordering of the nodes that reveals such a range-dependent structure is closely related to some sparse matrix reordering problems arising in scientific computation. The spectral, or Fiedler vector, approach for sparse matrix reordering has successfully been applied to biological data sets, revealing useful structures and subpatterns. In this work we argue that a periodic analogue of the standard reordering task is also highly relevant. Here, rather than encouraging nonzeros only to lie close to the diagonal of a suitably ordered adjacency matrix, we also allow them to inhabit the off-diagonal corners. Indeed, for the classic small-world model of Watts & Strogatz (1998, Collective dynamics of ‘small-world’ networks. Nature, 393, 440–442) this type of periodic structure is inherent. We therefore devise and test a new spectral algorithm for periodic reordering. By generalizing the range-dependent random graph class of Grindrod (2002, Range-dependent random graphs and their application to modeling large small-world proteome datasets. Phys. Rev. E, 66, 066702-1–066702-7) to the periodic case, we can also construct a computable likelihood ratio that suggests whether a given network is inherently linear or periodic. Tests on synthetic data show that the new algorithm can detect periodic structure, even in the presence of noise. Further experiments on real biological data sets then show that some networks are better regarded as periodic than linear. Hence, we find both qualitative (reordered networks plots) and quantitative (likelihood ratios) evidence of periodicity in biological networks.

Impact of sewage sludge applications on the biogeochemistry of soils

This report describes an investigation into the bioavailability and fate of trace metals and their subsequent impact on important soil microbiological functions such as nitrification, denitrification and methane oxidation in low and high Cu containing soils in the presence and absence of residual organic matter from sewage sludge additions made 10 years earlier. The soils being studied are part of long term sewage sludge trials and include a low Cu soil ( 13.3mg Cu/ kg soil, 4.18 LOI %), left un- amended to serve as a control soil, soil amended with a high Cu sewage sludge ( 278.3mg Cu/ kg soil, 6.52 LOI %) and soil amended with a low Cu sewage sludge ( 46.3mg Cu/ kg soil, 6.18 LOI %). Soil was also amended with inorganic metal salts ( 273.4mg Cu/ kg soil, 4.52 LOI %) to further investigate the impact of Cu in the absence of additional organic matter contained in applied sewage sludge. Data from the first two years of a project are presented which has included field- based studies at long term sewage sludge trials based in Watlington, Oxford, UK and laboratory based studies at the Institute of Grassland & Environmental Research, North Wyke, Devon, UK.

Lateinische Epigraphik zur Zeit des dreissigjährigen Krieges: Eine Trouvaille

Discussion of the epigraphical exploits of the Danish scholar Henrik Ernst during the Thirty-Years war.

Quantitative response of the longevity of seed of twelve crops to temperature and moisture in hermetic storage

Seeds of 39 seed lots of a total of twelve different crops were stored hermetically in a wide range of air-dry environments (2-25% moisture content at 0-50 degrees C), viability assessed periodically, and the seed viability equation constants estimated. Within a species, estimates of the constants which quantify absolute longevity (K-E) and the relative effects on longevity of moisture content (C-W) and temperature (C-H and C-Q) did not differ (P >0.05 to P >0.25) among lots. Comparison among the 12 crops provided variant estimates of K-E and C-W (P< 0.01), but common values of C-H and C-Q (0.0322 and 0.000454, respectively, P >0.25). Maize (Zea mays) provided the greatest estimate of K-E (9.993, s.e.= 0.456), followed by sorghum (Sorghum bicolor) (9.381, s.e. 0.428), pearl millet (Pennisetum typhoides) (9.336, s.e.= 0.408), sugar beet (Beta vulgaris) (8.988, s.e.= 0.387), African rice (Oryza glaberrima) (8.786, s.e.= 0.484), wheat (Triticum aestivum) (8.498, s.e.= 0.431), foxtail millet (Setaria italica) (8.478, s.e.= 0.396), sugarcane (Saccharum sp.) (8.454, s.e.= 0.545), finger millet (Eleusine coracana) (8.288, s.e.= 0.392), kodo millet (Paspalum scrobiculatum) (8.138, s.e.= 0.418), rice (Oryza sativa) (8.096, s.e.= 0.416) and potato (Solanum tuberosum) (8.037, s.e.= 0.397). Similarly, estimates of C-W were ranked maize (5.993, s.e.= 0.392), pearl millet (5.540, s.e.= 0.348), sorghum (5.379, s.e.=0.365), potato (5.152, s.e.= 0.347), sugar beet (4.969, s.e.= 0.328), sugar cane (4.964, s.e.= 0.518), foxtail millet (4.829, s.e.= 0.339), wheat (4.836, s.e.= 0.366), African rice (4.727, s.e.= 0.416), kodo millet (4.435, s.e.= 0.360), finger millet (4.345, s.e.= 0.336) and rice (4.246, s.e.= 0.355). The application of these constants to long-term seed storage is discussed.

Fungicide and cultivar affect post-anthesis patterns of nitrogen uptake, remobilization and utilization efficiency in wheat

Three successive field experiments (2000/01-2002/03) assessed the effect of wheat cultivar (Consort.. Hereward and Shamrock) and fungicide (epoxiconazole and azoxystrobin) applied at and after flag leaf emergence on the nitrogen in the above-ground crop (Total N) and grain (Grain N), net nitrogen remobilization from non-grain tissues (Remobilized N). grain dry matter (Grain Dill), and nitrogen utilization efficiency (NUtE(g) = Grain DM/Total N). Ordinary logistic curves were fitted to the accumulation of Grain N, Grain DM and Remobilized N against thermal time after anthesis and used to simultaneously derive fits for Total N and NUtE(g). When disease was controlled, Consort achieved the greatest Grain DM, Total N, Grain N and NUtEg; in each case due mostly to longer durations, rather than quicker rates, of accumulation. Fungicide application increased final Grain Dill.. Grant N, Total N and Remobilized N, also mostly through effects on duration rather than rate of accumulation. Completely senesced leaf laminas retained less nitrogen when fungicide had been applied compared with leaf laminas previously infected severely with brown rust (Puccinia recondita) and Septoria tritici, or with just S. tritici. Late movement of nitrogen out of fungicide-treated laminas contributed to extended duration of both nitrogen remobilization and grain N filling, and meant that increases in NUtE(g) could occur without simultaneous reductions in grain N concentration.

Livelihood diversification and moneylending in a Rajasthan village: what lessons for rural financial services?

The complexity of rural economies in developing countries is increasingly recognised, as is the need to tailor poverty reduction policies according to the diversity of rural households and their requirements. By reference to a village in Western India, the paper examines the results of a longitudinal micro-level research approach, employed for the study of livelihood diversification and use of informal finance. Over a 25-year period, livelihoods are shown to have become more complex, in terms of location, types of non-farm activities, and combinations of activities. Moreover, livelihood pathways taken continue to be critically affected by economic and social inequalities implicit in the caste system and tribal economy. A longitudinal micro-level research approach is shown to be one that can effectively identify the many complexities of rural livelihoods and the continued dependence on the informal financial sector, providing important insights into the requirements for rural financial products and services.

Plumatella geimermassardi, a newly recognized freshwater bryozoan from Britain, Ireland, and continental Europe (Bryozoa : Phylactolaemata)

Plumatella geimermassardi is a newly recognized species of phylactolaemate bryozoan. Its known range extends from Ireland east through southern Norway and south into Italy. Colonies grow close to the substrate with little free branching; the body wall is mostly transparent and without an obvious raphe. Floatoblasts are broadly oval and relatively small, with distinctively large dorsal fenestra and uniformly narrow ventral annulus. The sessoblast basal valve is low and dish-shaped; the annulus bears tubercles which vary in their prominence. This species brings to 14 the number of phylactolaemate bryozoans known in the region.