Preconditioning and iterative solution of symmetric indefinite linear systems arising from interior point methods for linear programming

We study the preconditioning of symmetric indefinite linear systems of equations that arise in interior point solution of linear optimization problems. The preconditioning method that we study exploits the block structure of the augmented matrix to design a similar block structure preconditioner to improve the spectral properties of the resulting preconditioned matrix so as to improve the convergence rate of the iterative solution of the system. We also propose a two-phase algorithm that takes advantage of the spectral properties of the transformed matrix to solve for the Newton directions in the interior-point method. Numerical experiments have been performed on some LP test problems in the NETLIB suite to demonstrate the potential of the preconditioning method discussed.

Ring-chain interconversion in high-performance polymer systems. 3. Cyclodepolymerization of poly(m-phenylene isophthalamide) (Nomex) and entropically driven ring-opening polymerization of the macrocyclic oligomers so produced

A homologous series of macrocyclic oligoamides has been prepared in high yield by reaction of isophthaloyl chloride with m-phenylenediamine under pseudo-high-dilution conditions. The products were characterized by infrared and H-1 NMR spectroscopies, matrix assisted laser desorption-ionization time-of-flight mass spectrometry, and gel permeation chromatography (GPC). A series of linear oligomers was prepared for comparison. The macrocycles ranged in size from the cyclic trimer up to at least the cyclic nonamer (90 ring atoms). The same homologous series of macrocyclic oligomers was prepared in high yield by the cyclodepolymerization of poly(m-phenylene isophthalamide) (Nomex). Cyclodepolymerization was best achieved by treating a 1% w/v solution of the polymer in dimethyl sulfoxide containing calcium chloride or lithium chloride with 3-4 mol % of sodium hydride or the sodium salt of benzanilide at 150 degreesC for 70 h. Treatment of a concentrated solution of the macrocyclic oligomers (25% w/v) with 4 mol % of sodium hydride or the sodium salt of benzanilide in a solution of lithium chloride in dimethyl sulfoxide at 170 degreesC for 6 h resulted in efficient entropically driven ring-opening polymerizations to give poly(m-phenylene isophthalamide), characterized by infrared and H-1 NMR spectroscopies and by GPC. The molecular weights obtained were comparable with those of the commercial polymer.

Parallel Monte Carlo approach for integration of the rendering equation

This paper is addressed to the numerical solving of the rendering equation in realistic image creation. The rendering equation is integral equation describing the light propagation in a scene accordingly to a given illumination model. The used illumination model determines the kernel of the equation under consideration. Nowadays, widely used are the Monte Carlo methods for solving the rendering equation in order to create photorealistic images. In this work we consider the Monte Carlo solving of the rendering equation in the context of the parallel sampling scheme for hemisphere. Our aim is to apply this sampling scheme to stratified Monte Carlo integration method for parallel solving of the rendering equation. The domain for integration of the rendering equation is a hemisphere. We divide the hemispherical domain into a number of equal sub-domains of orthogonal spherical triangles. This domain partitioning allows to solve the rendering equation in parallel. It is known that the Neumann series represent the solution of the integral equation as a infinity sum of integrals. We approximate this sum with a desired truncation error (systematic error) receiving the fixed number of iteration. Then the rendering equation is solved iteratively using Monte Carlo approach. At each iteration we solve multi-dimensional integrals using uniform hemisphere partitioning scheme. An estimate of the rate of convergence is obtained using the stratified Monte Carlo method. This domain partitioning allows easy parallel realization and leads to convergence improvement of the Monte Carlo method. The high performance and Grid computing of the corresponding Monte Carlo scheme are discussed.

Approximate Riemann solutions of the two-dimensional shallow-water equations

A finite-difference scheme based on flux difference splitting is presented for the solution of the two-dimensional shallow-water equations of ideal fluid flow. A linearised problem, analogous to that of Riemann for gasdynamics, is defined and a scheme, based on numerical characteristic decomposition, is presented for obtaining approximate solutions to the linearised problem. The method of upwind differencing is used for the resulting scalar problems, together with a flux limiter for obtaining a second-order scheme which avoids non-physical, spurious oscillations. An extension to the two-dimensional equations with source terms, is included. The scheme is applied to a dam-break problem with cylindrical symmetry.

Numerical solution of some nonlocal, nonlinear dispersive wave equations

We use a spectral method to solve numerically two nonlocal, nonlinear, dispersive, integrable wave equations, the Benjamin-Ono and the Intermediate Long Wave equations. The proposed numerical method is able to capture well the dynamics of the solutions; we use it to investigate the behaviour of solitary wave solutions of the equations with special attention to those, among the properties usually connected with integrability, for which there is at present no analytic proof. Thus we study in particular the resolution property of arbitrary initial profiles into sequences of solitary waves for both equations and clean interaction of Benjamin-Ono solitary waves. We also verify numerically that the behaviour of the solution of the Intermediate Long Wave equation as the model parameter tends to the infinite depth limit is the one predicted by the theory.

In vitro examination of the effect of Orlistat on the ability of the faecal microbiota to utilize dietary lipids

Orlistat is an anti-obesity treatment with which several gastrointestinal (GI) side-effects are commonly associated in the initial stages of therapy. There is no physiological explanation as to why two-thirds of those who take the drug experience one or more side-effects. It has been hypothesized that the GI microbiota may protect from or contribute to these GI disturbances. Using in vitro batch culture and human gut model systems, studies were conducted to determine whether increased availability of dietary lipids and/or orlistat affect the composition and/or activity of the faecal microbiota. Results from 24-h batch culture fermentation experiments demonstrated no effect of orlistat in the presence or absence of a dietary lipid (olive oil) on the composition of bacterial communities [as determined by fluorescence in situ hybridization (FISH) and denaturing gradient gel electrophoresis (DGGE) analyses], but did show there was great variability in the lipolytic activities of the microbiotas of individuals, as determined by gas chromatography analysis of long-chain fatty acids in samples. Subsequent studies focused on the effect of orlistat in the presence and absence of lipid in in vitro human gut model systems. Systems were run for 14 days with gut model medium (GMM) only (to steady state, SS), then fed at 12-h intervals with 50 mg orlistat, 2 g olive oil or a mixture of both for 14 days. FISH and DGGE were used to monitor changes in bacterial populations. Bacteria were cultivated from the GMM only (control) systems at SS. All strains isolated were screened for lipolytic activity using tributyrin agar. FISH and DGGE demonstrated that none of the compounds (singly or in combination) added to the systems had any notable effect on microbial population dynamics for any of the donors, although Subdoligranulum populations appeared to be inhibited by orlistat in the presence or absence of lipid. Orlistat had little or no effect on the metabolism of indigenous and added lipids in the fermentation systems, but there was great variability in the way the faecal microbiotas of the donors were able to degrade added lipids. Variability in lipid degradation could be correlated with the number and activity of isolated lipolytic bacteria. The mechanism by which orlistat and the GI microbiota cause side-effects in individuals is unknown, but several hypotheses have been proposed to account for their manifestation. The demonstration of great variability in the lipolytic activity of microbiotas to degrade lipids led to a large-scale cultivation-based study of lipolytic/lipase-positive bacteria present in the human faecal microbiota. Of 4,000 colonies isolated from 15 donors using five different agars, 378 strains were identified that had lipase activity. Molecular identification of strains isolated from five donors demonstrated that lipase activity is more prevalent in the human GI microbiota than previously thought, with members of the phyla Firmicutes, Bacteroidetes and Actinobacteria identified. Molecular identification and characterization of the substrate specificities of the strains will be carried out as part of ongoing work.

Synthesis, X-ray crystal structure and reactivity of the polymeric copper(II) dicarboxylic acid complex {Cu2(η1η1μ2-oda)2(py)4(H2O)2}n(odaH2 = octanedioic acid, PY = pyridine)

An aqueous solution of the α-ω-dicarboxylic acid octanedioic acid (odaH2) reacts with [Cu2(μ-O2CCH3)4(H2O)2] in the presence of an excess of pyridine (py) to give the crystalline copper(II) complex {Cu2(η1η1μ2-oda)2(py)4(H2O)2}n (1). structure of 1, as determined by X-ray crystallography, consists of polymeric chains in which bridging oda2− anions link two crystallographically identical copper atoms. The copper atoms are also ligated by two transoidal pyridine nitrogens and an oxygen atom from an apical water molecule, giving the metals an overall N2O3 square-pyramidal geometry. If the blue solid 1 is gently heated, or if it is left to stand in its mother liquor for prolonged periods, it loses one molecule of pyridine and half a molecule of water and the green complex {Cu (oda)(py)(H2O)0.5}n (2) is formed. Spectroscopic and magnetic data for both complexes are given, together with the electrochemical and thermogravimetric measurements for 1.

Approximate solution of second kind integral equations on infinite cylindrical surfaces

The paper considers second kind integral equations of the form $\phi (x) = g(x) + \int_S {k(x,y)} \phi (y)ds(y)$ (abbreviated $\phi = g + K\phi $), in which S is an infinite cylindrical surface of arbitrary smooth cross section. The “truncated equation” (abbreviated $\phi _a = E_a g + K_a \phi _a $), obtained by replacing S by $S_a $, a closed bounded surface of class $C^2 $, the boundary of a section of the interior of S of length $2a$, is also discussed. Conditions on k are obtained (in particular, implying that K commutes with the operation of translation in the direction of the cylinder axis) which ensure that $I - K$ is invertible, that $I - K_a $ is invertible and $(I - K_a )^{ - 1} $ is uniformly bounded for all sufficiently large a, and that $\phi _a $ converges to $\phi $ in an appropriate sense as $a \to \infty $. Uniform stability and convergence results for a piecewise constant boundary element collocation method for the truncated equations are also obtained. A boundary integral equation, which models three-dimensional acoustic scattering from an infinite rigid cylinder, illustrates the application of the above results to prove existence of solution (of the integral equation and the corresponding boundary value problem) and convergence of a particular collocation method.

Gaussian anamorphosis in the analysis step of the EnKF: a joint state-variable/observation approach

The analysis step of the (ensemble) Kalman filter is optimal when (1) the distribution of the background is Gaussian, (2) state variables and observations are related via a linear operator, and (3) the observational error is of additive nature and has Gaussian distribution. When these conditions are largely violated, a pre-processing step known as Gaussian anamorphosis (GA) can be applied. The objective of this procedure is to obtain state variables and observations that better fulfil the Gaussianity conditions in some sense. In this work we analyse GA from a joint perspective, paying attention to the effects of transformations in the joint state variable/observation space. First, we study transformations for state variables and observations that are independent from each other. Then, we introduce a targeted joint transformation with the objective to obtain joint Gaussianity in the transformed space. We focus primarily in the univariate case, and briefly comment on the multivariate one. A key point of this paper is that, when (1)-(3) are violated, using the analysis step of the EnKF will not recover the exact posterior density in spite of any transformations one may perform. These transformations, however, provide approximations of different quality to the Bayesian solution of the problem. Using an example in which the Bayesian posterior can be analytically computed, we assess the quality of the analysis distributions generated after applying the EnKF analysis step in conjunction with different GA options. The value of the targeted joint transformation is particularly clear for the case when the prior is Gaussian, the marginal density for the observations is close to Gaussian, and the likelihood is a Gaussian mixture.

The slowly evolving background state of the atmosphere

The theory of wave–mean flow interaction requires a partition of the atmospheric flow into a notional background state and perturbations to it. Here, a background state, known as the Modified Lagrangian Mean (MLM), is defined as the zonally symmetric state obtained by requiring that every potential vorticity (PV) contour lying within an isentropic layer encloses the same mass and circulation as in the full flow. For adiabatic and frictionless flow, these two integral properties are time-invariant and the MLM state is a steady solution of the primitive equations. The time dependence in the adiabatic flow is put into the perturbations, which can be described by a wave-activity conservation law that is exact even at large amplitude. Furthermore, the effects of non-conservative processes on wave activity can be calculated from the conservation law. A new method to calculate the MLM state is introduced, where the position of the lower boundary is obtained as part of the solution. The results are illustrated using Northern Hemisphere ERA-Interim data. The MLM state evolves slowly, implying that the net non-conservative effects are weak. Although ‘adiabatic eddy fluxes’ cannot affect the MLM state, the effects of Rossby-wave breaking, PV filamentation and subsequent dissipation result in sharpening of the polar vortex edge and meridional shifts in the MLM zonal flow, both at tropopause level and on the winter stratospheric vortex. The rate of downward migration of wave activity during stratospheric sudden warmings is shown to be given by the vertical scale associated with polar vortex tilt divided by the time-scale for wave dissipation estimated from the wave-activity conservation law. Aspects of troposphere–stratosphere interaction are discussed. The new framework is suitable to examine the climate and its interactions with disturbances, such as midlatitude storm tracks, and makes a clean partition between adiabatic and non-conservative processes.

Conditioning of the weak-constraint variational data assimilation problem for numerical weather prediction

4-Dimensional Variational Data Assimilation (4DVAR) assimilates observations through the minimisation of a least-squares objective function, which is constrained by the model flow. We refer to 4DVAR as strong-constraint 4DVAR (sc4DVAR) in this thesis as it assumes the model is perfect. Relaxing this assumption gives rise to weak-constraint 4DVAR (wc4DVAR), leading to a different minimisation problem with more degrees of freedom. We consider two wc4DVAR formulations in this thesis, the model error formulation and state estimation formulation. The 4DVAR objective function is traditionally solved using gradient-based iterative methods. The principle method used in Numerical Weather Prediction today is the Gauss-Newton approach. This method introduces a linearised `inner-loop' objective function, which upon convergence, updates the solution of the non-linear `outer-loop' objective function. This requires many evaluations of the objective function and its gradient, which emphasises the importance of the Hessian. The eigenvalues and eigenvectors of the Hessian provide insight into the degree of convexity of the objective function, while also indicating the difficulty one may encounter while iterative solving 4DVAR. The condition number of the Hessian is an appropriate measure for the sensitivity of the problem to input data. The condition number can also indicate the rate of convergence and solution accuracy of the minimisation algorithm. This thesis investigates the sensitivity of the solution process minimising both wc4DVAR objective functions to the internal assimilation parameters composing the problem. We gain insight into these sensitivities by bounding the condition number of the Hessians of both objective functions. We also precondition the model error objective function and show improved convergence. We show that both formulations' sensitivities are related to error variance balance, assimilation window length and correlation length-scales using the bounds. We further demonstrate this through numerical experiments on the condition number and data assimilation experiments using linear and non-linear chaotic toy models.

The role of an insulating surface layer on the relaxation time of the ionic redistribution in an electrolytic cell

We analyze the influence of a surface dielectric layer on the transient phenomena related to the ionic redistribution in an electrolytic cell submitted to a step-like external voltage. The adsorption-desorption phenomenon is taken into account in the famework of the Gouy-Chapman approximation, where the ions are assumed dimensionless. In the limit of small amplitude of the applied voltage, where the equations of the problem can be linearized, we obtain an analytical solution for the surface densities of ions, for the electrical potential and for the relaxation time for the transient phenomena. In the general case, when the linearized analysis is no longer valid, the solution of the problem is obtained numerically. The role of the thickness of the dielectric layer on the relaxation time is also discussed.

Thermal treatment of superconductor thin film of the BSCCO system using domestic microwave oven

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Influence of physical and chemical factors during foraging and culture of the symbiont fungus in Atta sexdens rubropilosa (Hymenoptera : Formicidae)

The aim of this paper is to investigate the influence of physical and chemical factors on transport and use of substrate for Atta sexdens rubropilosa workers. Three types of rectangular fragments were used to study the physical influence factors: filter paper with paraffin, filter paper without paraffin and polyester film. To study the chemical factors, some fragments were impregnated with organic extract of orange albedo, others were soaked with soybean oil and for the remaining ones nothing was applied. The following parameters were evaluated: (i) attractiveness of substrate for transport and number of loading workers per treatment; (ii) foraged material incorporation; (iii) rejection by numbers of fragments deposited in the garbage or beside the fungus garden. All the polyester film fragments carried out to the fungus garden were subsequently rejected. We verified that chemical factors of the substrate were more quickly detected by the workers, whereas physical factors were used as a criterion in the decision-making to reject or accept the substrate collected.

Preliminary data on the feeding habits of the freshwater stingrays Potamotrygon falkneri and Potamotrygon motoro (Potamotrygonidae) from the Upper Paraná River basin, Brazil

As raias da família Potamotrygonidae representam um grupo singular da ictiofauna Neotropical. Apesar de serem antigos os relatos sobre o grupo, ainda são muitas as questões que permanecem sem resposta, sobretudo no que diz respeito à biologia das espécies que ocorrem na Bacia do Paraná-Paraguai. No presente trabalho foi analisada a dieta de Potamotrygon falkneri e Potamotrygon motoro, capturadas no Alto Rio Paraná, a jusante da Usina Hidrelétrica Engenheiro Souza Dias (UHE Jupiá). As duas espécies de raias apresentaram dieta diversificada, ingerindo 14 itens, entre moluscos, crustáceos, insetos e peixes, porém com predominância de insetos aquáticos em diversidade e abundância. Somente um indivíduo de cada espécie ingeriu peixe. Potamotrygon motoro consumiu principalmente Ephemeroptera, enquanto P. falkneri, principalmente Mollusca, Hemiptera e Trichoptera. Os dados aparentemente indicam uma dieta mais especializada de P. motoro, com maior consumo de Ephemeroptera (Baetidae), e uma dieta mais generalizada de P. falkneri. A análise dos indivíduos capturados em três micro-hábitats, que diferem quanto ao tipo de substrato e presença de vegetação marginal, sugere diferenças nos tipos de alimentos consumidos.