The nonlinear optimization problem in heat conduction

In this paper we study the existence and geometric properties of an optimal configuration to a nonlinear optimization problem in heat conduction. The quantity to be minimized is , where D is a fixed domain. A nonconstant temperature distribution is prescribed on and a volume constraint on the set where the temperature is positive is imposed. Among other regularity properties of an optimal configuration, we prove analyticity of the free boundary.Received: 6 October 2004, Accepted: 19 October 2004, Published online: 22 December 2004     

Chromotropic acid-functionalized polyurethane foam: A new sorbent for on-line preconcentration and determination of cobalt and nickel in lettuce samples

A chromotropic acid-functionalized polyurethane foam has been developed for use in an on-line preconcentration system for cobalt and nickel determination. The packing material was prepared by covalent coupling of chromotropic acid with the polyurethane foam through an azo group. Co and Ni ions were sorbed in the mini-column, from which they could be eluted directly to the nebulizer-burner system of a flame atomic absorption spectrometer. Elution of cobalt and nickel from the mini-column can be accomplished with 0.50 and 0.75 M HCl solutions, respectively. The enrichment factors obtained were 22 (Co) and 27 (Ni), for 60 s preconcentration time, and 57 (Co) and 59 (Ni), if a preconcentration time of 180 s was used. Under the optimum conditions, the proposed procedure allowed the determination of metals with detection limits of 0.43 (cobalt) and 0.52 microg/L (nickel), respectively, on using preconcentration periods of 180 s. The accuracy of the developed procedure was evaluated by analysis of the certified reference materials NIST 1515 Apple Leaves and NIST 1570a Spinach Leaves. The method was applied to the analysis of lettuce samples. The contents of cobalt in the samples analyzed varied from 0.75 to 0.98 microg/g. Nickel was not detected in the lettuce samples.     

Infrared study of the acidic and basic forms of betaxolol

Betaxolol and its respective hydrochloride salt were studied in solution by computational calculations and infrared spectroscopy. The solution molecular conformations were taken to be the same as those exhibited by the compounds in the solid state given by X-ray diffraction and calculated after full geometry optimization by ab initio Hartree-Fock methods using the 6-31G(d) basis set. Infrared spectra of carbon tetrachloride solutions provide valuable information on the structure of the compounds in non-polar solvents at different concentrations.     

Synthesis and structural characterization of 1- and 2-substituted indazoles: ester and carboxylic acid derivatives

A series of indazoles substituted at the N-1 and N-2 positions with ester-containing side chains -(CH2)(n)CO2R of different lengths (n = 0-6, 9, 10) are described.Nucleophilic substitution reactions on halo esters (X(CH2)(n)CO2R) by 1H-indazole inalkaline solution lead to mixtures of N-1 and N-2 isomers, in which the N-1 isomer predominates. Basic hydrolysis of the ester derivatives allowed the synthesis of the corresponding indazole carboxylic acids. All compounds were fully characterised by multinuclear NMR and IR spectroscopies, MS spectrometry and elemental analysis; the NMR spectroscopic data were used for structural assignment of the N-1 and N-2 isomers.The molecular structure of indazol-2-yl-acetic acid (5b) was determined by X-ray diffraction, which shows a supramolecular architecture involving O2-H...N1 intermolecular hydrogen bonds.     

Critical exponents for Fréedericskz transition in nematics between concentric cylinders

The equilibrium tilt angle profile in a cell limited by two concentric cylinders filled with nematic liquid crystals is determined for strong homeotropic anchoring at the surfaces. The anchoring condition is such that the nematic director is perpendicular to the cylinder axes and a radial nonuniform electric field is applied to investigate a Fréedericksz transition. The distortions induced by the field remain in the plane perpendicular to the cylinder axes, and a threshold field is analytically determined indicating a transition from a pure splay to a splay-bend conformation of the director. It is shown that this transition can be induced by the thickness of the region between the two cylinders, and can be detected even in the absence of an external field. If the maximum value of the tilt angle is assumed as an order parameter, its behavior near to the transition can be used to obtain the critical exponent, which is the same as the one obtained in the mean field approximation. These results are indications that nontrivial consequences may occur when complex fluids are subject to non-planar geometries.     

Nematics in Hybrid Cylindrical Cells

A hybrid (weak-strong anchoring) cylindrical cell with antagonistic boundary conditions (planar–homeotropic) at the outer confining surface and at a central coaxial cylindrical core and filled with nematic liquid crystals is investigated by means of the Elastic Theory and Monte Carlo Simulations. The director orientation profile on the surface characterized by weak anchoring is built as a function of the extrapolation length and other relevant parameters. By considering the angle on the surface as an order parameter, a transition in the orientation is found when the extrapolation length becomes smaller than a critical value and the orientation of the surface with strong anchoring is dominant. The order parameter critical exponent is numerically calculated, and the mean field value (β≈1/2) is found in all cases. These transitions are essentially confirmed by Monte Carlo simulations even if some numerical discrepancies are found. The analysis show similarities between planar and cylindrical geometries, but non-usual consequences are found more easily in the latter one.     

Sample Preparation for the Determination of Metals in Food Samples Using Spectroanalytical Methods—A Review

Abstract

The present article gives an overview of recent publications and modern techniques of sample preparation for food analysis employing atomic and inorganic mass spectrometric techniques, such as flame atomic absorption spectrometry, chemical vapor generation atomic absorption and atomic fluorescence spectrometry, graphite furnace atomic absorption spectrometry, inductively coupled plasma optical emission spectrometry, and inductively coupled plasma mass spectrometry. Among the most frequently applied sample preparation techniques for food analysis are dry ashing, usually with the addition of an ashing aid, and acid digestion, preferably with the assistance of microwave energy. Slurry preparation, particularly with the assistance of ultrasound, is increasingly used to reduce acid consumption and sample preparation time. Direct analysis of solid samples is gaining importance in the field of food analysis as it offers the highest sensitivity, avoids the use of acids and other aggressive reagents, makes possible the analysis of micro‐samples, and can be applied for fast screening analysis, e.g., of fresh meat.     

Structural characterization of MnNi and MnPt antiferromagnetic materials for spintronic applications

MnNi and MnPt become antiferromagnetic (AFM) when annealed at high enough temperatures, for which a face-centered cubic (fcc) to face-centered tetragonal (fct) structural transition occurs. Thus, structural information is essential when optimizing exchange bias in these materials. We performed structural (X-ray diffraction), magnetic (Magneto-Optical Kerr effect) and magneto-transport (magnetoresistance) measurements on MnNi based spin valves subjected to different annealing procedures and MnPt/CoFe bilayers with different MnPt thicknesses. We show that high annealing temperatures can in fact lead to the fct antiferromagnetic phase in both materials, but the annealing procedure is also an important factor on the obtained exchange field values. Also, MnPt/CoFe bilayers allowed us to probe the influence of average AFM-grain size on exchange bias.