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.

Singularities of optimal control problems on some 6-D lie groups

This paper considers the motion planning problem for oriented vehicles travelling at unit speed in a 3-D space. A Lie group formulation arises naturally and the vehicles are modeled as kinematic control systems with drift defined on the orthonormal frame bundles of particular Riemannian manifolds, specifically, the 3-D space forms Euclidean space E-3, the sphere S-3, and the hyperboloid H'. The corresponding frame bundles are equal to the Euclidean group of motions SE(3), the rotation group SO(4), and the Lorentz group SO (1, 3). The maximum principle of optimal control shifts the emphasis for these systems to the associated Hamiltonian formalism. For an integrable case, the extremal curves are explicitly expressed in terms of elliptic functions. In this paper, a study at the singularities of the extremal curves are given, which correspond to critical points of these elliptic functions. The extremal curves are characterized as the intersections of invariant surfaces and are illustrated graphically at the singular points. It. is then shown that the projections, of the extremals onto the base space, called elastica, at these singular points, are curves of constant curvature and torsion, which in turn implies that the oriented vehicles trace helices.