Second-order negative-curvature methods for box-constrained and general constrained optimization

A Nonlinear Programming algorithm that converges to second-order stationary points is introduced in this paper. The main tool is a second-order negative-curvature method for box-constrained minimization of a certain class of functions that do not possess continuous second derivatives. This method is used to define an Augmented Lagrangian algorithm of PHR (Powell-Hestenes-Rockafellar) type. Convergence proofs under weak constraint qualifications are given. Numerical examples showing that the new method converges to second-order stationary points in situations in which first-order methods fail are exhibited.

Existence Results for Second Order Differential Equations with Nonlocal Conditions in Banach Spaces

This work is concerned with implicit second order abstract differential equations with nonlocal conditions. Assuming that the involved operators satisfy sonic compactness properties, we establish the existence of local mild solutions, the existence of global mild solutions and the existence of asymptotically almost periodic solutions.

Positive solutions for a fourth order equation with nonlinear boundary conditions

Existence of positive solutions for a fourth order equation with nonlinear boundary conditions, which models deformations of beams on elastic supports, is considered using fixed points theorems in cones of ordered Banach spaces. Iterative and numerical solutions are also considered. (C) 2010 IMACS. Published by Elsevier B.V. All rights reserved.

Monotone positive solutions for a fourth order equation with nonlinear boundary conditions

This work is concerned with the existence of monotone positive solutions for a class of beam equations with nonlinear boundary conditions. The results are obtained by using the monotone iteration method and they extend early works on beams with null boundary conditions. Numerical simulations are also presented. (C) 2009 Elsevier Ltd. All rights reserved.

A Direct Numerov Sixth-order Numerical Scheme to Accurately Solve the Unidimensional Poisson Equation with Dirichlet Boundary Conditions

In this article, we present an analytical direct method, based on a Numerov three-point scheme, which is sixth order accurate and has a linear execution time on the grid dimension, to solve the discrete one-dimensional Poisson equation with Dirichlet boundary conditions. Our results should improve numerical codes used mainly in self-consistent calculations in solid state physics.

Aerobic and anaerobic metabolism for the zebrafish, Danio rerio, reared under normoxic and hypoxic conditions and exposed to acute hypoxia during development

In order to verify the influence of chronic and acute ambient oxygen levels from egg to adult stage of the zebrafish, in vivo oxygen consumption (MO2), critical tensions of oxygen (Pcrit), heart rate (fH) and total body lactate concentration (Lc) were determined for Danio rerio (Hamilton, 1822) raised at 28 °C under normoxic (7.5 mgO2.L-1 or 80 mm.Hg-1) and hypoxic conditions (4.3 mgO2.L-1) and exposed to acute hypoxia during different developmental stages. Our findings confirmed that very early stages do not respond effectively to ambient acute hypoxia. However, after the stage corresponding to the age of 30 days, D. rerio was able to respond to acute hypoxia through effective physiological mechanisms involving aerobic and anaerobic metabolism. Such responses were more efficient for the fishes reared under hypoxia which showed that D. rerio survival capability increased during acclimation to mild hypoxia. Measurements of body mass and length showed that moderate hypoxia did not affect growth significantly until the fish reached the stage of 60 days. Moreover, a growth delay was verified for the hypoxic-reared animals. Also, the D. rerio eggs-to-larvae survival varied from 87.7 to 62.4% in animals reared under normoxia and mild hypoxia, respectively. However, the surviving animals raised under moderated hypoxia showed a better aptitude to regulate aerobic and anaerobic capacities when exposed to acute hypoxia.

Environmental conditions and rodent infestation in Campo Limpo district, Sao Paulo municipality, Brazil

Rodents are involved in the transmission to human beings of several diseases, including liptospirosis, which shows high lethality rates in Sao Paulo municipality. Despite this, few studies have assessed the relationship existing between urban environmental conditions and building rodent infestation. With the purpose of clarifying this relationship, an analysis has been conducted in order to quantify the influence of environmental factors upon rodent infestation on a low-income district. Diagnosis of the environmental situation has been performed to evaluate the frequency according to which harborage, food and access sources occur, and a survey on infestation rates in 2175 dwellings in the area studied. The logistic regression analysis showed that among the environmental variables, the one that showed the closest association with rodent infestation was access; followed by harborage, and food. It was concluded that poor socioeconomic and environmental conditions in the area propitiate the occurrence of high rodent infestation rates

LOCAL WELL POSEDNESS, ASYMPTOTIC BEHAVIOR AND ASYMPTOTIC BOOTSTRAPPING FOR A CLASS OF SEMILINEAR EVOLUTION EQUATIONS OF THE SECOND ORDER IN TIME

A class of semilinear evolution equations of the second order in time of the form u(tt)+Au+mu Au(t)+Au(tt) = f(u) is considered, where -A is the Dirichlet Laplacian, 92 is a smooth bounded domain in R(N) and f is an element of C(1) (R, R). A local well posedness result is proved in the Banach spaces W(0)(1,p)(Omega)xW(0)(1,P)(Omega) when f satisfies appropriate critical growth conditions. In the Hilbert setting, if f satisfies all additional dissipativeness condition, the nonlinear Semigroup of global solutions is shown to possess a gradient-like attractor. Existence and regularity of the global attractor are also investigated following the unified semigroup approach, bootstrapping and the interpolation-extrapolation techniques.

SYNCHRONIZATION OF A CLASS OF SECOND-ORDER NONLINEAR SYSTEMS

The asymptotic behavior of a class of coupled second-order nonlinear dynamical systems is studied in this paper. Using very mild assumptions on the vector-field, conditions on the coupling parameters that guarantee synchronization are provided. The proposed result does not require solutions to be ultimately bounded in order to prove synchronization, therefore it can be used to study coupled systems that do not globally synchronize, including synchronization of unbounded solutions. In this case, estimates of the synchronization region are obtained. Synchronization of two-coupled nonlinear pendulums and two-coupled Duffing systems are studied to illustrate the application of the proposed theory.

Dendritic Arm Spacing Affecting Mechanical Properties and Wear Behavior of Al-Sn and Al-Si Alloys Directionally Solidified under Unsteady-State Conditions

Alloys of Al-Sn and Al-Si are widely used in tribological applications such as cylinder liners and journal bearings. Studies of the influence of the as-cast microstructures of these alloys on the final mechanical properties and wear resistance can be very useful for planning solidification conditions in order to permit a desired level of final properties to be achieved. The aim of the present study was to contribute to a better understanding about the relationship between the scale of the dendritic network and the corresponding mechanical properties and wear behavior. The Al-Sn (15 and 20 wt pct Sn) and Al-Si (3 and 5 wt pct Si) alloys were directionally solidified under unsteady-state heat flow conditions in water-cooled molds in order to permit samples with a wide range of dendritic spacings to be obtained. These samples were subjected to tensile and wear tests, and experimental quantitative expressions correlating the ultimate tensile strength (UTS), yield tensile strength, elongation, and wear volume to the primary dendritic arm spacing (DAS) have been determined. The wear resistance was shown to be significantly affected by the scale of primary dendrite arm spacing. For Al-Si alloys, the refinement of the dendritic array improved the wear resistance, while for the Al-Sn alloys, an opposite effect was observed, i.e., the increase in primary dendrite arm spacing improved the wear resistance. The effect of inverse segregation, which is observed for Al-Sn alloys, on the wear resistance is also discussed.

Verification of a mixed high-order accurate DNS code for laminar turbulent transition by the method of manufactured solutions

This paper presents results on a verification test of a Direct Numerical Simulation code of mixed high-order of accuracy using the method of manufactured solutions (MMS). This test is based on the formulation of an analytical solution for the Navier-Stokes equations modified by the addition of a source term. The present numerical code was aimed at simulating the temporal evolution of instability waves in a plane Poiseuille flow. The governing equations were solved in a vorticity-velocity formulation for a two-dimensional incompressible flow. The code employed two different numerical schemes. One used mixed high-order compact and non-compact finite-differences from fourth-order to sixth-order of accuracy. The other scheme used spectral methods instead of finite-difference methods for the streamwise direction, which was periodic. In the present test, particular attention was paid to the boundary conditions of the physical problem of interest. Indeed, the verification procedure using MMS can be more demanding than the often used comparison with Linear Stability Theory. That is particularly because in the latter test no attention is paid to the nonlinear terms. For the present verification test, it was possible to manufacture an analytical solution that reproduced some aspects of an instability wave in a nonlinear stage. Although the results of the verification by MMS for this mixed-order numerical scheme had to be interpreted with care, the test was very useful as it gave confidence that the code was free of programming errors. Copyright (C) 2009 John Wiley & Sons, Ltd.

Design constraints for third-order PLL nodes in master-slave clock distribution networks

Clock signal distribution in telecommunication commercial systems usually adopts a master-slave architecture, with a precise time basis generator as a master and phase-locked loops (PLLs) as slaves. In the majority of the networks, second-order PLLs are adopted due to their simplicity and stability. Nevertheless, in some applications better transient responses are necessary and, consequently, greater order PLLs need to be used, in spite of the possibility of bifurcations and chaotic attractors. Here a master-slave network with third-order PLLs is analyzed and conditions for the stability of the synchronous state are derived, providing design constraints for the node parameters, in order to guarantee stability and reachability of the synchronous state for the whole network. Numerical simulations are carried out in order to confirm the analytical results. (C) 2009 Elsevier B.V. All rights reserved.

Route to chaos in a third-order phase-locked loop network

Phase-locked loops (PLLs) are widely used in applications related to control systems and telecommunication networks. Here we show that a single-chain master-slave network of third-order PLLs can exhibit stationary, periodic and chaotic behaviors, when the value of a single parameter is varied. Hopf, period-doubling and saddle-saddle bifurcations are found. Chaos appears in dissipative and non-dissipative conditions. Thus, chaotic behaviors with distinct dynamical features can be generated. A way of encoding binary messages using such a chaos-based communication system is suggested. (C) 2009 Elsevier B.V. All rights reserved.

Using bifurcations in the determination of lock-in ranges for third-order phase-locked loops

Transmission and switching in digital telecommunication networks require distribution of precise time signals among the nodes. Commercial systems usually adopt a master-slave (MS) clock distribution strategy building slave nodes with phase-locked loop (PLL) circuits. PLLs are responsible for synchronizing their local oscillations with signals from master nodes, providing reliable clocks in all nodes. The dynamics of a PLL is described by an ordinary nonlinear differential equation, with order one plus the order of its internal linear low-pass filter. Second-order loops are commonly used because their synchronous state is asymptotically stable and the lock-in range and design parameters are expressed by a linear equivalent system [Gardner FM. Phaselock techniques. New York: John Wiley & Sons: 1979]. In spite of being simple and robust, second-order PLLs frequently present double-frequency terms in PD output and it is very difficult to adapt a first-order filter in order to cut off these components [Piqueira JRC, Monteiro LHA. Considering second-harmonic terms in the operation of the phase detector for second order phase-locked loop. IEEE Trans Circuits Syst [2003;50(6):805-9; Piqueira JRC, Monteiro LHA. All-pole phase-locked loops: calculating lock-in range by using Evan`s root-locus. Int J Control 2006;79(7):822-9]. Consequently, higher-order filters are used, resulting in nonlinear loops with order greater than 2. Such systems, due to high order and nonlinear terms, depending on parameters combinations, can present some undesirable behaviors, resulting from bifurcations, as error oscillation and chaos, decreasing synchronization ranges. In this work, we consider a second-order Sallen-Key loop filter [van Valkenburg ME. Analog filter design. New York: Holt, Rinehart & Winston; 1982] implying a third order PLL The resulting lock-in range of the third-order PLL is determined by two bifurcation conditions: a saddle-node and a Hopf. (C) 2008 Elsevier B.V. All rights reserved.

Technical and economical evaluation of a harvester, working under different spacing and planting arrangement conditions in eucalypts plantations

Plantation spacing selection has the primary objective of assigning each tree enough space for maximum growth and best quality to be attained with a minimum cost. From the harvest standpoint, an increase in stand density directly implies a decrease of individual tree volume, reducing also harvester productive capacity. The objective of this research is to assess the effects of several initial spacings and arrangements in eucalyptus plantations on production capacity, operational capacity and costs of forest harvester. Real operational data were collected from two eucalypt plantations at different initial spacing of 6.0, 7.5, 9.0, 12 and 18 m(2) per tree. Simulation data were obtained from a forest harvester simulator. Using spacing (E), mean tree volume (MV), diameter at breast height (DBH) and height (H) values, a stepwise regression test procedure was run, and correlations computed in order to measure their participation in operational capacity. Operational costs were computed with an accounting method proposed by FAO. Mean tree volume (MV) explained 88% of forest harvester operational capacity. Spacing (E) affected 8.5% of harvester operational capacity; wider spacings were related to higher individual tree volumes. Harvesting operation costs were lower in wider spaced treatments.