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.

Magnetic behavior of poly(3-methylthiophene): Metamagnetism and room-temperature weak ferromagnetism

A weak ferromagnetic phase is shown in pressed pellets of partially doped poly(3-methylthiophene) (P3MT) in the whole range from 1.8 to 300 K in magnetic measurements. Thermoremanence data have been used to estimate the suppression of this phase to be around 815 K. We also show that instead of the classical antiferromagnetism for the first-order interaction that gives weak ferromagnetism as a second-order effect, metamagnetic behavior is observed. X-band electron spin resonance (ESR) measurements and magnetization measurements allowed us to estimate that 8.1% of the total number of spins contributes to the weak ferromagnetism at room temperature. The doping level obtained from the ESR data is in good agreement with that estimated from electron dispersive spectroscopy measurements.

Photoelectrocatalytic degradation of Remazol Brilliant Orange 3R on titanium dioxide thin-film electrodes

Degradation of reactive dye Remazol Brilliant Orange 3R (RBO) has been performed using photoeletrocatalysis. A biased potential is applied across a titanium dioxide thin-film photoelectrode illuminated by UV light. It is suggested that charges photogenerated at the electrode surface give rise to chlorine generation and powerful oxidants (OH) that causes the dye solution to decolorize. Rate constants calculated from color decay versus time reveal a first-order reaction up to 5.0×10-5 mol l-1 in dye concentration. The best experimental conditions were found to be pH 6.0 and 1.0 mol l-1 NaCl when the photoelectrode was biased at +1V (versus SCE). Almost complete mineralization of the dye content (70% TOC reduction) was achieved in a 3-h period using these conditions. Effects of other electrolytes, dye concentration and applied potentials also have been investigated and are discussed. © 2003 Elsevier Science B.V. All rights reserved.

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.

A low-voltage low-sensitivity sinusoidal VCO for DPLL realizations

A quasi-sinusoidal linearly tunable OTA-C VCO built with triode-region transconductors is presented. Oscillation upon power-on is ensured by RHP poles associated with gate-drain capacitances of OTA input devices. Since the OTA nonlinearity stabilizes the amplitude, the oscillation frequency f0 is first-order independent of VDD, making the VCO adequate to mixed-mode designs. A range of simulations attests the theoretical analysis. As part of a DPLL, the VCO was prototyped on a 0.8μm CMOS process, occupying an area of 0.15mm2. Nominal f0 is 1MHz, with K VCo=8.4KHz/mV. Measured sensitivity to VDD is below 2.17, while phase noise is -86dBc at 100-KHz offset. The feasibility of the VCO for higher frequencies is verified by a redesign based on a 0.35μm CMOS process and VDD=3.3V, with a linear frequency-span of l3.2MHz - 61.5MHz.

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.

Ferromagnetic nanoclusters formed by Mn implantation in GaAs

Ferromagnetic clusters were incorporated into GaAs samples by Mn implantation and subsequent annealing. The composition and structural properties of the Mn-based nanoclusters formed at the surface and buried into the GaAs sample were analyzed by x-ray and microscopic techniques. Our measurements indicate the presence of buried MnAs nanoclusters with a structural phase transition around 40 °C, in accord with the first-order magneto-structural phase transition of bulk MnAs. We discuss the structural behavior of these nanoclusters during their formation and phase transition, which is an important point for technological applications. © 2005 American Institute of Physics.

Simulations of incompressible fluid flows by a least squares finite element method

In this work simulations of incompressible fluid flows have been done by a Least Squares Finite Element Method (LSFEM) using velocity-pressure-vorticity and velocity-pressure-stress formulations, named u-p-ω) and u-p-τ formulations respectively. These formulations are preferred because the resulting equations are partial differential equations of first order, which is convenient for implementation by LSFEM. The main purposes of this work are the numerical computation of laminar, transitional and turbulent fluid flows through the application of large eddy simulation (LES) methodology using the LSFEM. The Navier-Stokes equations in u-p-ω and u-p-τ formulations are filtered and the eddy viscosity model of Smagorinsky is used for modeling the sub-grid-scale stresses. Some benchmark problems are solved for validate the numerical code and the preliminary results are presented and compared with available results from the literature. Copyright © 2005 by ABCM.

Photo-oxidation of polyphenylenevinylene chains in Langmuir-Blodgett and cast films

Poly(p-phenylene vinylene) (PPV) derivatives are well known for their applications in polymer light emitting diodes (PLEDs). These derivatives are highly susceptible to photooxidation though, which is mainly caused by the scission of the vinyl double bond on the polymer backbone. In this work, we show that Langmuir-Blodgett (LB) films are less degraded than cast films of a PPV derivative (OC1OC6-PPV). Both films had similar thickness (∼50 nm) to allow for a more realistic comparison. Photodegradation experiments were carried out by illuminating the films with white light from a halogen lamp (50W, 12 V), placed at a fixed dstance from the sample. The decay was monitored by UV-Vis and FTIR spectroscopies. The results showed that cast films are completely degraded in ca. 300 min, while LB took longer times, ca. 1000 min, i.e. 3 times the values for the cast films. The degradation process occurs in at least two stages, the rates of which were calculated assuming that the reaction follows a first order kinetics. The characteristic times for the first stage were 3.6×10-2 and 1.3×10-3 min-1 for cast and LB films, respectively. For the second stage the characteristic times were 5.6×10-2 and 5.0×10 -3 min-1. The differences can be attributed to the more compact morphology in the LB than in the cast films. With a compact morphology the diffusion of oxygen in the LB film is hampered and this causes a delay in the degradation process.

Phase constraint for the waves diffracted by lossless symmetrical gratings at Littrow mount

The energy conservation of grating diffraction is analyzed in a particular condition of incidence in which two incident waves reach a symmetrical grating from the two sides of the grating normal at the first-order Littrow mounting. In such a situation the incident waves generate an interference pattern with the same period as the grating. Thus in each direction of diffraction, interference occurs between two consecutive diffractive orders of the symmetrical incident waves. By applying only energy conservation and the geometrical symmetry of the grating profile to this problem it is possible to establish a general constraint for the phases and amplitudes of the diffracted orders of the same incident wave. Experimental and theoretical results are presented confirming the obtained relations. © 2006 Optical Society of America.

Ecology and morphological characterization of gametophyte and 'Chantransia' stages of Sirodotia huillensis (Batrachospermales, Rhodophyta) from a stream in central Mexico

The morphology and phenology of Sirodotia huillensis was evaluated seasonally in a central Mexican first-order calcareous stream. Water temperature was constant (24-25°C) and pH circumneutral to alkaline (6.7-7.9), and calcium and sulfates were the dominant ions. The gametophyte stages were characterized by the presence of a distinctive mucilaginous layer, a marked difference in phycocyanin to phycoerythrin ratio between female and male plants, and the presence of a carpogonia with a large trichogyne (>60 μm). Occasionally three capogonia were observed on a single basal cell. The 'Chantransia' stages were morphologically similar to those described for the other members of Batrachospermales. A remarkable observation was the formation of dome-shaped structures, consisting of prostrate filaments that are related with the development of new gametophytes. Chromosome numbers were n = 4 for fascicle cells, cortical filament cells and dome-shaped cells, and 2n = 8 for gonimoblast filament cells and 'Chantransia' stage filaments. Gametophytes and 'Chantransia' stages occurred in fast current velocities (60-170 cm/s) and shaded (33.1-121 μmol photons/m2/s) stream segments. The population fluctuated throughout the study period in terms of percentage cover and frequency: the 'Chantransia' stages were most abundant in the rainy season, whereas gametophytic plants had the highest frequency values during the dry season. These results were most likely a result of fluctuations in rainfall and related changes in current velocity. Some characteristics of this population can be viewed as probable adaptations to high current velocities: the mucilaginous layer around plants that reduces drag; potential increase in fertilization by the elongate and plentiful trichogynes and abundant dome-shaped structures producing several gametophytes.

Metal-insulator transition in Nd1-xEuxNiO 3 compounds

Polycrystalline Nd1-xEuxNiO3 (0≤x≤0.5) compounds were synthesized in order to investigate the character of the metal-insulator (MI) phase transition in this series. Samples were prepared through the sol-gel route and subjected to heat treatments at ∼1000 °C under oxygen pressures as high as 80bar. X-ray diffraction (XRD) and neutron powder diffraction (NPD), electrical resistivity ρ(T), and magnetization M(T) measurements were performed on these compounds. The NPD and XRD results indicated that the samples crystallize in an orthorhombic distorted perovskite structure, space group Pbnm. The analysis of the structural parameters revealed a sudden and small expansion of ∼0.2% of the unit cell volume when electronic localization occurs. This expansion was attributed to a small increase of ∼0.003 of the average Ni-O distance and a simultaneous decrease of ∼-0.5° of the Ni-O-Ni superexchange angle. The ρ(T) measurements revealed a MI transition occurring at temperatures ranging from TMI∼193 to 336K for samples with x ≤ 0 and 0.50, respectively. These measurements also show a large thermal hysteresis in NdNiO3 during heating and cooling processes, suggesting a first-order character of the phase transition at TMI. The width of this thermal hysteresis was found to decrease appreciably for the sample Nd 0.7Eu0.3NiO3. The results indicate that cation disorder associated with increasing substitution of Nd by Eu is responsible for changing the first-order character of the transition in NdNiO3. © 2006 IOP Publishing Ltd.

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.

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.

A resolução do problema de despacho ótimo de reativos pelo método da função Lagrangiana-barreira relaxada

This work presents the application of the relaxed barrier-Lagrangian function method to the optimal reactive dispatch problem, which is a nonlinear nonconvex and large problem. In this approach the inequality constraints are treated by the association of modified barrier and primal-dual logarithmic barrier method. Those constraints are transformed in equalities through positive auxiliary variables and are perturbed by the barrier parameter. A Lagrangian function is associated to the modified problem. The first-order necessary conditions are applied generating a non-linear system which is solved by Newton's method. The auxiliary variables perturbation result in an expansion of the feasible set of the original problem, allowing the limits of the inequality constraints to be reach. Numeric tests with the systems CESP 53 buses and the south-southeast Brazilian and the comparative test with the primal-dual logarithmic barrier method indicate that presented method is efficient in the resolution of optimal reactive dispatch problem.