Approximate analytical states of a polynomial potential: an example of symmetry restoration

An approximate analytical expression for the first two eigenvalues of the Schrodinger equation for the potential V(x) = Ax(4) + Bx(2) is achieved by using the Symanzik scaling symmetry. A kind of symmetry restoration when one of the potential parameters changes conveniently is observed. (C) 2000 Published by Elsevier B.V. B.V. All rights reserved.

On an approximate analytical solution to a nonlinear vibrating problem, excited by a nonideal motor

This paper analyzes through Multiple Scales Method a response of a simplified nonideal and nonlinear vibrating system. Here, one verifies the interactions between the dynamics of the DC motor (excitation) and the dynamics of the foundation (spring, damper, and mass). We remarked that we consider cubic nonlinearity (spring) and quadratic nonlinearity (DC motor) of the same order of magnitude according to experimental results. Both analytical and numerical results that we have obtained had good agreement.

Analytical procedure for total mercury determination in fishes and shrimps by chronopotentiometric stripping analysis at gold film electrodes after microwave digestion

A method for the total mercury determination in fish and shrimps employing chronopotentiometric stripping analysis on gold film electrodes is described. Fish and shrimp tissues were digested using a microwave oven equipped with closed vessels. We developed a microwave heating program which decomposed all the samples employing diluted nitric acid and hydrogen peroxide. The proposed method was validated by analyzing a certified reference material and then applied for different fish species from fresh water and seawater acquired in local markets of São Paulo city, Brazil. The Brazilian legislation establishes 0.5 and 1 mg per kilogram of fish as upper limit of mercury for omnivorous and predator species, respectively. Except for blue shark tissues, the mercury content was situated below 0.5 mu g g(-1) for all the analyzed samples. The detection limit of the proposed method was calculated as 5 ng g(-1) of sample utilizing 5 minutes of electrodeposition (+300 mV vs. Ag/AgCl) on the gold electrode. (c) 2006 Elsevier Ltd. All rights reserved.

The application of interpolating MLS approximations to the analysis of MHD flows

The element-free Galerkin method (EFGM) is a very attractive technique for solutions of partial differential equations, since it makes use of nodal point configurations which do not require a mesh. Therefore, it differs from FEM-like approaches by avoiding the need of meshing, a very demanding task for complicated geometry problems. However, the imposition of boundary conditions is not straightforward, since the EFGM is based on moving-least-squares (MLS) approximations which are not necessarily interpolants. This feature requires, for instance, the introduction of modified functionals with additional unknown parameters such as Lagrange multipliers, a serious drawback which leads to poor conditionings of the matrix equations. In this paper, an interpolatory formulation for MLS approximants is presented: it allows the direct introduction of boundary conditions, reducing the processing time and improving the condition numbers. The formulation is applied to the study of two-dimensional magnetohydrodynamic flow problems, and the computed results confirm the accuracy and correctness of the proposed formulation. (C) 2002 Elsevier B.V. All rights reserved.

Analytical and Monte Carlo approaches to evaluate probability distributions of interruption duration

Regulatory authorities in many countries, in order to maintain an acceptable balance between appropriate customer service qualities and costs, are introducing a performance-based regulation. These regulations impose penalties-and, in some cases, rewards-that introduce a component of financial risk to an electric power utility due to the uncertainty associated with preserving a specific level of system reliability. In Brazil, for instance, one of the reliability indices receiving special attention by the utilities is the maximum continuous interruption duration (MCID) per customer.This parameter is responsible for the majority of penalties in many electric distribution utilities. This paper describes analytical and Monte Carlo simulation approaches to evaluate probability distributions of interruption duration indices. More emphasis will be given to the development of an analytical method to assess the probability distribution associated with the parameter MCID and the correspond ng penalties. Case studies on a simple distribution network and on a real Brazilian distribution system are presented and discussed.

Discrete approximations for strict convex continuous time problems and duality

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Collisional semiclassical approximations in phase-space representation

The Gaussian wave-packet phase-space representation is used to show that the expansion in powers of a of the quantum Liouville propagator leads, in the zeroth-order term, to results close to those obtained in the statistical quasiclassical method of Lee and Scully in the Weyl-Wigner picture. It is also verified that, propagating the Wigner distribution along the classical trajectories, the amount of error is less than that coming from propagating the Gaussian distribution along classical trajectories.

Error function approximations of interest in electrochemistry.

The error function is present in several equations describing eletrode processes. But, only approximations of this function are used. In this work, these and other approximations are studied and evaluated according to precision.

Surface-enhanced resonance Raman scattering as an analytical tool for single molecule detection

A perylene derivative, n-(n-butyl)-n'-(4-aminobutyl) perylene-3,4,9,10-tetracarboxylic acid diimide (simplified as nBu-PTCD-(CH2)(4)-NH2) has been chosen as the target molecule for studies involving single molecule detection (SMD) using Raman scattering. The enhancement of the Raman signal is the result of the multiplicative effects of two phenomena, resonance Raman scattering (RRS) and surface-enhanced Raman scattering (SERS), which leads to the resulting surface-enhanced resonance Raman scattering (SERRS) process. The SERRS spectra from a single molecule have been collected using both silver and gold colloids. The SMD detection of the fundamental vibrational frequencies characteristic of nBu-PTCD-(CH2)(4)-NH2 is complemented with the detection of some overtones and combinations from ring stretching modes at the single molecule level. The background characterization of the ensemble vibrational spectroscopy of the target perylene and its SERRS is also presented, which includes the UV-vis absorption, experimental and calculated Raman scattering and infrared absorption, and molecular organization using reflection-absorption infrared spectroscopy (RAIRS).

An analytical and numerical study of plane change maneuvers using aerodynamic force

The goal of the present work is to analyze space missions that use the terrestrial atmosphere to accomplish orbital maneuvers that involve a plane change. A set of analytical solutions is presented for the variation of the orbital elements due to a single passage through the atmosphere, assuming that the interval the spacecraft travels through the atmosphere is not too large. The study considers both the lift influence on the spacecraft orbit as well as drag. The final equations are tested with numerical integration and can be considered in accordance with the numerical results whenever the perigee height is larger than a critical value. Next, a numerical study of the ratio between the velocity increment required to correct the semimajor axis decay due to the atmospheric passage and the velocity variation required to obtain the change in the inclination is also presented. This analysis can be used to decide if a maneuver passing through the atmosphere can decrease the fuel consumption of the mission and, in the cases where this technique can be used, if a multiple passage is more efficient than a single passage.

Bayesian approximations in randomized response model

Practical Bayesian inference depends upon detailed examination of posterior distribution. When the prior and likelihood are conjugate, this is easily carried out; however, in general, one must resort to numerical approximation. In this paper, our aim is to solve, using MAPLE, the Bayesian paradigm, for a very special data collecting procedure, known as the randomized-response technique. This allows researchers to obtain sensitive information while guaranteeing privacy to respondents. This approach intends to reduce false responses on sensitive questions. Exact methods and approximations will be compared from the accuracy point of view as well as for the computational effort.