Approximate Gauss-Newton methods for nonlinear least squares problems

The Gauss–Newton algorithm is an iterative method regularly used for solving nonlinear least squares problems. It is particularly well suited to the treatment of very large scale variational data assimilation problems that arise in atmosphere and ocean forecasting. The procedure consists of a sequence of linear least squares approximations to the nonlinear problem, each of which is solved by an “inner” direct or iterative process. In comparison with Newton’s method and its variants, the algorithm is attractive because it does not require the evaluation of second-order derivatives in the Hessian of the objective function. In practice the exact Gauss–Newton method is too expensive to apply operationally in meteorological forecasting, and various approximations are made in order to reduce computational costs and to solve the problems in real time. Here we investigate the effects on the convergence of the Gauss–Newton method of two types of approximation used commonly in data assimilation. First, we examine “truncated” Gauss–Newton methods where the inner linear least squares problem is not solved exactly, and second, we examine “perturbed” Gauss–Newton methods where the true linearized inner problem is approximated by a simplified, or perturbed, linear least squares problem. We give conditions ensuring that the truncated and perturbed Gauss–Newton methods converge and also derive rates of convergence for the iterations. The results are illustrated by a simple numerical example. A practical application to the problem of data assimilation in a typical meteorological system is presented.

The effect of thermal conductivity of RIM moulds in kinetics cure

Reaction Injection Moulding (RIM) is a moulding technology used for the production of large size and complex plastic parts. The RIM process is characterized essentially by the injection of a highly reactive chemical system (usually polyurethane) and fast cure, in a mould properly closed and thermally controlled. Several studies show that rapid manufacturing moulds obtained in epoxy resins for Thermoplastic Injection Moulding (TIM) affect the moulding process and the final properties of parts. The cycle time and mechanical properties of final parts are reduced, due to a low thermal conductivity of epoxy materials. In contrast, the low conductivity of materials usually applied for the rapid manufacturing of RIM moulds, increase the mechanical properties of final injected parts and reduce the cycle time. This study shows the effect of the rapid manufacturing moulds material during the RIM process. Several materials have been tested for rapid manufacturing of RIM moulds and the analysis of both, temperature profile of moulded parts during injection and the cure data experimentally obtained in a mixing and reaction cell, allow to determine and model the real effect of the mould material on the RIM process.

Synthesis and characterization of thermally stable second-order nonlinear optical side-chain polyimides containing thiazole and benzothiazole push-pull chromophores

Push-pull nonlinear optical (NLO) chromophores containing thiazole and benzothiazole acceptors were synthesized and characterized. Using these chromophores a series of second-order NLO polyimides were Successfully prepared from 4,4'-(hexafluoroisopropylidene) diphthalic anhydride (6FDA), pyromellitic dianhydride (PMDA) and 3,3'4,4'-benzophenone tetracarboxylic dianhydride (BTDA) by a standard condensation polymerization technique. These polyimides exhibit high glass transition temperatures ranging from 160 to 188 degrees C. UV-vis spectrum of polyimide exhibited a slight blue shift and decreases in absorption due to birefringence. From the order parameters, it was found that chromophores were aligned effectively. Using in situ poling and temperature ramping technique, the optical temperatures for corona poling were obtained. It was found that the optimal temperatures of polyimides approach their glass transition temperatures. These polyimides demonstrate relatively large d(33) values range between 35.15 and 45.20 pm/V at 532 nm. (C) 2008 Elsevier B.V. All rights reserved.

Stochastic resonance in a nonlinear model of a rotating, stratified shear flow, with a simple stochastic inertia-gravity wave parameterization

We report on a numerical study of the impact of short, fast inertia-gravity waves on the large-scale, slowly-evolving flow with which they co-exist. A nonlinear quasi-geostrophic numerical model of a stratified shear flow is used to simulate, at reasonably high resolution, the evolution of a large-scale mode which grows due to baroclinic instability and equilibrates at finite amplitude. Ageostrophic inertia-gravity modes are filtered out of the model by construction, but their effects on the balanced flow are incorporated using a simple stochastic parameterization of the potential vorticity anomalies which they induce. The model simulates a rotating, two-layer annulus laboratory experiment, in which we recently observed systematic inertia-gravity wave generation by an evolving, large-scale flow. We find that the impact of the small-amplitude stochastic contribution to the potential vorticity tendency, on the model balanced flow, is generally small, as expected. In certain circumstances, however, the parameterized fast waves can exert a dominant influence. In a flow which is baroclinically-unstable to a range of zonal wavenumbers, and in which there is a close match between the growth rates of the multiple modes, the stochastic waves can strongly affect wavenumber selection. This is illustrated by a flow in which the parameterized fast modes dramatically re-partition the probability-density function for equilibrated large-scale zonal wavenumber. In a second case study, the stochastic perturbations are shown to force spontaneous wavenumber transitions in the large-scale flow, which do not occur in their absence. These phenomena are due to a stochastic resonance effect. They add to the evidence that deterministic parameterizations in general circulation models, of subgrid-scale processes such as gravity wave drag, cannot always adequately capture the full details of the nonlinear interaction.

Exploring the enzymatic landscape: distribution and kinetics of hydrolytic enzymes in soil particle-size fractions

The location of extracellular enzymes within the soil architecture and their association with the various soil components affects their catalytic potential. A soil fractionation study was carried out to investigate: (a) the distribution of a range of hydrolytic enzymes involved in C, N and P transformations, (b) the effect of the location on their respective kinetics, (c) the effect of long-term N fertilizer management on enzyme distribution and kinetic parameters. Soil (silty clay loam) from grassland which had received 0 or 200 kg N ha(-1) yr(-1) was fractionated, and four particle-size fractions (> 200, 200-63, 63-2 and 0. 1-2 mum) were obtained by a combination of wet-sieving and centrifugation, after low-energy ultrasonication. All fractions were assayed for four carbohydrases (beta-cellobiohydrolase, N-acetyl-beta-glucosammidase, beta-glucosidase and beta-xylosidase), acid phosphatase and leucine-aminopeptidase using a microplate fluorimetric assay based on MUB-substrates. Enzyme kinetics (V-max and K-m) were estimated in three particle-size fractions and the unfractionated soil. The results showed that not all particle-size fractions were equally enzymatically active and that the distribution of enzymes between fractions depended on the enzyme. Carbohydrases predominated in the coarser fractions while phosphatase and leucine-aminopeptidase were predominant in the clay-size fraction. The Michaelis constant (K.) varied among fractions, indicating that the association of the same enzyme with different particle-size fractions affected its substrate affinity. The same values of Km were found in the same fractions from the soil under two contrasting fertilizer management regimes, indicating that the Michaelis constant was unaffected by soil changes caused by N fertilizer management. (C) 2004 Elsevier Ltd. All rights reserved.

Uptake kinetics of metals by the earthworm Eisenia fetida exposed to field-contaminated soils

It is well known that earthworms can accumulate metals. However, most accumulation studies focus on Cd-, Cu-, Pb- or Zn-amended soils, additionally few studies consider accumulation kinetics. Here we model the accumulation kinetics of 18 elements by Eisenia fetida, exposed to 8 metal-contaminated and 2 uncontaminated soils. Tissue metal concentration was determined after 3, 7,14, 21, 28 and 42 days. Metal elimination rate was important in determining time to reach steady-state tissue metal concentration. Uptake flux to elimination rate ratios showed less variation and lower values for essential than for non-essential metals. In theory kinetic rate constants are dependent only on species and metal. Therefore it should be possible to predict steady-state tissue metal concentrations on the basis of very few measurements using the rate constants. However, our experiments show that it is difficult to extrapolate the accumulation kinetic constants derived using one soil to another. (C) 2009 Elsevier Ltd. All rights reserved.

Did they talk their way out of Africa?

Corballis suggests that fully vocal communication was invented by modern humans between 170,000 and 50,000 years ago. Because this new form of communication did not require hand gestures, he wondered whether this may have facilitated the development of lithic manufacture. I cast doubt on this interesting notion but offer an enhanced version that may have more potential.

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.