A novel approach to obtain analytical-numerical solutions of nonlinear Lorenz system

In this research we apply an analytic approach to solve the well-known Lorenz system in the non-chaotic regime. The proposed approach is based on modal expansion by infinite series. The analytical-numerical results show that for real initial conditions and under the non-convective regime the modal expansion series reproduce correctly the dynamical behavior of the solution of the Lorenz system. The validity and reliability of the proposed analytical approach with few terms is tested by its application to the convective and non-convective regime with various parameter values. The main advantage is that the obtained solution is global and is presented in analytical form.     

A new Eu(III)/Tb(III) binuclear coordination compound with crown ethers and bridging 4,4′-dipyridyl

A new Eu(III)/Tb(III) binuclear coordination compound with red and yellow emissions in solution and solid state, respectively, has been prepared. The lanthanide (Ln) ions are coordinated to crown ethers (C) and bridged by a dipyridyl (dipy) ligand. Ln/C and Ln/C/dipy complexes were also synthesized as precursors for the bimetallic compounds. The homo- and heterobimetallic Ln(III) complexes were characterized by elemental analysis as well as infra-red, absorption (UV-visible) and emission spectroscopies. The heterobimetallic complex geometry was predicted using the Sparkle/AM1 model and suggested to a chemical environment of very low symmetry around the lanthanide ions (C₁), in agreement with the luminescence spectrum. The Eu(III) and Tb(III) complexes display intense red and green emissions, respectively, in the solid state at room temperature.     

Harmonic Generation Via χ3 Intermodal Phase Matching in Microfibers

Abstract

Intermodally phase-matched up- and down-conversion processes based on third-order non-linearity have been proposed to efficiently generate light in the ultraviolet (UV) and mid-infrared (IR) wavelength regions in solid-core silica optical fibers and optical microfibers. Waveguide parameters and practical considerations required for optimum conversion are studied.     

Facile Formation of Redox‐Active Totally Organic Nanoparticles in Water by In Situ Reduction of Organic Precursors Stabilized through Aromatic–Aromatic Interactions by Aromatic Polyelectrolytes

The formation of redox‐active, totally organic nanoparticles in water is achieved following a strategy similar to that used to form metal nanoparticles. It is based on two fundamental concepts: i) complexation through aromatic–aromatic interactions of a water‐soluble precursor aromatic molecule with polyelectrolytes bearing complementary charged aromatic rings, and ii) reduction of the precursor molecule to achieve stabilized nanoparticles. Thus, formazan nanoparticles are synthesized by reduction of a tetrazolium salt with ascorbic acid using polyelectrolytes bearing benzene sulfonate residues of high linear aromatic density, but cannot be formed in the presence of nonaromatic polyelectrolytes. The red colored nanoparticles are efficiently encapsulated in calcium alginate beads, showing macroscopic homogeneity. Bleaching kinetics with chlorine show linear rates on the order of tenths of milli­meters per minute. A linear behavior of the dependence of the rate of bleaching on the chlorine concentration is found, showing the potential of the nanoparticles for chlorine sensing.

     

The eigenvalue problem for solitary waves of a boussinesq equation,via a generalization of the rouché theorem

We consider the study of an eigenvalue problem obtained by linearizing about solitary wave solutions of a Boussinesq equation. Instead of using the technique of Evans functions as done by Pego and Weinstein in [R. Pego and M. Weinstein, Convective Linear Stability of Solitary Waves for Boussinesq equation. AMS, 99, 311–375] for this particular problem, we perform Fourier analysis to characterize solutions of the eigenvalue problem in terms of a multiplier operator and use the strong relationship between the eigenvalue problem for the linearized Boussinesq equation and the eigenvalue problem associated with the linearization about solitary wave solutions of a special form of the KdV equation. By using a generalization of the Rouché Theorem and the asymptotic behavior of the Fourier symbol corresponding to the eigenvalues problem for the Boussinesq equation and the Fourier symbol corresponding to the eigenvalues problem for the KdV equation, we show nonexistence of eigenvalues with respect to weighted space in a planar region containing the right-half plane.     

Analysis of cocaine and two metabolites in dried blood spots by liquid chromatography with fluorescence detection: a novel test for cocaine and alcohol intake

An original HPLC method coupled to spectrofluorimetric detection is presented for the simultaneous analysis in dried blood spots (DBS) of cocaine and two important metabolites, namely benzoylecgonine (its main metabolite) and cocaethylene (the active metabolite formed in the presence of ethanol). The chromatographic analysis was carried out on a C8 column, using a mobile phase containing phosphate buffer (pH 3.0)-acetonitrile (85:15, v/v). Native analyte fluorescence was monitored at 315 nm while exciting at 230 nm. A fast and feasible sample pre-treatment was implemented by solvent extraction, obtaining good extraction yields (>91%) and satisfactory precision values (RSD<4.8%). The method was successfully applied to DBS samples collected from some cocaine users, both with and without concomitant ethanol intake. The results were in good agreement with those obtained from plasma samples subjected to an original solid-phase extraction procedure on C8 cartridges. The method has demonstrated to be suitable for the monitoring of cocaine/ethanol use by means of DBS or plasma testing. Assays are in progress to apply this method on the street, for the control of subjects suspected of driving under the influence of psychotropic substances.     

Simultaneous determination of disulfiram and bupropion in human plasma of alcohol and nicotine abusers

An isocratic high-performance liquid-chromatographic method has been developed for the simultaneous determination of disulfiram and bupropion in human plasma samples. Analyses were carried out on a C₈ reversed-phase column using a mobile phase composed of 50% acetonitrile and 50% aqueous phosphate buffer, containing triethylamine. Diode-array detection was used, operating at a wavelength of 250 nm. For the clean-up of plasma samples, a solid phase extraction procedure, based on C₂ cartridges, was implemented. Extraction yields of the analytes were satisfactory, being always higher than 84%. The calibration curve was linear over the 5–500 ng mL^-1 plasma concentration range for both disulfiram and bupropion. The method showed a high sensitivity (limit of detection of 1.5 ng mL^-1) and satisfactory precision, selectivity and accuracy. The application to human plasma samples obtained from some alcohol and nicotine abusers also gave good results.     

Entropy, entropy flux and entropy rate of granular materials

The aim of this work is to analyze the entropy, entropy flux and entropy rate of granular materials within the frameworks of the Boltzmann equation and continuum thermodynamics. It is shown that the entropy inequality for a granular gas that follows from the Boltzmann equation differs from the one of a simple fluid due to the presence of a term which can be identified as the entropy density rate. From the knowledge of a non-equilibrium distribution function-valid for processes closed to equilibrium-it is obtained that the entropy density rate is proportional to the internal energy density rate divided by the temperature, while the entropy flux is equal to the heat flux vector divided by the temperature. A thermodynamic theory of a granular material is also developed whose objective is the determination of the basic fields of mass density, momentum density and internal energy density. The constitutive laws are restricted by the principle of material frame indifference and by the entropy principle. Through the exploitation of the entropy principle with Lagrange multipliers, it is shown that the results obtained from the kinetic theory for granular gases concerning the entropy density rate and entropy flux are valid in general for processes close to equilibrium of granular materials, where linearized constitutive equations hold.     

Tachyonization of the ΛCDM cosmological model

In this work a tachyonization of the ΛCDM model for a spatially flat Friedmann–Robertson–Walker space–time is proposed. A tachyon field and a cosmological constant are considered as the sources of the gravitational field. Starting from a stability analysis and from the exact solutions for a standard tachyon field driven by a given potential, the search for a large set of cosmological models which contain the ΛCDM model is investigated. By the use of internal transformations two new kinds of tachyon fields are derived from the standard tachyon field, namely, a complementary and a phantom tachyon fields. Numerical solutions for the three kinds of tachyon fields are determined and it is shown that the standard and complementary tachyon fields reproduces the ΛCDM model as a limiting case. The standard tachyon field can also describe a transition from an accelerated to a decelerated regime, behaving as an inflationary field at early times and as a matter field at late times. The complementary tachyon field always behaves as a matter field. The phantom tachyon field is characterized by a rapid expansion where its energy density increases with time.