Analytical solutions for Tokamak equilibria with reversed toroidal current

In tokamaks, an advanced plasma confinement regime has been investigated with a central hollow electric current with negative density which gives rise to non-nested magnetic surfaces. We present analytical solutions for the magnetohydrodynamic equilibria of this regime in terms of non-orthogonal toroidal polar coordinates. These solutions are obtained for large aspect ratio tokamaks and they are valid for any kind of reversed hollow current density profiles. The zero order solution of the poloidal magnetic flux function describes nested toroidal magnetic surfaces with a magnetic axis displaced due to the toroidal geometry. The first order correction introduces a poloidal field asymmetry and, consequently, magnetic islands arise around the zero order surface with null poloidal magnetic flux gradient. An analytic expression for the magnetic island width is deduced in terms of the equilibrium parameters. We give examples of the equilibrium plasma profiles and islands obtained for a class of current density profile. (C) 2011 American Institute of Physics. [doi: 10.1063/1.3624551]

Magnetoconfined levels in a parabolic quantum dot: An analytical solution of a three-dimensional Fock-Darwin problem in a tilted magnetic field

The energy spectrum of an electron confined in a quantum dot (QD) with a three-dimensional anisotropic parabolic potential in a tilted magnetic field was found analytically. The theory describes exactly the mixing of in-plane and out-of-plane motions of an electron caused by a tilted magnetic field, which could be seen, for example, in the level anticrossing. For charged QDs in a tilted magnetic field we predict three strong resonant lines in the far-infrared-absorption spectra.

Analytical results on Muller's ratchet effect in growing populations

Fontanari introduced [Phys. Rev. Lett. 91, 218101 (2003)] a model for studying Muller's ratchet phenomenon in growing asexual populations. They studied two situations, either including a death probability for each newborn or not, but were able to find analytical (recursive) expressions only in the no-decay case. In this Brief Report a branching process formalism is used to find recurrence equations that generalize the analytical results of the original paper besides confirming the interesting effects their simulations revealed.

Full-dimensional analytical ab initio potential energy surface of the ground state of HOI

Extensive ab initio calculations using a complete active space second-order perturbation theory wavefunction, including scalar and spin-orbit relativistic effects with a quadruple-zeta quality basis set were used to construct an analytical potential energy surface (PES) of the ground state of the [H, O, I] system. A total of 5344 points were fit to a three-dimensional function of the internuclear distances, with a global root-mean-square error of 1.26 kcal mol(-1). The resulting PES describes accurately the main features of this system: the HOI and HIO isomers, the transition state between them, and all dissociation asymptotes. After a small adjustment, using a scaling factor on the internal coordinates of HOI, the frequencies calculated in this work agree with the experimental data available within 10 cm(-1). (C) 2011 American Institute of Physics. [doi: 10.1063/1.3615545]

In vivo bioavailability of selenium in enriched Pleurotus ostreatus mushrooms

The in vivo bioavailability of Se was investigated in enriched Pleurotus ostreatus mushrooms. A bioavailability study was performed using 64 Wistar male rats separated in 8 groups and fed with different diets: without Se, with mushrooms without Se, with enriched mushrooms containing 0.15, 0.30 or 0.45 mg kg(-1) Se and a normal diet containing 0.15 mg kg(-1) of Se using sodium selenate. The experiment was performed in two periods: depletion (14 days) and repletion (21 days), according to the Association of Official Analytical Chemists. After five weeks, the rats were sacrificed under carbon dioxide, and blood was drawn by heart puncture. Blood plasma was separated by centrifugation. The total Se concentration in the plasma of rats fed with enriched mushrooms was higher than in rats fed with a normal diet containing sodium selenate. The plasma protein profiles were obtained using size exclusion chromatography (SEC) and UV detectors. Aliquots of effluents (0.5 mL per minute) were collected throughout in the end of the chomatographic column. However, Se was determined by graphite furnace atomic absorption spectrometry (GF AAS) only in the aliquots where proteins were detected by SEC-UV. The plasma protein pro. le of rats fed with different diets was similar. The highest Se concentration was observed in a peptide presenting 8 kDa. Furthermore, the higher Se concentration in this peptide was obtained for rats fed with a diet using enriched mushrooms (7 mu g L(-1) Se) compared to other diets (2-5 mu g L(-1) Se). These results showed that Se-enriched mushrooms can be considered as an alternative Se food source for humans, due to their high bioavailability.

Green Chemistry-Sensitive Analytical Procedure for Photometric Determination of Orthophosphate in River and Tap Water by Use of a Simple LED-Based Photometer

In the current work a Green Analytical Chemistry (GAC) procedure for photometric determination of orthophosphate in river water at mu g L-1 concentration level is described. The flow system module and the LED-based photometer were assembled together to constitute a compact unit in order to allow that a flow cell with optical path-length of 100mm was coupled to them. The photometric procedure based on the molybdenum blue method was implemented employing the multicommuted flow injection analysis approach, which provided facilities to allow reduction of reagent consumption and as well as waste generation. Aiming to prove the usefulness of the system, orthophosphate in river and tap waters was determined. Accuracy was ascertained by spiking samples with orthophosphate solution yielding recoveries ranging from 96% up to 107%. Other profitable features such as a wide linear response range between 10 to 800 mu g L-1 [image omitted]; a detection limit (3 sigma criterion) of 2.4 mu g L-1 [image omitted]; a relative standard deviation (n=7) of 2% using a typical water sample with concentration of 120 mu g L-1 [image omitted]; reagent consumption of 3.0mg ammonium molybdate, 0.3mg hydrazine sulfate, and 0.03mg stannous chloride per determination; a waste generation of 2.4mL per determination; and a sampling throughput of 20 determination per hours were also achieved.

A critical evaluation of a flow-cell based on a liquid core waveguide for chemiluminescence measurements

Liquid-core waveguides (LCWs), devices that constrain the emitted radiation minimizing losses during the transport, are an alternative to maximize the amount of detected radiation in luminescence. In this work, the performance of a LCW flow-cell was critically evaluated for chemiluminescence measurements, by using as model the oxidation of luminol by hydrogen peroxide or hypochlorite. An analytical procedure for hypochlorite determination was also developed, with linear response in the range 0.2-3.8 mg/L (2.7-51 mu mol/L), a detection limit estimated as 8 mu g/L (0.64 mu mol/L) at the 99.7% confidence level and luminol consumption of 50 mu g/determination. The coefficients of variation were 3.3% and 1.6% for 0.4 and 1.9 mg/L CIO(-), respectively, with a sampling rate of 164 determinations/h. The procedure was applied to the analysis of Dakin`s solution samples, yielding results in agreement with those obtained by iodometric titration at the 95% confidence level. Copyright (c) 2008 John Wiley & Sons, Ltd.

A flow-based analytical procedure for salbutamol determination exploiting chemiluminescence in a liquid-core waveguide

Salbutamol is a bronchodilator whose use is restricted due to its anabolic effects. A flow-based procedure for salbutamol determination based on the inhibition of chemiluminescence of the luminol/hypochlorite system was developed. A flow cell constructed with a liquid-core waveguide was employed to constrain the emitted radiation, minimizing losses during transport to detector. Linear response was observed within 2.5 x 10(-6) and 1.0 x 10(-5) mol L-1 with a detection limit estimated as 1 x 10(-7) mol L-1 at the 99.7% confidence level. The coefficient of variation (n = 20), sampling rate, and luminol consumption per determination were estimated as 2.8%, 164 determinations h(-1), and 50 mu g, respectively. Results for pharmaceutical samples were in agreement with those obtained by reference procedures at the 95% confidence level.

Analytical calculation of the transition to complete phase synchronization in coupled oscillators

Here we present a system of coupled phase oscillators with nearest neighbors coupling, which we study for different boundary conditions. We concentrate at the transition to the total synchronization. We are able to develop exact solutions for the value of the coupling parameter when the system becomes completely synchronized, for the case of periodic boundary conditions as well as for a chain with fixed ends. We compare the results with those calculated numerically.

DFT and electrochemical studies on nortriptyline oxidation sites

A study on the possible sites of oxidation and epoxidation of nortriptyline was performed using electrochemical and quantum chemical methods; these sites are involved in the biological responses (for example, hepatotoxicity) of nortriptyline and other similar antidepressants. Quantum chemical studies and electrochemical experiments demonstrated that the oxidation and epoxidation sites are located on the apolar region of nortriptyline, which will useful for understanding the molecule`s activity. Also, for the determination of the compound in biological fluids or in pharmaceutical formulations, we propose a useful analytical methodology using a graphite-polyurethane composite electrode, which exhibited the best performance when compared with boron-doped diamond or glassy carbon surfaces.

Analytical formulae for electromechanical effective properties of 3-1 longitudinally porous piezoelectric materials

A unidirectional fiber composite is considered here, the fibers of which are empty cylindrical holes periodically distributed in a transversely isotropic piezoelectric matrix, The empty-fiber cross-section is circular and the periodicity is the same in two directions at an angle pi/2 or pi/3. Closed-form formulae for all electromechanical effective properties of these 3-1 longitudinally periodic porous piezoelectric materials are presented. The derivation of such expressions is based on the asymptotic homogenization method as a limit of the effective properties of two-phase transversely isotropic parallel fiber-reinforced composites when the fibers properties tend to zero. The plane effective coefficients satisfy the corresponding Schulgasser-Benveniste-Dvorak universal type of relations, A new relation among the antiplane effective constants from the solutions of two antiplane strains and potential local problems is found. This relation is valid for arbitrary shapes of the empty-fiber cross-sections. Based on such a relation, and using recent numerical results for isotropic conductive composites, the antiplane effective properties are computed for different geometrical shapes of the empty-fiber cross-section. Comparisons with other analytical and numerical theories are presented. (c) 2008 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.

Analytical solutions for geometrically nonlinear trusses

This paper presents an analytical method for analyzing trusses with severe geometrically nonlinear behavior. The main objective is to find analytical solutions for trusses with different axial forces in the bars. The methodology is based on truss kinematics, elastic constitutive laws and equilibrium of nodal forces. The proposed formulation can be applied to hyper elastic materials, such as rubber and elastic foams. A Von Mises truss with two bars made by different materials is analyzed to show the accuracy of this methodology.

Coalescence of Water Droplets in Crude Oil Emulsions: Analytical Solution

In petroleum refineries, water is used in desalting units to remove the salt contained in crude oil. Typically, 7% of the volume of hot crude oil is water, forming a water-and-oil emulsion. The emulsion flows between two electrodes and is subjected to an electric field. The electrical forces promote the coalescence of small droplets of water dispersed in crude oil, and these form bigger droplets. This paper calculates the forces acting on the droplets, highlighting particularly the mechanisms proposed for droplet-droplet coalescence under the influence of an applied electric field. Moreover, a model is developed in order to calculate the displacement speed of the droplets and the time between droplet collisions. Thus, it is possible to simulate and optimize the process by changing the operational variables (temperature, electrical field, and water quantity). The main advantage of this study is to show that it is feasible to increase the volume of water recycled in desalting processes, thus reducing the use of freshwater and the generation of liquid effluents in refineries.

Non-linear modal analysis for beams subjected to axial loads: Analytical and finite-element solutions

A rigorous derivation of non-linear equations governing the dynamics of an axially loaded beam is given with a clear focus to develop robust low-dimensional models. Two important loading scenarios were considered, where a structure is subjected to a uniformly distributed axial and a thrust force. These loads are to mimic the main forces acting on an offshore riser, for which an analytical methodology has been developed and applied. In particular, non-linear normal modes (NNMs) and non-linear multi-modes (NMMs) have been constructed by using the method of multiple scales. This is to effectively analyse the transversal vibration responses by monitoring the modal responses and mode interactions. The developed analytical models have been crosschecked against the results from FEM simulation. The FEM model having 26 elements and 77 degrees-of-freedom gave similar results as the low-dimensional (one degree-of-freedom) non-linear oscillator, which was developed by constructing a so-called invariant manifold. The comparisons of the dynamical responses were made in terms of time histories, phase portraits and mode shapes. (C) 2008 Elsevier Ltd. All rights reserved.

Alternative Analytical Expressions for the General van Genuchten-Mualem and van Genuchten-Burdine Hydraulic Conductivity Models

The van Genuchten expressions for the unsaturated soil hydraulic properties, first published in 1980, are used frequently in various vadose zone flow and transport applications assuming a specific relationship between the m and n soil hydraulic parameters. By comparison, probably because of the complexity of the hydraulic conductivity equations, the more general solutions with independent m and n values are rarely used. We expressed the general van Genuchten-Mualem and van Genuchten-Burdine hydraulic conductivity equations in terms of hypergeometric functions, which can be approximated by infinite series that converge rapidly for relatively large values of the van Genuchten-Mualem parameter n but only very slowly when n is close to one. Alternative equations were derived that provide very close approximations of the analytical results. The newly proposed equations allow the use of independent values of the parameters m and n in the soil water retention model of van Genuchten for subsequent prediction of the van Genuchten-Mualem and van Genuchten-Burdine hydraulic conductivity models, thus providing more flexibility in fitting experimental pressure-head-dependent water content, theta(h), and hydraulic conductivity, K(h), or K(theta) data.