Effects of Variations in Nonlinear Damping Coefficients on the Parametric Vibration of a Cantilever Beam with a Lumped Mass

Uncertainties in damping estimates can significantly affect the dynamic response of a given flexible structure. A common practice in linear structural dynamics is to consider a linear viscous damping model as the major energy dissipation mechanism. However, it is well known that different forms of energy dissipation can affect the structure's dynamic response. The major goal of this paper is to address the effects of the turbulent frictional damping force, also known as drag force on the dynamic behavior of a typical flexible structure composed of a slender cantilever beam carrying a lumped-mass on the tip. First, the system's analytical equation is obtained and solved by employing a perturbation technique. The solution process considers variations of the drag force coefficient and its effects on the system's response. Then, experimental results are presented to demonstrate the effects of the nonlinear quadratic damping due to the turbulent frictional force on the system's dynamic response. In particular, the effects of the quadratic damping on the frequency-response and amplitude-response curves are investigated. Numerically simulated as well as experimental results indicate that variations on the drag force coefficient significantly alter the dynamics of the structure under investigation. Copyright (c) 2008 D. G. Silva and P. S. Varoto.

Combining Legendre's Polynomials and Genetic Algorithm in the Solution of Nonlinear Initial-Value Problems

This work develops a method for solving ordinary differential equations, that is, initial-value problems, with solutions approximated by using Legendre's polynomials. An iterative procedure for the adjustment of the polynomial coefficients is developed, based on the genetic algorithm. This procedure is applied to several examples providing comparisons between its results and the best polynomial fitting when numerical solutions by the traditional Runge-Kutta or Adams methods are available. The resulting algorithm provides reliable solutions even if the numerical solutions are not available, that is, when the mass matrix is singular or the equation produces unstable running processes.

Influence of metallic nanoparticles on electric-dipole and magnetic-dipole transitions of Eu(3+) doped germanate glasses

Luminescence properties of Eu(3+) doped germanate glasses containing either silver or gold nanoparticles (NPs) were investigated for excitation at 405 nm. Enhanced emissions and luminescence quenching of the Eu(3+) transitions in the range from 570 to 720 nm were observed for samples having various concentrations of metallic NPs. Electric-dipole and magnetic-dipole transitions that originate from the Eu(3+) level (5)D(0) exhibit large enhancement due to the presence of the metallic NPs. The results suggest that the magnetic response of rare-earth doped metal-dielectric composites at optical frequencies can be as strong as their electric response due to the confinement of the optical magnetic field. (C) 2010 American Institute of Physics. [doi:10.1063/1.3431347]

Food profitability affects intranidal recruitment behaviour in the stingless bee Nannotrigona testaceicornis

Does the food's sugar concentration affect recruitment behaviour in the stingless bee Nan-notrigona testaceicornis? We recorded intranidal forager behaviour while offering sugar water of constant, increasing, or decreasing concentrations. Running speed was not correlated with sugar concentration but the jostling contacts/sec were. Food profitability also affected the recruiter's thorax vibrations: Pulse duration and duty cycle followed both concentration increases and decreases. Sugar concentration also influenced the number of recruited bees. In comparison to the phylogenetically closely related Scaptotrigona, Nan-notrigona's intranidal recruitment behaviour showed a more elaborate association with food profitability. This is likely to reflect differences in ecology and foraging strategies as Nannotrigona - in contrast to Scaptotrigona - does not lay scent trails to guide recruits to a food source.

Stress at Work among Electric Utility Workers

In the last decades there was an increase in stress at work and its effects on workers' health. These issues are still little studied in the electric utility sector. This study aims to evaluate factors associated with stress at work and to verify its associations with health status among workers of an electric company in Sao Paulo State, Brazil. A cross-sectional study was conducted with 474 subjects (87.5% of the eligible workers). Data were collected using self-reported questionnaires. A descriptive analysis, a multiple linear hierarchical regression analysis and a correlation analysis were performed. The majority of participants were males (91.1%) and the mean age was 37.5 yr. The mean score of stress level was 2.3 points (scale ranging from 1.0 to 5.0). Hierarchical multiple analyses showed that: regular practice of physical activities (p=0.025) and individual monthly income (p=0.002) were inversely associated with stress level; BMI was marginally associated with the stress level (p=0.074). The demographic characteristics were not associated with stress. Stress at work was significantly associated with physical and mental health status (p<0.001). To improve health of electric utility workers, actions are suggested to decrease stress by remuneration and an appropriate practice of physical activity aiming reduction of BMI.

A frequency approach to identifying asteroid families II. Families interacting with nonlinear secular resonances and low-order mean-motion resonances

Aims. In an earlier paper we introduced a new method for determining asteroid families where families were identified in the proper frequency domain (n, g, g + s) ( where n is the mean-motion, and g and s are the secular frequencies of the longitude of pericenter and nodes, respectively), rather than in the proper element domain (a, e, sin(i)) (semi-major axis, eccentricity, and inclination). Here we improve our techniques for reliably identifying members of families that interact with nonlinear secular resonances of argument other than g or g + s and for asteroids near or in mean-motion resonant configurations. Methods. We introduce several new distance metrics in the frequency space optimal for determining the diffusion in secular resonances of argument 2g - s, 3g - s, g - s, s, and 2s. We also regularize the dependence of the g frequency as a function of the n frequency (Vesta family) or of the eccentricity e (Hansa family). Results. Our new approaches allow us to recognize as family members objects that were lost with previous methods, while keeping the advantages of the Carruba & Michtchenko (2007, A& A, 475, 1145) approach. More important, an analysis in the frequency domain permits a deeper understanding of the dynamical evolution of asteroid families not always obtainable with an analysis in the proper element domain.

PARTIAL STABILITY FOR A CLASS OF NONLINEAR SYSTEMS

This paper studies a nonlinear, discrete-time matrix system arising in the stability analysis of Kalman filters. These systems present an internal coupling between the state components that gives rise to complex dynamic behavior. The problem of partial stability, which requires that a specific component of the state of the system converge exponentially, is studied and solved. The convergent state component is strongly linked with the behavior of Kalman filters, since it can be used to provide bounds for the error covariance matrix under uncertainties in the noise measurements. We exploit the special features of the system-mainly the connections with linear systems-to obtain an algebraic test for partial stability. Finally, motivated by applications in which polynomial divergence of the estimates is acceptable, we study and solve a partial semistability problem.

X-ray phase measurements as a probe of small structural changes in doped nonlinear optical crystals

X-ray multiple diffraction experiments with synchrotron radiation were carried out on pure and doped nonlinear optical crystals: NH(4)H(2)PO(4) and KH(2)PO(4) doped with Ni and Mn, respectively. Variations in the intensity profiles were observed from pure to doped samples, and these variations correlated with shifts in the structure factor phases, also known as triplet phases. This result demonstrates the potential of X-ray phase measurements to study doping in this type of single crystal. Different methodologies for probing structural changes were developed. Dynamical diffraction simulations and curve fitting procedures were also necessary for accurate phase determination. Structural changes causing the observed phase shifts are discussed.

Reduction of chaotic particle transport driven by drift waves in sheared flows

Investigations of chaotic particle transport by drift waves propagating in the edge plasma of tokamaks with poloidal zonal flow are described. For large aspect ratio tokamaks, the influence of radial electric field profiles on convective cells and transport barriers, created by the nonlinear interaction between the poloidal flow and resonant waves, is investigated. For equilibria with edge shear flow, particle transport is seen to be reduced when the electric field shear is reversed. The transport reduction is attributed to the robust invariant tori that occur in nontwist Hamiltonian systems. This mechanism is proposed as an explanation for the transport reduction in Tokamak Chauffage Alfven Bresilien [R. M. O. Galvao , Plasma Phys. Controlled Fusion 43, 1181 (2001)] for discharges with a biased electrode at the plasma edge.

Matter-wave two-dimensional solitons in crossed linear and nonlinear optical lattices

The existence of multidimensional matter-wave solitons in a crossed optical lattice (OL) with a linear optical lattice (LOL) in the x direction and a nonlinear optical lattice (NOL) in the y direction, where the NOL can be generated by a periodic spatial modulation of the scattering length using an optically induced Feshbach resonance is demonstrated. In particular, we show that such crossed LOLs and NOLs allow for stabilizing two-dimensional solitons against decay or collapse for both attractive and repulsive interactions. The solutions for the soliton stability are investigated analytically, by using a multi-Gaussian variational approach, with the Vakhitov-Kolokolov necessary criterion for stability; and numerically, by using the relaxation method and direct numerical time integrations of the Gross-Pitaevskii equation. Very good agreement of the results corresponding to both treatments is observed.

Two-dimensional supersonic nonlinear Schrodinger flow past an extended obstacle

Supersonic flow of a superfluid past a slender impenetrable macroscopic obstacle is studied in the framework of the two-dimensional (2D) defocusing nonlinear Schroumldinger (NLS) equation. This problem is of fundamental importance as a dispersive analog of the corresponding classical gas-dynamics problem. Assuming the oncoming flow speed is sufficiently high, we asymptotically reduce the original boundary-value problem for a steady flow past a slender body to the one-dimensional dispersive piston problem described by the nonstationary NLS equation, in which the role of time is played by the stretched x coordinate and the piston motion curve is defined by the spatial body profile. Two steady oblique spatial dispersive shock waves (DSWs) spreading from the pointed ends of the body are generated in both half planes. These are described analytically by constructing appropriate exact solutions of the Whitham modulation equations for the front DSW and by using a generalized Bohr-Sommerfeld quantization rule for the oblique dark soliton fan in the rear DSW. We propose an extension of the traditional modulation description of DSWs to include the linear ""ship-wave"" pattern forming outside the nonlinear modulation region of the front DSW. Our analytic results are supported by direct 2D unsteady numerical simulations and are relevant to recent experiments on Bose-Einstein condensates freely expanding past obstacles.

Nonlinear diffraction of light beams propagating in photorefractive media with embedded reflecting wire

The theory of nonlinear diffraction of intensive light beams propagating through photorefractive media is developed. Diffraction occurs on a reflecting wire embedded in the nonlinear medium at a relatively small angle with respect to the direction of the beam propagation. It is shown that this process is analogous to the generation of waves by a flow of a superfluid past an obstacle. The ""equation of state"" of such a superfluid is determined by the nonlinear properties of the medium. On the basis of this hydrodynamic analogy, the notion of the ""Mach number"" is introduced where the transverse component of the wave vector plays the role of the fluid velocity. It is found that the Mach cone separates two regions of the diffraction pattern: inside the Mach cone oblique dark solitons are generated and outside the Mach cone the region of ""optical ship waves"" (the wave pattern formed by a two-dimensional packet of linear waves) is situated. Analytical theory of the ""optical ship waves"" is developed and two-dimensional dark soliton solutions of the generalized two-dimensional nonlinear Schrodinger equation describing the light beam propagation are found. Stability of dark solitons with respect to their decay into vortices is studied and it is shown that they are stable for large enough values of the Mach number.

Localized modes of binary mixtures of Bose-Einstein condensates in nonlinear optical lattices

The properties of the localized states of a two-component Bose-Einstein condensate confined in a nonlinear periodic potential (nonlinear optical lattice) are investigated. We discuss the existence of different types of solitons and study their stability by means of analytical and numerical approaches. The symmetry properties of the localized states with respect to nonlinear optical lattices are also investigated. We show that nonlinear optical lattices allow the existence of bright soliton modes with equal symmetry in both components and bright localized modes of mixed symmetry type, as well as dark-bright bound states and bright modes on periodic backgrounds. In spite of the quasi-one-dimensional nature of the problem, the fundamental symmetric localized modes undergo a delocalizing transition when the strength of the nonlinear optical lattice is varied. This transition is associated with the existence of an unstable solution, which exhibits a shrinking (decaying) behavior for slightly overcritical (undercritical) variations in the number of atoms.

Hyperpolarizabilities of the methanol molecule: A CCSD calculation including vibrational corrections

In this work we present the results for hyperpolarizabilities of the methanol molecule including vibrational corrections and electron correlation effects at the CCSD level. Comparisons to random phase approximation results previously reported show that the electron correlation is in general important for both electronic contribution and vibrational corrections. The role played by the anharmonicities on the calculations of the vibrational corrections has also been analyzed and the obtained results indicate that the anharmonic terms are important for the dc-Pockels and dc-Kerr effects. For the other nonlinear optical properties studied the double-harmonic approximation is found to be suitable. Comparison to available experimental result in gas phase for the dc-second harmonic generation second hyperpolarizability shows a very good agreement with the electronic contribution calculated here while our total value is 14% larger than the experimental value.

Extra phase noise from thermal fluctuations in nonlinear optical crystals

We show theoretically and experimentally that scattered light by thermal phonons inside a second-order nonlinear crystal is the source of additional phase noise observed in optical parametric oscillators. This additional phase noise reduces the quantum correlations and has hitherto hindered the direct production of multipartite entanglement in a single nonlinear optical system. We cooled the nonlinear crystal and observed a reduction in the extra noise. Our treatment of this noise can be successfully applied to different systems in the literature.