Analysis of numeric conditioning of Hessian matrix of Lagrangian via singular values

This paper presents an analyze of numeric conditioning of the Hessian matrix of Lagrangian of modified barrier function Lagrangian method (MBFL) and primal-dual logarithmic barrier method (PDLB), which are obtained in the process of solution of an optimal power flow problem (OPF). This analyze is done by a comparative study through the singular values decomposition (SVD) of those matrixes. In the MBLF method the inequality constraints are treated by the modified barrier and PDLB methods. The inequality constraints are transformed into equalities by introducing positive auxiliary variables and are perturbed by the barrier parameter. The first-order necessary conditions of the Lagrangian function are 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. The electric systems IEEE 14, 162 and 300 buses were used in the comparative analysis. ©2007 IEEE.

Avaliação de interpoladores estatísticos e determinísticos na estimativa de atributos do solo em agricultura de precisão

The obtaining of the correct space distribution for attributes of the soil is relevant in the agricultural planning, in what concerns to the installation and maintenance of the cultures. The objective of that work was to compare statistical interpolation methods (ordinary krigagem) and deterministic methods (inverse square distance) in the estimate of CTC and V% in a distrophic yellow-red Latossolo. The study was accomplished in the State of Experimental Hands on of the Instituto Capixaba de Pesquisa, Assistência Técnica e Extensão Rural (INCAPER), in an irregular grading with 109 points. The data were collected in the layer of 0 - 0,20 m in the projection of the cup of the plants, in the superior part of the slope. The performance of the interpolators was obtained and compared using the criterion of the medium mistake. The observations are dependent in space until a maximum reach of 14,1 m, considering the isotropy. IDW presented larger mistake in the estimate of the data; however its difference in relation to KRIG was small for both variables.

A structure excited by a DC motor of limited power supply and controlled by a pendulum like device

In this paper, a mathematical model is derived via Lagrange's Equation for a shear building structure that acts as a foundation of a non-ideal direct current electric motor, controlled by a mass loose inside a circular carving. Non-ideal sources of vibrations of structures are those whose characteristics are coupled to the motion of the structure, not being a function of time only as in the ideal case. Thus, in this case, an additional equation of motion is written, related to the motor rotation, coupled to the equation describing the horizontal motion of the shear building. This kind of problem can lead to the so-called Sommerfeld effect: steady state frequencies of the motor will usually increase as more power (voltage) is given to it in a step-by-step fashion. When a resonance condition with the structure is reached, the better part of this energy is consumed to generate large amplitude vibrations of the foundation without sensible change of the motor frequency as before. If additional increase steps in voltage are made, one may reach a situation where the rotor will jump to higher rotation regimes, no steady states being stable in between. As a device of passive control of both large amplitude vibrations and the Sommerfeld effect, a scheme is proposed using a point mass free to bounce back and forth inside a circular carving in the suspended mass of the structure. Numerical simulations of the model are also presented Copyright © 2007 by ASME.

Multi-areas optimal reactive power flow

This paper describes a method for the decentralized solution of the optimal reactive power flow (ORPF) problem in interconnected power systems. The ORPF model is solved in a decentralized framework, consisting of regions, where the transmission system operator in each area operates its system independently of the other areas, obtaining an optimal coordinated but decentralized solution. The proposed scheme is based on an augmented Lagrangian approach using the auxiliary problem principle (APP). An implementation of an interior point method is described to solve the decoupled problem in each area. The described method is successfully implemented and tested using the IEEE two area RTS 96 test system. Numerical results comparing the solutions obtained by the traditional and the proposed decentralized methods are presented for validation. ©2008 IEEE.

Swarm control designs applied to a non-ideal load transportation system

In this paper, a load transport system in platforms is considered. It is a transport device and is modelled as an inverted pendulum built on a car driven by a DC motor. The motion equations were obtained by Lagrange's equations. The mathematical model considers the interaction between the DC motor and the dynamic system. The dynamic system was analysed and a Swarm Control Design was developed to stabilize the model of this load transport system. ©2010 IEEE.

Métodos de interpolação para estimar o ph em solo sob dois manejos de café Arábica

There are many methods used to estimate values in places no sampled for construction of contours maps. The aim of this study was to use the methods of interpolation kriging, inverse of the square of the distance and polynomial in the representation of the spatial variability of the pH of the soil in the organic and conventional management in the culture of the coffee plantation. For that, irregular meshes were built for soil sampling in the depth of 0-0,10 meters, totaling 40 points sampling in each area. For gauging of the interpolation methods they were solitary 10% of the total of points, for each area. Initially, the data were appraised through the classic statistics (descriptive and exploratory) and spatial analysis. The method inverse square of the distance and kriging has low error in estimating dados. The method of kriging presented low variation around the average in different managements.

Non-exhaustive test for aerobic capacity determination in running rats

A simple and applicable method for non-exhaustive aerobic evaluation in running rats is described. Wistar rats were submitted to running test at different velocities (10, 15, 20, 25 m/min) with 48 h recovery among them. At each velocity, the rats ran two bouts of 5 min with 2 min of rest between bouts. Blood samples were collected at the end of each bout for lactate determination. For each intensity, delta lactate was calculated and using deltas obtained by four tests, an individual linear interpolation was plotted. The y-intercept of linear interpolation was the null delta lactate equivalent to the critical velocity (CV). To verify the lactate stabilization at CV, the animals were submitted to 25 min of continuous exercise (15, 20, 25 m/min), with blood collection every 5 min. The estimated CV was 16.6±0.7 m/min, with significant linear regressions (R=0.90±0.03). The rats presented maximal lactate steady state (MLSS) at 3.9±0.4 mmol/L, at 20 m/min. The CV was less than MLSS but significantly correlated with this parameter (r=0.78). This non-exhaustive test seems to be valid for the aerobic evaluation of sedentary rats and this protocol underestimates the MLSS in 20%. This test seems to be the interesting method for the evaluation of rats submitted to acute exercise or physical training.

Charged particle transverse momentum spectra in pp collisions at √s = 0:9 and 7 TeV

The charged particle transverse momentum (pT) spectra are presented for pp collisions at √s = 0:9 and 7TeV. The data samples were collected with the CMS detector at the LHC and correspond to integrated luminosities of 231 μb-1 and 2.96 pb-1, respectively. Calorimeter-based high-transverse-energy triggers are employed to enhance the statistical reach of the high-pT measurements. The results are compared with leading and next-toleading order QCD and with an empirical scaling of measurements at different collision energies using the scaling variable xT - 2pT=ps over the pT range up to 136 GeV/c. Using a combination of xT scaling and direct interpolation at fixed pT, a reference transverse momentum spectrum at √s = 2:76TeV is constructed, which can be used for studying high-pT particle suppression in the dense QCD medium produced in heavy-ion collisions at that centre-of-mass energy. Copyright CERN.

Interaction between wave and coastal structure: Validation of two lagrangian numerical models with experimental results marine 2011

Numerical modeling of the interaction among waves and coastal structures is a challenge due to the many nonlinear phenomena involved, such as, wave propagation, wave transformation with water depth, interaction among incident and reflected waves, run-up / run-down and wave overtopping. Numerical models based on Lagrangian formulation, like SPH (Smoothed Particle Hydrodynamics), allow simulating complex free surface flows. The validation of these numerical models is essential, but comparing numerical results with experimental data is not an easy task. In the present paper, two SPH numerical models, SPHysics LNEC and SPH UNESP, are validated comparing the numerical results of waves interacting with a vertical breakwater, with data obtained in physical model tests made in one of the LNEC's flume. To achieve this validation, the experimental set-up is determined to be compatible with the Characteristics of the numerical models. Therefore, the flume dimensions are exactly the same for numerical and physical model and incident wave characteristics are identical, which allows determining the accuracy of the numerical models, particularly regarding two complex phenomena: wave-breaking and impact loads on the breakwater. It is shown that partial renormalization, i.e. renormalization applied only for particles near the structure, seems to be a promising compromise and an original method that allows simultaneously propagating waves, without diffusion, and modeling accurately the pressure field near the structure.

Optimal low cost transfer to L4 and L5 lagrangian points

Lagrangian points L4 and L5 lie at 60 degrees ahead of and behind Moon in its orbit with respect to the Earth. Each one of them is a third point of an equilateral triangle with the base of the line defined by those two bodies. These Lagrangian points are stable for the Earth-Moon mass ratio. Because of their distance electromagnetic radiations from the Earth arrive on them substantially attenuated. As so, these Lagrangian points represent remarkable positions to host astronomical observatories. However, this same distance characteristic may be a challenge for periodic servicing mission. In this work, we introduce a new low-cost orbital transfer strategy that opportunistically combine chaotic and swing-by transfers to get a very efficient strategy that can be used for servicing mission on astronomical mission placed on Lagrangian points L4 or L5. This strategy is not only efficient with respect to thrust requirement, but also its time transfer is comparable to others known transfer techniques based on time optimization. Copyright ©2010 by the International Astronautical Federation. All rights reserved.

Espacialização das estimativas de contaminação de águas subterrâneas por Tebuthiuron

Improper use of pesticides can lead to significant environmental impacts such as, contamination of environmental compartments, being the aquatic compartments the most vulnerable. In this context, the spatialization of pesticides concentrations estimative in groundwater provides important insights for decision making in managing and monitoring pesticides use. This study aimed to spatialize estimatives of groundwater contamination by Tebuthiuron, from different irrigation depths in the Rio Pardo basin, Pardinho-SP, Brazil. The simulations were performed using the ARAquá computer system, considering 0mm, 200 mm and 400 mm annual irrigation depths. Geostatistical techniques were used to obtain the spatial distribution of the simulated estimative. Tebuthiuron maps estimating concentration in groundwater were obtained by Kriging interpolation method, and indicated the areas with high potential for groundwater contamination. Considering all the simulations, it was concluded that there was no risk of groundwater contamination by Tebuthiuron in the study area.

New optimality conditions for nonsmooth control problems

This work considers nonsmooth optimal control problems and provides two new sufficient conditions of optimality. The first condition involves the Lagrange multipliers while the second does not. We show that under the first new condition all processes satisfying the Pontryagin Maximum Principle (called MP-processes) are optimal. Conversely, we prove that optimal control problems in which every MP-process is optimal necessarily obey our first optimality condition. The second condition is more natural, but it is only applicable to normal problems and the converse holds just for smooth problems. Nevertheless, it is proved that for the class of normal smooth optimal control problems the two conditions are equivalent. Some examples illustrating the features of these sufficient concepts are presented. © 2012 Springer Science+Business Media New York.

The fractional-nonlinear robotic manipulator: Modeling and dynamic simulations

In this paper, we applied the Riemann-Liouville approach and the fractional Euler-Lagrange equations in order to obtain the fractional-order nonlinear dynamics equations of a two link robotic manipulator. The aformentioned equations have been simulated for several cases involving: integer and non-integer order analysis, with and without external forcing acting and some different initial conditions. The fractional nonlinear governing equations of motion are coupled and the time evolution of the angular positions and the phase diagrams have been plotted to visualize the effect of fractional order approach. The new contribution of this work arises from the fact that the dynamics equations of a two link robotic manipulator have been modeled with the fractional Euler-Lagrange dynamics approach. The results reveal that the fractional-nonlinear robotic manipulator can exhibit different and curious behavior from those obtained with the standard dynamical system and can be useful for a better understanding and control of such nonlinear systems. © 2012 American Institute of Physics.

Submerged macrophytes height estimation by echosounder data sample

Traditional methods of submerged aquatic vegetation (SAV) survey last long and then, they are high cost. Optical remote sensing is an alternative, but it has some limitations in the aquatic environment. The use of echosounder techniques is efficient to detect submerged targets. Therefore, the aim of this study is to evaluate different kinds of interpolation approach applied on SAV sample data collected by echosounder. This study case was performed in a region of Uberaba River - Brazil. The interpolation methods evaluated in this work follow: Nearest Neighbor, Weighted Average, Triangular Irregular Network (TIN) and ordinary kriging. Better results were carried out with kriging interpolation. Thus, it is recommend the use of geostatistics for spatial inference of SAV from sample data surveyed with echosounder techniques. © 2012 IEEE.

Optimal low-cost transfer to L4 and L5 lagrangian points based on G-family of periodic orbits

An alternative transfer strategy to send spacecrafts to stable orbits around the Lagrangian equilibrium points L4 and L5 based in trajectories derived from the periodic orbits around LI is presented in this work. The trajectories derived, called Trajectories G, are described and studied in terms of the initial generation requirements and their energy variations relative to the Earth through the passage by the lunar sphere of influence. Missions for insertion of spacecrafts in elliptic orbits around L4 and L5 are analysed considering the Restricted Three-Body Problem Earth- Moon-particle and the results are discussed starting from the thrust, time of flight and energy variation relative to the Earth. Copyright© (2012) by the International Astronautical Federation.