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.

Stability and ergodicity of piecewise deterministic Markov processes

The main goal of this paper is to establish some equivalence results on stability, recurrence, and ergodicity between a piecewise deterministic Markov process ( PDMP) {X( t)} and an embedded discrete-time Markov chain {Theta(n)} generated by a Markov kernel G that can be explicitly characterized in terms of the three local characteristics of the PDMP, leading to tractable criterion results. First we establish some important results characterizing {Theta(n)} as a sampling of the PDMP {X( t)} and deriving a connection between the probability of the first return time to a set for the discrete-time Markov chains generated by G and the resolvent kernel R of the PDMP. From these results we obtain equivalence results regarding irreducibility, existence of sigma-finite invariant measures, and ( positive) recurrence and ( positive) Harris recurrence between {X( t)} and {Theta(n)}, generalizing the results of [ F. Dufour and O. L. V. Costa, SIAM J. Control Optim., 37 ( 1999), pp. 1483-1502] in several directions. Sufficient conditions in terms of a modified Foster-Lyapunov criterion are also presented to ensure positive Harris recurrence and ergodicity of the PDMP. We illustrate the use of these conditions by showing the ergodicity of a capacity expansion model.

AVERAGE CONTINUOUS CONTROL OF PIECEWISE DETERMINISTIC MARKOV PROCESSES

This paper deals with the long run average continuous control problem of piecewise deterministic Markov processes (PDMPs) taking values in a general Borel space and with compact action space depending on the state variable. The control variable acts on the jump rate and transition measure of the PDMP, and the running and boundary costs are assumed to be positive but not necessarily bounded. Our first main result is to obtain an optimality equation for the long run average cost in terms of a discrete-time optimality equation related to the embedded Markov chain given by the postjump location of the PDMP. Our second main result guarantees the existence of a feedback measurable selector for the discrete-time optimality equation by establishing a connection between this equation and an integro-differential equation. Our final main result is to obtain some sufficient conditions for the existence of a solution for a discrete-time optimality inequality and an ordinary optimal feedback control for the long run average cost using the so-called vanishing discount approach. Two examples are presented illustrating the possible applications of the results developed in the paper.

Near-infrared third-order nonlinearity of PbO-GeO(2) films containing Cu and Cu(2)O nanoparticles

We report measurements of the nonlinear (NL) refractive index n(2) of lead-germanium films (LGFs) containing Cu and Cu(2)O nanoparticles (NPs). The thermally managed eclipse Z-scan technique with 150 fs pulses from a laser operating at 800 nm was used. The NL refractive index measured, n(2)=6.3x10(-12) cm(2)/W has electronic origin and the NL absorption coefficient alpha(2) is smaller than 660 cm/GW. The figure of merit n(2)/lambda alpha(2) is enhanced by more than two orders of magnitude in comparison with the result for the LGFs without the copper based NPs. (C) 2008 American Institute of Physics.

Pulse train fluorescence technique for measuring triplet state dynamics

We report on a method to study the dynamics of triplet formation based on the fluorescence signal produced by a pulse train. Basically, the pulse train acts as sequential pump-probe pulses that precisely map the excited-state dynamics in the long time scale. This allows characterizing those processes that affect the population evolution of the first excited singlet state, whose decay gives rise to the fluorescence. The technique was proven to be valuable to measure parameters of triplet formation in organic molecules. Additionally, this single beam technique has the advantages of simplicity, low noise and background-free signal detection. (C) 2011 Optical Society of America

Possibility for a full optical determination of photodynamic therapy outcome

The efficacy of photodynamic therapy (PDT) depends on a variety of parameters: concentration of the photosensitizer at the time of treatment, light wavelength, fluence, fluence rate, availability of oxygen within the illuminated volume, and light distribution in the tissue. Dosimetry in PDT requires the congregation of adequate amounts of light, drug, and tissue oxygen. The adequate dosimetry should be able to predict the extension of the tissue damage. Photosensitizer photobleaching rate depends on the availability of molecular oxygen in the tissue. Based on photosensitizers photobleaching models, high photobleaching has to be associated with high production of singlet oxygen and therefore with higher photodynamic action, resulting in a greater depth of necrosis. The purpose of this work is to show a possible correlation between depth of necrosis and the in vivo photosensitizer (in this case, Photogem (R)) photodegradation during PDT. Such correlation allows possibilities for the development of a real time evaluation of the photodynamic action during PDT application. Experiments were performed in a range of fluence (0-450 J/cm(2)) at a constant fluence rate of 250 mW/cm(2) and applying different illumination times (0-1800 s) to achieve the desired fluence. A quantity was defined (psi) as the product of fluorescence ratio (related to the photosensitizer degradation at the surface) and the observed depth of necrosis. The correlation between depth of necrosis and surface fluorescence signal is expressed in psi and could allow, in principle, a noninvasive monitoring of PDT effects during treatment. High degree of correlation is observed and a simple mathematical model to justify the results is presented.

Multifilter rotating shadowband radiometer calibration for spectral aerosol optical depth retrievals over Sao Paulo City, Brazil

Multifilter rotating shadowband radiometer (MFRSR) calibration values for aerosol optical depth (AOD) retrievals were determined by means of the general method formulated by Forgan [Appl. Opt. 33, 4841 (1994)] at a polluted urban site. The obtained precision is comparable with the classical method, the Langley plot, applied on clean mountaintops distant of pollution sources. The AOD retrieved over Sao Paulo City with both calibration procedures is compared with the Aerosol Robotic Network data. The observed results are similar, and, except for the shortest wavelength (415 nm), the MFRSR`s AOD is systematically overestimated by similar to 0.03. (c) 2008 Optical Society of America.

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.

Optical identification of the transient supersoft X-ray source RX J0527.8-6954, in the LMC

Context. Close binary supersoft X-ray sources (CBSS) are binary systems that contain a white dwarf with stable nuclear burning on its surface. These sources, first discovered in the Magellanic Clouds, have high accretion rates and near-Eddington luminosities (10(37)-10(38) erg s(-1)) with high temperatures (T = 2-7 x 10(5) K). Aims. The total number of known objects in the MC is still small and, in our galaxy, even smaller. We observed the field of the unidentified transient supersoft X-ray source RX J0527.8-6954 in order to identify its optical counterpart. Methods. The observation was made with the IFU-GMOS on the Gemini South telescope with the purpose of identifying stars with possible He II or Balmer emission or else of observing nebular extended jets or ionization cones, features that may be expected in CBSS. Results. The X-ray source is identified with a B5e V star that is associated with subarcsecond extended H alpha emission, possibly bipolar. Conclusions. If the primary star is a white dwarf, as suggested by the supersoft X-ray spectrum, the expected orbital period exceeds 21 h; therefore, we believe that the 9.4 h period found so far is not associated to this system.

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.

Polar organic marker compounds in atmospheric aerosols during the LBA-SMOCC 2002 biomass burning experiment in Rondonia, Brazil: sources and source processes, time series, diel variations and size distributions

Measurements of polar organic marker compounds were performed on aerosols that were collected at a pasture site in the Amazon basin (Rondonia, Brazil) using a high-volume dichotomous sampler (HVDS) and a Micro-Orifice Uniform Deposit Impactor (MOUDI) within the framework of the 2002 LBA-SMOCC (Large-Scale Biosphere Atmosphere Experiment in Amazonia - Smoke Aerosols, Clouds, Rainfall, and Climate: Aerosols From Biomass Burning Perturb Global and Regional Climate) campaign. The campaign spanned the late dry season (biomass burning), a transition period, and the onset of the wet season (clean conditions). In the present study a more detailed discussion is presented compared to previous reports on the behavior of selected polar marker compounds, including levoglucosan, malic acid, isoprene secondary organic aerosol (SOA) tracers and tracers for fungal spores. The tracer data are discussed taking into account new insights that recently became available into their stability and/or aerosol formation processes. During all three periods, levoglucosan was the most dominant identified organic species in the PM(2.5) size fraction of the HVDS samples. In the dry period levoglucosan reached concentrations of up to 7.5 mu g m(-3) and exhibited diel variations with a nighttime prevalence. It was closely associated with the PM mass in the size-segregated samples and was mainly present in the fine mode, except during the wet period where it peaked in the coarse mode. Isoprene SOA tracers showed an average concentration of 250 ng m(-3) during the dry period versus 157 ng m(-3) during the transition period and 52 ng m(-3) during the wet period. Malic acid and the 2-methyltetrols exhibited a different size distribution pattern, which is consistent with different aerosol formation processes (i.e., gas-to-particle partitioning in the case of malic acid and heterogeneous formation from gas-phase precursors in the case of the 2-methyltetrols). The 2-methyltetrols were mainly associated with the fine mode during all periods, while malic acid was prevalent in the fine mode only during the dry and transition periods, and dominant in the coarse mode during the wet period. The sum of the fungal spore tracers arabitol, mannitol, and erythritol in the PM(2.5) fraction of the HVDS samples during the dry, transition, and wet periods was, on average, 54 ng m(-3), 34 ng m(-3), and 27 ng m(-3), respectively, and revealed minor day/night variation. The mass size distributions of arabitol and mannitol during all periods showed similar patterns and an association with the coarse mode, consistent with their primary origin. The results show that even under the heavy smoke conditions of the dry period a natural background with contributions from bioaerosols and isoprene SOA can be revealed. The enhancement in isoprene SOA in the dry season is mainly attributed to an increased acidity of the aerosols, increased NO(x) concentrations and a decreased wet deposition.

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.

Spectral dependence of aerosol light absorption over the Amazon Basin

In this study, we examine the spectral dependence of aerosol absorption at different sites and seasons in the Amazon Basin. The analysis is based on measurements performed during three intensive field experiments at a pasture site (Fazenda Nossa Senhora, Rondonia) and at a primary forest site (Cuieiras Reserve, Amazonas), from 1999 to 2004. Aerosol absorption spectra were measured using two Aethalometers: a 7-wavelength Aethalometer (AE30) that covers the visible (VIS) to near-infrared (NIR) spectral range, and a 2-wavelength Aethalometer (AE20) that measures absorption in the UV and in the NIR. As a consequence of biomass burning emissions, about 10 times greater absorption values were observed in the dry season in comparison to the wet season. Power law expressions were fitted to the measurements in order to derive the absorption Angstrom exponent, defined as the negative slope of absorption versus wavelength in a log-log plot. At the pasture site, about 70% of the absorption Angstrom exponents fell between 1.5 and 2.5 during the dry season, indicating that biomass burning aerosols have a stronger spectral dependence than soot carbon particles. Angstrom exponents decreased from the dry to the wet season, in agreement with the shift from biomass burning aerosols, predominant in the fine mode, to biogenic and dust aerosols, predominant in the coarse mode. The lowest absorption Angstrom exponents (90% of data below 1.5) were observed at the forest site during the dry season. Also, results indicate that low absorption coefficients were associated with low Angstrom exponents. This finding suggests that biogenic aerosols from Amazonia have a weaker spectral dependence for absorption than biomass burning aerosols, contradicting our expectations of biogenic particles behaving as brown carbon. In a first order assessment, results indicate a small (<1 %) effect of variations in absorption Angstrom exponents on 24-h aerosol forcings, at least in the spectral range of 450-880 nm. Further studies should be taken to assess the corresponding impact in the UV spectral range. The assumption that soot spectral properties represent all ambient light absorbing particles may cause a misjudgment of absorption towards the UV, especially in remote areas. Therefore, it is recommended to measure aerosol absorption at several wavelengths to accurately assess the impact of non-soot aerosols on climate and on photochemical atmospheric processes.

Evaluation of the carbon content of aerosols from the burning of biomass in the Brazilian Amazon using thermal, optical and thermal-optical analysis methods

Aerosol samples were collected at a pasture site in the Amazon Basin as part of the project LBA-SMOCC-2002 (Large-Scale Biosphere-Atmosphere Experiment in Amazonia - Smoke Aerosols, Clouds, Rainfall and Climate: Aerosols from Biomass Burning Perturb Global and Regional Climate). Sampling was conducted during the late dry season, when the aerosol composition was dominated by biomass burning emissions, especially in the submicron fraction. A 13-stage Dekati low-pressure impactor (DLPI) was used to collect particles with nominal aerodynamic diameters (D(p)) ranging from 0.03 to 0.10 mu m. Gravimetric analyses of the DLPI substrates and filters were performed to obtain aerosol mass concentrations. The concentrations of total, apparent elemental, and organic carbon (TC, EC(a), and OC) were determined using thermal and thermal-optical analysis (TOA) methods. A light transmission method (LTM) was used to determine the concentration of equivalent black carbon (BC(e)) or the absorbing fraction at 880 nm for the size-resolved samples. During the dry period, due to the pervasive presence of fires in the region upwind of the sampling site, concentrations of fine aerosols (D(p) < 2.5 mu m: average 59.8 mu g m(-3)) were higher than coarse aerosols (D(p) > 2.5 mu m: 4.1 mu g m(-3)). Carbonaceous matter, estimated as the sum of the particulate organic matter (i.e., OC x 1.8) plus BC(e), comprised more than 90% to the total aerosol mass. Concentrations of EC(a) (estimated by thermal analysis with a correction for charring) and BC(e) (estimated by LTM) averaged 5.2 +/- 1.3 and 3.1 +/- 0.8 mu g m(-3), respectively. The determination of EC was improved by extracting water-soluble organic material from the samples, which reduced the average light absorption Angstrom exponent of particles in the size range of 0.1 to 1.0 mu m from >2.0 to approximately 1.2. The size-resolved BC(e) measured by the LTM showed a clear maximum between 0.4 and 0.6 mu m in diameter. The concentrations of OC and BC(e) varied diurnally during the dry period, and this variation is related to diurnal changes in boundary layer thickness and in fire frequency.

Hidden vorticity in binary Bose-Einstein condensates

We consider a binary Bose-Einstein condensate (BEC) described by a system of two-dimensional (2D) Gross-Pitaevskii equations with the harmonic-oscillator trapping potential. The intraspecies interactions are attractive, while the interaction between the species may have either sign. The same model applies to the copropagation of bimodal beams in photonic-crystal fibers. We consider a family of trapped hidden-vorticity (HV) modes in the form of bound states of two components with opposite vorticities S(1,2) = +/- 1, the total angular momentum being zero. A challenging problem is the stability of the HV modes. By means of a linear-stability analysis and direct simulations, stability domains are identified in a relevant parameter plane. In direct simulations, stable HV modes feature robustness against large perturbations, while unstable ones split into fragments whose number is identical to the azimuthal index of the fastest growing perturbation eigenmode. Conditions allowing for the creation of the HV modes in the experiment are discussed too. For comparison, a similar but simpler problem is studied in an analytical form, viz., the modulational instability of an HV state in a one-dimensional (1D) system with periodic boundary conditions (this system models a counterflow in a binary BEC mixture loaded into a toroidal trap or a bimodal optical beam coupled into a cylindrical shell). We demonstrate that the stabilization of the 1D HV modes is impossible, which stresses the significance of the stabilization of the HV modes in the 2D setting.