Analytical functions for the calculation of hyperspherical potential curves of atomic systems

We present angular basis functions for the Schrödinger equation of two-electron systems in hyperspherical coordinates. By using the hyperspherical adiabatic approach, the wave functions of two-electron systems are expanded in analytical functions, which generalizes the Jacobi polynomials. We show that these functions, obtained by selecting the diagonal terms of the angular equation, allow efficient diagonalization of the Hamiltonian for all values of the hyperspherical radius. The method is applied to the determination of the 1S e energy levels of the Li + and we show that the precision can be improved in a systematic and controllable way. ©2000 The American Physical Society.

One-dimensional analytical model for oxide thin film growth on Ti metal layers during laser heating in air

This paper presents the theoretical and experimental results for oxide thin film growth on titanium films previously deposited over glass substrate. Ti films of thickness 0.1 μm were heated by Nd:YAG laser pulses in air. The oxide tracks were created by moving the samples with a constant speed of 2 mm/s, under the laser action. The micro-topographic analysis of the tracks was performed by a microprofiler. The results taken along a straight line perpendicular to the track axis revealed a Gaussian profile that closely matches the laser's spatial mode profile, indicating the effectiveness of the surface temperature gradient on the film's growth process. The sample's micro-Raman spectra showed two strong bands at 447 and 612 cm -1 associated with the TiO 2 structure. This is a strong indication that thermo-oxidation reactions took place at the Ti film surface that reached an estimated temperature of 1160 K just due to the action of the first pulse. The results obtained from the numerical integration of the analytical equation which describes the oxidation rate (Wagner equation) are in agreement with the experimental data for film thickness in the high laser intensity region. This shows the partial accuracy of the one-dimensional model adopted for describing the film growth rate. © 2001 Elsevier Science B.V.

An analytical solution to the optimal power flow

This letter presents an approach for a geometrical solution of an optimal power flow (OPF) problem for a two-bus system (slack and PV busses). The algebraic equations for the calculation of the Lagrange multipliers and for the minimum losses value are obtained. These equations are used to validate the results obtained using an OPF program.

Electrochemical sensors: A powerful tool in analytical chemistry

Potentiometric, amperometric and conductometric electrochemical sensors have found a number of interesting applications in the areas of environmental, industrial, and clinical analyses. This review presents a general overview of the three main types of electrochemical sensors, describing fundamental aspects, developments and their contribution to the area of analytical chemistry, relating relevant aspects of the development of electrochemical sensors in Brazil.

HPLC-EICD: An Useful Tool for the Pursuit of Novel Analytical Strategies for the Detection of Antioxidant Secondary Metabolites

Living cells are continuously exposed to a variety of challenges that exert oxidative stress and are directly related with senescence and the onset of various pathological conditions such as coronary heart disease, rheumatoid arthritis and cancer. Nevertheless, living organisms have developed a complex antioxidant network to counteract reactive species that are detrimental to life. With the aim of bio-prospecting plant species from the Brazilian Cerrado and Atlantic Forest, we have established a methodology to detect secondary antioxidant metabolites in crude extracts and fractions obtained from plant species. Combining HPLC with an electrochemical detector allowed us to detect micromolecules that showed antioxidant activities in Chimarrhis turbinata (DC) leaf extracts. Comparison with purified flavonoid standards led us to identify the compounds in their natural matrices giving valuable information on their antioxidant capacity.

Analytical/numerical hybrid solution for one-dimensional ablation problem

Ablation is a thermal protection process with several applications in engineering, mainly in the field of airspace industry. The use of conventional materials must be quite restricted, because they would suffer catastrophic flaws due to thermal degradation of their structures. However, the same materials can be quite suitable once being protected by well-known ablative materials. The process that involves the ablative phenomena is complex, could involve the whole or partial loss of material that is sacrificed for absorption of energy. The analysis of the ablative process in a blunt body with revolution geometry will be made on the stagnation point area that can be simplified as a one-dimensional plane plate problem, hi this work the Generalized Integral Transform Technique (GITT) is employed for the solution of the non-linear system of coupled partial differential equations that model the phenomena. The solution of the problem is obtained by transforming the non-linear partial differential equation system to a system of coupled first order ordinary differential equations and then solving it by using well-established numerical routines. The results of interest such as the temperature field, the depth and the rate of removal of the ablative material are presented and compared with those ones available in the open literature.

Simple analytical expression for vector hypernuclear asymmetry in nonmesonic decay ofΛ 5He andΛ 12C

We present general explicit expressions for a shell-model calculation of the vector hypernuclear parameter in nonmesonic weak decay. We use a widely accepted effective coupling Hamiltonian involving the exchange of the complete pseudoscalar and vector meson octets (π, η, K, ρ, ω, K*). In contrast to the approximated formula widely used in the literature, we correctly treat the contribution of transitions originated from single-proton states beyond the s-shell. Exact and simple analytical expressions are obtained for the particular cases of Λ 5He and Λ 12C, within the one-pion-exchange model. Numerical computations of the asymmetry parameter, aΛ, are presented. Our results show a qualitative agreement with other theoretical estimates but also a contradiction with recent experimental determinations. Our simple analytical formulas provide a guide in searching the origin of such discrepancies, and they will be useful for helping to solve the hypernuclear weak decay puzzle.

On the analytical solution for the slewing flexible beam-like system: analysis of the linear part of the perturbed problem

The dynamical system investigated in this work is a nonlinear flexible beam-like structure in slewing motion. Non-dimensional and perturbed governing equations of motion are presented. The analytical solution for the linear part of these perturbed equations for ideal and for non-ideal cases are obtained. This solution is necessary for the investigation of the complete weak nonlinear problem where all nonlinearities are small perturbations around a linear known solution. This investigation shall help the analyst in the modelling of dynamical systems with structure- actuator interactions.

Quasiconformal mappings in octonionic algebra: A graphical and analytical comparison

In this article, we present quasiconformal mappings related to octonionic algebra. Based on the metric definition of quasiconformal mappings and using transformations of the type f(z)=zn, we compare the graphical and analytic results. © 2009 Pushpa Publishing House.

Chemical properties of different peats depending on origin and analytical method

The chemical properties of 12 different peats have been analyzed by methods from VDLUFA (German Association of Agricultural Analysis and Research Institutes) and EN (European Committee for Standardization, Technical Committee 223: Soil improvers and growing media). The analyses of pH (CaCl 2), contents of salts (H 2O), nutrients (CAT), and Na and Cl (H 2O) were carried out by VDLUFA methods, while those of pH (H 2O), EC (H 2O), nutrients (CAT), Na (CAT and H 2O) and Cl (H 2O) according to EN. Ten milled or sod white peats and two dredged frozen black peats of different degrees of decomposition were used. All of them contained high amounts of Mg, while black peats were additionally high in N, Fe and Zn. The pH-values were about the same for all peats. N- and Mn-contents depended most on peat origin. Analytical values of both CAT-methods were in the same range. Extraction with H 2O (EN) as compared to CAT (EN) resulted in considerably lower values.

Analytical model for heterogeneous crystallization kinetics of spherical glass particles

An analytical model developed to describe the crystallization kinetics of spherical glass particles has been derived in this work. A continuous phase transition from three-dimensional (3D)-like to 1D-like crystal growth has been considered and a procedure for the quantitative evaluation of the critical time for this 3D-1D transition is proposed. This model also allows straightforward determination of the density of surface nucleation sites on glass powders using differential scanning calorimetry data obtained under different thermal conditions. © 2009 The American Ceramic Society.

Monte Carlo and analytical calculation of lateral deflection of proton beams in homogeneous targets

Proton radiation therapy is a precise form of radiation therapy, but the avoidance of damage to critical normal tissues and the prevention of geographical tumor misses require accurate knowledge of the dose delivered to the patient and the verification of his position demand a precise imaging technique. In proton therapy facilities, the X-ray Computed Tomography (xCT) is the preferred technique for the planning treatment of patients. This situation has been changing nowadays with the development of proton accelerators for health care and the increase in the number of treated patients. In fact, protons could be more efficient than xCT for this task. One essential difficulty in pCT image reconstruction systems came from the scattering of the protons inside the target due to the numerous small-angle deflections by nuclear Coulomb fields. The purpose of this study is the comparison of an analytical formulation for the determination of beam lateral deflection, based on Molière's theory and Rutherford scattering with Monte Carlo calculations by SRIM 2008 and MCNPX codes. © 2010 American Institute of Physics.

Recent applications of analytical techniques for quantitative pharmaceutical analysis: A review

The intension of this paper was to review and discuss some of the current quantitative analytical procedures which are used for quality control of pharmaceutical products. The selected papers were organized according to the analytical technique employed. Several techniques like ultraviolet/visible spectrophotometry, fluorimetry, titrimetry, electroanalytical techniques, chromatographic methods (thin-layer chromatography, gas chromatography and high-performance liquid chromatography), capillary electrophoresis and vibrational spectroscopies are the main techniques that have been used for the quantitative analysis of pharmaceutical compounds. In conclusion, although simple techniques such as UV/VIS spectrophotometry and TLC are still extensively employed, HPLC is the most popular instrumental technique used for the analysis of pharmaceuticals. Besides, a review of recent works in the area of pharmaceutical analysis showed a trend in the application of techniques increasingly rapid such as ultra performance liquid chromatography and the use of sensitive and specific detectors as mass spectrometers.

Representation of transmission lines in modal domain using analytical transformation matrices

The phases of a transmission line are tightly coupled due to mutual impedances and admittances of the line. One way to accomplish the calculations of currents and voltages in multi-phase lines consists in representing them in modal domain, where its n coupled phases are represented by their n propagation modes. The separation line in their modes of propagation is through the use of a modal transformation matrix whose columns are eigenvectors associated with the parameters of the line. Usually, this matrix is achieved through numerical methods which does not allow the achievement of an analytical model for line developed directly in the phases domain. This work will show the modal transformation matrix of a hypothetical two-phase obtained with numerical and analytical procedures. It will be shown currents and voltage s at terminals of the line taking into account the use of modal transformation matrices obtained by using numerical and analytical procedures. © 2011 IEEE.