An algorithm for solving sparse Nonlinear Least Squares problems

We introduce a new method for solving Nonlinear Least Squares problems when the Jacobian matrix of the system is large and sparse. The main features of the new method are the following:

1. The Gauss-Newton equation is “partially” solved at each iteration using a preconditioned Conjugate Gradient algorithm.
2. The new point is obtained using a two-dimensional trust region scheme, similar to the one introduced by Bulteau and Vial.

We prove global and local convergence results and we present some numerical experiments.     

Current oscillations in austenitic stainless steel induced by the presence of chloride ions

The conditions for current oscillations in austenitic stainless steel (AISI Type 303) in 1M H₂SO₄ containing Cl^? ions are given. The periodic oscillations are produced in a close potential range determined at the active-passive transition region. It requires a non-homogeneous distribution of inclusions and carbides at the metal surface and a concentration range of Cl^? ion where active and passive areas coexist on the metal surface. The constraints at the surface determining these two regions are related to the Cl^? ion competitive adsorption and the local accumulation of corrosion products. Electrochemical data and SEM observations are correlated.     

Surface Areas of Nitrated Hydrotalcites

Hydrotalcites in the nitrate form were prepared using microwave irradiation in the hydrotreatment step. The surface area (BET) of nitrated hydrotalcites was evaluated. Solids were characterized by atomic absorption, X-ray diffraction and BET analysis. Thermal pretreatment temperature determined the surface area of the hydrotalcites.     

Crystallinity and thermal properties of ethylene-1-decene copolymers

Summary Three copolymers of ethylene and 1-decene, covering a wide range of compositions, have been synthesized with a MgCl₂-supported Ziegler-Natta catalyst. The analysis by DSC and X-ray shows a great degree of heterogeneity in these copolymers and appreciable levels of crystallinity, corresponding to the orthorhombic lattice of polyethylene, are present even for very high 1-decene contents.     

PMMA‐modified divinylester/styrene resins: Phase diagrams and morphologies

Binary and ternary experimental cloud‐point curves (CPCs) for systems formulated with a low molar mass synthesized divinylester (DVE) resin, styrene (St), and poly(methyl methacrylate) (PMMA) were determined. The CPCs results were analyzed with the Flory–Huggins (F‐H) thermodynamic model taking into account the polydispersity of the DVE and PMMA components, to calculate the different binary interaction parameters and their temperature dependences. The St‐DVE system is miscible in all the composition range and down to the crystallization temperature of the St; therefore, the interaction parameter expression reported for a higher molar mass DVE was adapted. The interaction parameters obtained were used to calculate the phase diagrams of the St‐PMMA and the DVE‐PMMA binary systems and that of the St‐DVE‐PMMA ternary system at three different temperatures. Quasiternary phase diagrams show liquid–liquid partial miscibility of the St‐PMMA and DVE‐PMMA pairs. At room temperature, the St‐DVE‐PMMA system is miscible at all compositions. Final morphologies of PMMA‐modified cured St‐DVE materials were generated by polymerization‐induced phase separation (PIPS) mechanism from initial homogeneous mixtures. SEM and TEM micrographs were obtained to analyze the generated final morphologies, which showed a direct correlation with the initial miscibility of the system. © 2006 Wiley Periodicals, Inc. J Appl Polym Sci 100: 4539–4549, 2006     

Analysis of pentasodium triphosphate hydration kinetics

The present work analyzes the effect of various factors on the hydration of pentasodium triphosphate. The experimental method is based on application of the hydration test. Technical-quality products with different proportions of phase I and phase II have been used. The variables studied are phase I/phase II ratio, initial temperature, particle size, stirring rate and composition of the slurry (presence of hexahydrate crystals and water hardness). The results have been discussed according to a kinetics model that includes a series of stages of a physical nature (dissolution of anhydrous salt and the crystallization of the hexahydrate), as well as of a chemical nature (solvation of the ions in solution). Crystallization of the hexahydrate may be the controlling stage in the process.     

Influence of the components in the flow properties and physical aging of spray coating PVC plastisols

A study of the rheological properties and aging characteristics of 15 poly(vinyl chloride) (PVC) plastisols formulated for spray coating is made. The influence of the PVC type, plasticizer, filler, diluent, and thixotropic agent is analyzed and discussed in terms of the yield stress value, a shear thinning index, and an aging characterizing parameter.     

Functional properties of a protein product from Caryodendron orinocense (Barinas nut)

The functional properties of Caryodendron orinocense protein product were investigated and compared with those of soybean (Glycina maxima). The product protein content was 24.47 g/100 g (Nx6.25). Solubility increased at both sides of the isoelectric point (pH 4.0) and with increased NaCl concentration up to 0.5M. Compared with soybean flour (50% protein), the protein product exhibited higher water and oil absorption, but lower emulsifying activity, emulsion stability, foaming capacity, and foam stability, the last one increase at higher pH. Emulsifying activity, foaming capacity, and foam stability were ionic strength dependent. C. orinocense protein product increased its emulsifying activity steadily from 0.05M to 0.75M NaCl, while it remained almost constant for soybean flour. Foaming capacity increased drastically at pH 10. The minimum time and concentration to form a gel was 20% in 4 min and 10% in 8 min for the Caryodendron protein product and soybean flour, respectively. The bulk density was 0.5056+/-0.0041 g/mL.     

Coking kinetics of a Cr2O3/Al2O3 catalyst during 1-butene dehydrogenation: Effect of H2 partial pressure

The influence has been studied of the partial pressure of hydrogen (0–30 kPa) upon the coking rate of a Cr₂O₃/Al₂O₃ commercial catalyst during 1-butene dehydrogenation. Coke deposition has been analysed using a monolayer-multilayer reversible coke growth model (MMRC model). This model provides good fits to the experimental data, within the range of partial pressure of H₂ studied, and allows us to estimate the main kinetic parameters involved in the coking-deactivation process. The results obtained reveal a dual effect of hydrogen: competition against 1-butene for the active sites and the removal of coke precursors from the catalyst surface. Bom effects diminish the coking rate as the H₂ partial pressure is increased.     

The photooxidative gelation of cis-1,4- polybutadiene in solution

Irradiation of dilute solution of cis-1,4-polybutadiene in carbon tetrachloride with UV light in the presence of air causes fast formation of white precipitate—insoluble gel. It has been shown that carbon tetrachloride was effective photosensitizer for oxidation of cis-1,4-polybutadiene. Separated sol and gel fractions were analysed by infrared spectroscopy for better understanding of gelation process and structure of the gel. Three stages were detected in the process of oxidative photogelation of cis-1,4-polybutadiene in carbon tetrachloride solution: pre-gelation(sol-stage), gelation (sol/gel-stage) and post-gelation (gel-stage). In the first stage intensive photooxidative reactions between cis-1,4-polybutadiene, carbon tetrachloride and oxygen take place, giving products with high content of hydroperoxide and bounded chlorine. When hydroperoxide and chlorine content reached critical value, precipitation-gelation takes place. It is proposed sequence of free radical reactions which involves: photolysis of carbon tetrachloride to free radicals, addition of solvent radicals to the double bonds of rubber followed by combining of resulting radicals with oxigen to chlorinated polymeric peroxy radicals. Initially formed gel is peroxidic in nature, which photolyses to the more stabile ether gel by prolonged irradiation.