Fourth-order method for solving the Navier-Stokes equations in a constricting channel

A fourth-order numerical method for solving the Navier-Stokes equations in streamfunction/vorticity formulation on a two-dimensional non-uniform orthogonal grid has been tested on the fluid flow in a constricted symmetric channel. The family of grids is generated algebraically using a conformal transformation followed by a non-uniform stretching of the mesh cells in which the shape of the channel boundary can vary from a smooth constriction to one which one possesses a very sharp but smooth corner. The generality of the grids allows the use of long channels upstream and downstream as well as having a refined grid near the sharp corner. Derivatives in the governing equations are replaced by fourth-order central differences and the vorticity is eliminated, either before or after the discretization, to form a wide difference molecule for the streamfunction. Extra boundary conditions, necessary for wide-molecule methods, are supplied by a procedure proposed by Henshaw et al. The ensuing set of non-linear equations is solved using Newton iteration. Results have been obtained for Reynolds numbers up to 250 for three constrictions, the first being smooth, the second having a moderately sharp corner and the third with a very sharp corner. Estimates of the error incurred show that the results are very accurate and substantially better than those of the corresponding second-order method. The observed order of the method has been shown to be close to four, demonstrating that the method is genuinely fourth-order. © 1977 John Wiley & Sons, Ltd.

Solid mass falling into the reservoirs shallow water equations validity from the engineering point of view

Water waves generated by a solid mass is a complex phenomenon discussed in this paper by numerical and experimental approaches. A model based on shallow water equations with shocks (Saint Venant) has developed. It can reproduce the amplitude and the energy of the wave quite well, but because it consistently generates a hydraulic jump, it is able to reproduce the profile, in the case of high relative thickness of slide, but in the case of small relative thickness it is unable to reproduce the amplitude of the wave. As the momentum conservation is not verified during the phase of wave creation, a second technique based on discharge transfer coefficient α, is introduced at the zone of impact. Numerical tests have been performed and validated this technique from the experimental results of the wave's height obtained in a flume.

Production grinding burn detection using acoustic emission and electric power signals

This work uses a monitoring system based on a PC platform, where the acoustic emission and electric power signals generated during the grinding process are used to investigate superficial burning occurrence in a surface grinding operation using two types of steel, three grinding conditions and an Al203 vitrified grinding wheel. Acoustic emission signals on the workpiece and grinding power were measured during a surface plunge operation until the grinding burn happened. From the results the standard deviation of the acoustic emission signal and the maximum electric power were calculated for each grinding pass. The proposed DPO parameter is the product between the power level and acoustic emission standard deviation. The results show that both signals can be used for burning detection, and the parameter DPO is the best indicator for the burning studied in this work. This can be explained by the high dispersion of the acoustic emission RMS level associated to the high power consumption when the grinding wheel lose its sharpness.

On the regularization of mixed complementarity problems

A variational inequality problem (VIP) satisfying a constraint qualification can be reduced to a mixed complementarity problem (MCP). Monotonicity of the VIP implies that the MCP is also monotone. Introducing regularizing perturbations, a sequence of strictly monotone mixed complementarity problems is generated. It is shown that, if the original problem is solvable, the sequence of computable inexact solutions of the strictly monotone MCP's is bounded and every accumulation point is a solution. Under an additional condition on the precision used for solving each subproblem, the sequence converges to the minimum norm solution of the MCP. Copyright © 2000 by Marcel Dekker, Inc.

An analog implementation of radial basis neural networks (RBNN) using BiCMOS technology

This paper describes a analog implementation of radial basis neural networks (RBNN) in BiCMOS technology. The RBNN uses a gaussian function obtained through the characteristic of the bipolar differential pair. The gaussian parameters (gain, center and width) is changed with programmable current source. Results obtained with PSPICE software is showed.

Case-based system: Indexing and retrieval with fuzzy hypercube

In some applications with case-based system, the attributes available for indexing are better described as linguistic variables instead of receiving numerical treatment. In these applications, the concept of fuzzy hypercube can be applied to give a geometrical interpretation of similarities among cases. This paper presents an approach that uses geometrical properties of fuzzy hypercube space to make indexing and retrieval processes of cases.

On the solution of mathematical programming problems with equilibrium constraints

Mathematical programming problems with equilibrium constraints (MPEC) are nonlinear programming problems where the constraints have a form that is analogous to first-order optimality conditions of constrained optimization. We prove that, under reasonable sufficient conditions, stationary points of the sum of squares of the constraints are feasible points of the MPEC. In usual formulations of MPEC all the feasible points are nonregular in the sense that they do not satisfy the Mangasarian-Fromovitz constraint qualification of nonlinear programming. Therefore, all the feasible points satisfy the classical Fritz-John necessary optimality conditions. In principle, this can cause serious difficulties for nonlinear programming algorithms applied to MPEC. However, we show that most feasible points do not satisfy a recently introduced stronger optimality condition for nonlinear programming. This is the reason why, in general, nonlinear programming algorithms are successful when applied to MPEC.

Free expansion of attractive and repulsive Bose-Einstein condensed vortex states

A numerical study of the time-dependent Gross-Pitaevskii equation for an axially symmetric trap to obtain insight into the free expansion of vortex states of BEC is presented. As such, the ratio of vortex-core radius to radia rms radius xc/xrms(<1) is found to play an interesting role in the free expansion of condensed vortex states. the larger this ratio, the more prominent is the vortex core and the easier is the possibility of experimental detection of vortex states.

On non-ideal and non-linear portal frame dynamics analysis using Bogoliubov averaging method

We apply the Bogoliubov Averaging Method to the study of the vibrations of an elastic foundation, forced by a Non-ideal energy source. The considered model consists of a portal plane frame with quadratic nonlinearities, with internal resonance 1:2, supporting a direct current motor with limited power. The non-ideal excitation is in primary resonance in the order of one-half with the second mode frequency. The results of the averaging method, plotted in time evolution curve and phase diagrams are compared to those obtained by numerically integrating of the original differential equations. The presence of the saturation phenomenon is verified by analytical procedures.

Optimization of neutral hydrolysis reaction of post-consumer PET for chemical recycling

The neutral hydrolysis reaction of post-consumer poly(ethylene terephthalate) in solid state was studied through the reaction of the polymer with water at the molar ratio 1:91 with autogenous pressure. Two sizes of post-consumer PET flakes and temperatures of 135 °C, 170°C and 205°C with pressures of 4.0 atm, 7.5 atm and 13.5 atm, respectively, were considered. With reaction time equal to 6h, the method reached 99% depolymerization at 205°C, 8.2% at 170 °C and 1.7% at 135°C. The reaction extension was measured by separating the terephthalic acid formed in the process and calculating by gravimetry how much material could still be reacted. Through the viscosimetry of diluted, solutions and the counting of carboxylic end groups in the remaining material from the gravimetric assay, it was possible to suggest that the reaction occurs randomly and in the whole volume of the polymeric particle and not solely on the surface. The terephthalic acid obtained and then purified was characterized by elemental analysis, magnetic nuclear resonance, size and panicle size distribution and spectrophotometry in the visible spectrum, and it was similar to the petrochemical equivalent, with purity recorded in carbon base equal to 99.9%.

Modified barrier method for optimal power flow problem

In this paper is presented a new approach for optimal power flow problem. This approach is based on the modified barrier function and the primal-dual logarithmic barrier method. A Lagrangian function is associated with the modified problem. The first-order necessary conditions for optimality are fulfilled by Newton's method, and by updating the barrier terms. The effectiveness of the proposed approach has been examined by solving the Brazilian 53-bus, IEEE118-bus and IEEE162-bus systems.

Allocation of the cost of transmission losses in a multimarket framework

The paper addresses the issue of apportioning of the cost of transmission losses to generators and demands in a multimarket framework. Line flows are unbundled using equivalent bilateral exchanges on a DC-network model and allocated to generators and demands. Losses are then calculated based on unbundled flows and straightforwardly apportioned to generators and demands. The proposed technique is particularly useful in a multimarket framework, where all markets have a common grid operator with complete knowledge of all network data, as is the case of the Brazilian electric-energy system. The methodology proposed is illustrated using the IEEE Reliability Test System and compared numerically with an alternative technique. Appropriate conclusions are drawn. © The Institution of Engineering and Technology 2006.

Identification of structural damage in flexible structures using system norm and neural networks

Nowadays there is great interest in damage identification using non destructive tests. Predictive maintenance is one of the most important techniques that are based on analysis of vibrations and it consists basically of monitoring the condition of structures or machines. A complete procedure should be able to detect the damage, to foresee the probable time of occurrence and to diagnosis the type of fault in order to plan the maintenance operation in a convenient form and occasion. In practical problems, it is frequent the necessity of getting the solution of non linear equations. These processes have been studied for a long time due to its great utility. Among the methods, there are different approaches, as for instance numerical methods (classic), intelligent methods (artificial neural networks), evolutions methods (genetic algorithms), and others. The characterization of damages, for better agreement, can be classified by levels. A new one uses seven levels of classification: detect the existence of the damage; detect and locate the damage; detect, locate and quantify the damages; predict the equipment's working life; auto-diagnoses; control for auto structural repair; and system of simultaneous control and monitoring. The neural networks are computational models or systems for information processing that, in a general way, can be thought as a device black box that accepts an input and produces an output. Artificial neural nets (ANN) are based on the biological neural nets and possess habilities for identification of functions and classification of standards. In this paper a methodology for structural damages location is presented. This procedure can be divided on two phases. The first one uses norms of systems to localize the damage positions. The second one uses ANN to quantify the severity of the damage. The paper concludes with a numerical application in a beam like structure with five cases of structural damages with different levels of severities. The results show the applicability of the presented methodology. A great advantage is the possibility of to apply this approach for identification of simultaneous damages.

Efeito do desbaste seletivo sobre a divergência genética em progênies de Pinus caribaea Morelet var. bahamensis

The objective of this work was to study the effect of selective thinning on the genetic divergence in progenies of Pinus caribaea var. bahamensis, aiming to identify the most productive and divergent progenies for the use of improvement program. The test of progenies containing 119 progenies and two commercial controls were planted in March 1990, using 11 × 11 square lattice design, sextuple, partially balanced, disposed in lineal plots with six trees in the spacing of 3,0 × 3,0m. 13 years after planting thinning was realized (selection for DBH), with 50% selection intensity based on Multi-effect index, leaving three trees per plot in all the experiment. The evaluations were done at four situations: A (before the thinning); B (thinned trees); C (remaining trees after thinning) and D (one year after thinning). The analyzed traits were: height, diameter at breast height (DBH), volume, form of stem and wood density. The genetic divergence among the progenies was studied with aid of the canonical variables and of clustering of Tocher method, using the generalized distance matrix of Mahalanobis (D2) as estimate of the genetic similarity. The progenies were grouped in four groups in situation A, fourteen in the situation B, two in the situation C and three in the situation D. The selective thinning of the trees within of the progenies caused a change in the genetic divergence among the progenies, genetically homogenizing the progenies, as demonstrated by the generalized distances of Mahalanobis, clustering of Tocher' and canonical variables methods. The thinning made possible a high uniformity in respect to the relative contribution of the traits for the total genetic divergence. The techniques of clustering were efficient to identify groups of divergent progenies for the use hybridization and little divergent progenies for the use in backcross program.

Optimal power flow via interior-exterior method

This paper presents a new approach to the resolution of the Optimal Power Flow problem. In this approach the inequality constraints are treated by the Modified Barrier and Primal-Dual Logarithmic Barrier methods. The inequality constraints are transformed into equalities by introducing positive auxiliary variables, which are perturbed by the barrier parameter. A Lagrangian function is associated with the modified problem. The first-order necessary conditions are applied to the Lagrangian, generating a nonlinear system which is solved by Newton's method. The perturbation of the auxiliary variables results in an expansion of the feasible set of the original problem, allowing the limits of the inequality constraints to be reached. Numerical tests on the Brazilian CESP and South-Southeast systems and a comparative test indicated that the new approach efficiently resolves of the Optimal Power Flow problem. © 2007 IEEE.