Stirring in 3-d spherical models of convection in the Earth's mantle

On a global scale basalts from mid-ocean ridges are strikingly more homogeneous than basalts from intraplate volcanism. The observed geochemical heterogeneity argues strongly for the existence of distinct reservoirs in the Earth's mantle. It is an unresolved problem of Geodynamics as to how these findings can be reconciled with large-scale convection. We review observational constraints, and investigate stirring properties of numerical models of mantle convection. Conditions in the early Earth may have supported layered convection with rapid stirring in the upper layers. Material that has been altered near the surface is transported downwards by small-scale convection. Thereby a layer of homogeneous depleted material develops above pristine mantle. As the mantle cools over Earth history, the effects leading to layering become reduced and models show the large-scale convection favoured for the Earth today. Laterally averaged, the upper mantle below the lithosphere is least affected by material that has experienced near-surface differentiation. The geochemical signature obtained during the previous episode of small-scale convection may be preserved there for the longest time. Additionally, stirring is less effective in the high viscosity layer of the central lower mantle [1, 2], supporting the survival of medium-scale heterogeneities there. These models are the first, using 3-d spherical geometry and mostly Earth-like parameters, to address the suggested change of convective style. Although the models are still far from reproducing our planet, we find that proposal might be helpful towards reconciling geochemical and geophysical constraints.

Robust multivariable control of complex biological processes

This paper addresses advanced control of a biological nutrient removal (BNR) activated sludge process. Based on a previously validated distributed parameter model of the BNR activated sludge process, we present robust multivariable controller designs for the process, involving loop shaping of plant model, robust stability and performance analyses. Results from three design case studies showed that a multivariable controller with stability margins of 0.163, 0.492 and 1.062 measured by the normalised coprime factor, multiplicative and additive uncertainties respectively give the best results for meeting performance robustness specifications. The controller robustly stabilises effluent nutrients in the presence of uncertainties with the behaviour of phosphorus accumulating organisms as well as to effectively attenuate major disturbances introduced as step changes. This study also shows that, performance of the multivariable robust controller is superior to multi-loops SISO PI controllers for regulating the BNR activated sludge process in terms of robust stability and performance and controlling the process using inlet feed flowrate is infeasible. (C) 2003 Elsevier Ltd. All rights reserved.