Integrability and exact solution for coupled BCS systems associated with the su(4) Lie algebra

We introduce an integrable model for two coupled BCS systems through a solution of the Yang-Baxter equation associated with the Lie algebra su(4). By employing the algebraic Bethe ansatz, we determine the exact solution for the energy spectrum. An asymptotic analysis is conducted to determine the leading terms in the ground state energy, the gap and some one point correlation functions at zero temperature. (C) 2002 Published by Elsevier Science B.V.

Investigations into a power-combining structure using a reflect array of dual-feed aperture-coupled microstrip patch antennas

This paper details an investigation of a power combiner that uses a reflect array of dual-feed aperture-coupled microstrip patch antennas and a corporate-fed dual-polarized array as a signal distributing/combining device. In this configuration, elements of the reflect array receive a linearly polarized wave and retransmit it with an orthogonal polarization using variable-length sections of microstrip lines connecting receive and transmit ports. By applying appropriate lengths of these delay lines, the array focuses the transmitted wave onto the feed array. The operation of the combiner is investigated for a small-size circular reflect array for the cases of -3 dB, -6 dB and -10 dB edge illumination by the 2 x 2-element dual-polarized array.

Quantum dynamics of two coupled qubits

We investigate the difference between classical and quantum dynamics of coupled magnetic dipoles. We prove that in general the dynamics of the classical interaction Hamiltonian differs from the corresponding quantum model, regardless of the initial state. The difference appears as nonpositive-definite diffusion terms in the quantum evolution equation of an appropriate positive phase-space probability density. Thus, it is not possible to express the dynamics in terms of a convolution of a positive transition probability function and the initial condition as can be done in the classical case. It is this feature that enables the quantum system to evolve to an entangled state. We conclude that the dynamics are a quantum element of nuclear magnetic resonance quantum-information processing. There are two limits where our quantum evolution coincides with the classical one: the short-time limit before spin-spin interaction sets in and the long-time limit when phase diffusion is incorporated.

Crack detection in hollow section structures through coupled response measurements

Detection of a circumferential crack in a hollow section beam is investigated using coupled response measurements. The crack section is represented by a local flexibility matrix connecting two undamaged beam segments. This matrix defines the relationship between the displacements and forces across the crack section and is derived by applying fundamental fracture mechanics theory. The suitability of the mode coupling methodology is first demonstrated analytically. Laboratory test results are then presented for circular hollow section beams with artificially generated cracks of varying severity. It is shown that this method has the potential as a damage detection tool for mechanical structures. (C) 2002 Elsevier Science Ltd. All rights reserved.

Exact results for a tunnel-coupled pair of trapped Bose-Einstein condensates

A model describing coherent quantum tunnelling between two trapped Bose-Einstein condensates is discussed. It is not well known that the model admits an exact solution, obtained some time ago, with the energy spectrum derived through the algebraic Bethe ansatz. An asymptotic analysis of the Bethe ansatz equations leads us to explicit expressions for the energies of the ground and the first excited states in the limit of weak tunnelling and all energies for strong tunnelling. The results are used to extract the asymptotic limits of the quantum fluctuations of the boson number difference between the two Bose-Einstein condensates and to characterize the degree of coherence in the system.

A coupled knowledge-based expert system for design of liquid-retaining structures

This paper describes a coupled knowledge-based system (KBS) for the design of liquid-retaining structures, which can handle both the symbolic knowledge processing based on engineering heuristics in the preliminary synthesis stage and the extensive numerical crunching involved in the detailed analysis stage. The prototype system is developed by employing blackboard architecture and a commercial shell VISUAL RULE STUDIO. Its present scope covers design of three types of liquid-retaining structures, namely, a rectangular shape with one compartment, a rectangular shape with two compartments and a circular shape. Through custom-built interactive graphical user interfaces, the user is directed throughout the design process, which includes preliminary design, load specification, model generation, finite element analysis, code compliance checking and member sizing optimization. It is also integrated with various relational databases that provide the system with sectional properties, moment and shear coefficients and final member details. This system can act as a consultant to assist novice designers in the design of liquid-retaining structures with increase in efficiency and optimization of design output and automated record keeping. The design of a typical example of the liquid-retaining structure is also illustrated. (C) 2003 Elsevier B.V All rights reserved.

Implementação e validação do método de determinação de metais e fósforo por ICP-OES (inductively coupled plasma-optical emission spectometry) em biodiesel

O objectivo do presente trabalho foi desenvolver, implementar e validar métodos de determinação de teor de cálcio (Ca), magnésio (Mg), sódio (Na), potássio (K) e fósforo (P) em biodiesel, por ICP-OES. Este método permitiu efectuar o controlo de qualidade do biodiesel, com a vantagem de proporcionar uma análise multi-elementar, reflectindo-se numa diminuição do tempo de análise. Uma vez que o biodiesel é uma das principais fontes de energia renovável e alternativa ao diesel convencional, este tipo de análises revela-se extremamente útil para a sua caracterização. De acordo com a análise quantitativa e qualitativa e após a validação dos respectivos ensaios, apresentam-se, na Tabela 1 as condições optimizadas para cada elemento em estudo. As condições de trabalho do ICP-OES foram escolhidas tendo em conta as características do elemento em estudo, o tipo de equipamento utilizado para a sua análise, e de modo a obter a melhor razão sinal/intensidade de fundo. Para a validação dos ensaios foram efectuados ensaios de recuperação, determinados limites de detecção e quantificação, ensaios de repetibilidade e reprodutibilidade, e verificação das curvas de calibração. Na tabela 2 apresentam-se os comprimentos de onda escolhidos (livres de interferências) e respectivos limites de detecção e quantificação dos elementos analisados por ICP-OES, na posição radial e radial atenuado.

Toplological Entropy in the Syncronization of Piecewise Linear and Monotone Maps. Coupled Duffing Oscillators

In this paper is presented a relationship between the synchronization and the topological entropy. We obtain the values for the coupling parameter, in terms of the topological entropy, to achieve synchronization of two unidirectional and bidirectional coupled piecewise linear maps. In addition, we prove a result that relates the synchronizability of two m-modal maps with the synchronizability of two conjugated piecewise linear maps. An application to the unidirectional and bidirectional coupled identical chaotic Duffing equations is given. We discuss the complete synchronization of two identical double-well Duffing oscillators, from the point of view of symbolic dynamics. Working with Poincare cross-sections and the return maps associated, the synchronization of the two oscillators, in terms of the coupling strength, is characterized.

Surprises of the transformer as a coupled oscillator system

We study a system of two RLC oscillators coupled through a variable mutual inductance. The system is interesting because it exhibits some peculiar features of coupled oscillators: (i) there are two natural frequencies; (ii) in general, the resonant frequencies do not coincide with the natural frequencies; (iii) the resonant frequencies of both oscillators differ; (iv) for certain choices of parameters, there is only one resonant frequency, instead of the two expected.

Determination of ametryn in soils via microwave-assisted solvent extraction coupled to anodic stripping voltammetry with a gold ultramicroelectrode

An extraction-anodic adsorptive stripping voltammetric procedure using microwave-assisted solvent extraction and a gold ultramicroelectrode was developed for determining the pesticide ametryn in soil samples. The method is based on the use of acetonitrile as extraction solvent and on controlled adsorptive accumulation of the herbicide at the potential of 0.50 V (vs. Ag/AgCl) in the presence of Britton-Robinson buffer (pH 3.3). Soil sample extracts were analysed directly after drying and redissolution with the supporting electrolyte but without other pre-treatment. The limit of detection obtained for a 10 s collection time was 0.021 µg g-1. Recovery experiments for the global procedure, at the 0.500 µg g-1 level, gave satisfactory mean and standard deviation results which were comparable to those obtained by HPLC with UV detection.

Optimization of QuEChERS procedure coupled to GC-ECD for organochlorine pesticide determination in carrot samples

An optimised version of the Quick, Easy, Cheap, Effective, Rugged and Safe (QuEChERS) method for simultaneous determination of 14 organochlorine pesticides in carrots was developed using gas chromatography coupled with electron-capture detector (GC-ECD) and confirmation by gas chromatography tandem mass spectrometry (GC-MS/MS). A citrate-buffered version of QuEChERS was applied for the extraction of the organochlorine pesticides, and for the extract clean-up, primary secondary amine, octadecyl-bonded silica (C18), magnesium sulphate (MgSO4) and graphitized carbon black were used as sorbents. The GC-ECD determination of the target compounds was achieved in less than 20 min. The limits of detection were below the EUmaximum residue limits (MRLs) for carrots, 10–50 μg kg−1, while the limit of quantification did exceed 10 μg kg−1 for hexachlorobenzene (HCB). The introduction of a sonication step was shown to improve the recoveries. The overall average recoveries in carrots, at the four tested levels (60, 80, 100 and 140 μg kg−1), ranged from 66 to 111% with relative standard deviations in the range of 2– 15 % (n03) for all analytes, with the exception of HCB. The method has been applied to the analysis of 21 carrot samples from different Portuguese regions, and β-HCH was the pesticide most frequently found, with concentrations oscillating between less than the limit of quantification to 14.6 μg kg−1. Only one sample had a pesticide residue (β-HCH) above the MRL, 14.6 μg kg−1. This methodology combines the advantages of both QuEChERS and GC-ECD, producing a very rapid, sensitive and reliable procedure which can be applied in routine analytical laboratories.

Determination of ochratoxin A in bread: evaluation of microwave-assisted extraction using an orthogonal composite design coupled with response surface methodology

An analytical method using microwave-assisted extraction (MAE) and liquid chromatography (LC) with fluorescence detection (FD) for the determination of ochratoxin A (OTA) in bread samples is described. A 24 orthogonal composite design coupled with response surface methodology was used to study the influence of MAE parameters (extraction time, temperature, solvent volume, and stirring speed) in order to maximize OTA recovery. The optimized MAE conditions were the following: 25 mL of acetonitrile, 10 min of extraction, at 80 °C, and maximum stirring speed. Validation of the overall methodology was performed by spiking assays at five levels (0.1–3.00 ng/g). The quantification limit was 0.005 ng/g. The established method was then applied to 64 bread samples (wheat, maize, and wheat/maize bread) collected in Oporto region (Northern Portugal). OTAwas detected in 84 % of the samples with a maximum value of 2.87 ng/g below the European maximum limit established for OTA in cereal products of 3 ng/g.

Exciting dynamical behavior in a network of two coupled rings of Chen oscillators

We study exotic patterns appearing in a network of coupled Chen oscillators. Namely, we consider a network of two rings coupled through a “buffer” cell, with Z3×Z5 symmetry group. Numerical simulations of the network reveal steady states, rotating waves in one ring and quasiperiodic behavior in the other, and chaotic states in the two rings, to name a few. The different patterns seem to arise through a sequence of Hopf bifurcations, period-doubling, and halving-period bifurcations. The network architecture seems to explain certain observed features, such as equilibria and the rotating waves, whereas the properties of the chaotic oscillator may explain others, such as the quasiperiodic and chaotic states. We use XPPAUT and MATLAB to compute numerically the relevant states.