On finite-size Lyapunov exponents in multiscale systems

We study the effect of regime switches on finite size Lyapunov exponents (FSLEs) in determining the error growth rates and predictability of multiscale systems. We consider a dynamical system involving slow and fast regimes and switches between them. The surprising result is that due to the presence of regimes the error growth rate can be a non-monotonic function of initial error amplitude. In particular, troughs in the large scales of FSLE spectra is shown to be a signature of slow regimes, whereas fast regimes are shown to cause large peaks in the spectra where error growth rates far exceed those estimated from the maximal Lyapunov exponent. We present analytical results explaining these signatures and corroborate them with numerical simulations. We show further that these peaks disappear in stochastic parametrizations of the fast chaotic processes, and the associated FSLE spectra reveal that large scale predictability properties of the full deterministic model are well approximated whereas small scale features are not properly resolved.Comment: Accepted for publication in Chao

Design and fabrication and delivery of fiberglass box beam assembly final report, 30 jun. 1964 - 15 mar. 1965

Glass fiber reinforced box beam - load test comparison with aluminum box bea

X-ray Spectroscopy of Candidate Ultracompact X-ray Binaries

We present high-resolution spectroscopy of the neutron star/low-mass X-ray binaries (LMXBs) 4U 1850-087 and 4U 0513-40 as part of our continuing study of known and candidate ultracompact binaries. The LMXB 4U 1850-087 is one of four systems in which we had previously inferred an unusual Ne/O ratio in the absorption along the line of sight, most likely from material local to the binaries. However, our recent Chandra X-ray Observatory LETGS spectrum of 4U 1850-087 finds a Ne/O ratio by number of 0.22+/-0.05, smaller than previously measured and consistent with the expected interstellar value. We propose that variations in the Ne/O ratio due to source variability, as previously observed in these sources, can explain the difference between the low- and high-resolution spectral results for 4U 1850-087. Our XMM-Newton RGS observation of 4U 0513-40 also shows no unusual abundance ratios in the absorption along the line of sight. We also present spectral results from a third candidate ultracompact binary, 4U 1822-000, whose spectrum is well fit by an absorbed power-law + blackbody model with absorption consistent with the expected interstellar value. Finally, we present the non-detection of a fourth candidate ultracompact binary, 4U 1905+000, with an upper limit on the source luminosity of < 1 x 10^{32} erg s^{-1}. Using archival data, we show that the source has entered an extended quiescent state.Comment: 8 pages, 3 figures, accepted for publication to the Astrophysical Journa

Using level-2 fuzzy sets to combine uncertainty and imprecision in fuzzy regions

In many applications, spatial data need to be considered but are prone to uncertainty or imprecision. A fuzzy region - a fuzzy set over a two dimensional domain - allows the representation of such imperfect spatial data. In the original model, points of the fuzzy region where treated independently, making it impossible to model regions where groups of points should be considered as one basic element or subregion. A first extension overcame this, but required points within a group to have the same membership grade. In this contribution, we will extend this further, allowing a fuzzy region to contain subregions in which not all points have the same membership grades. The concept can be used as an underlying model in spatial applications, e.g. websites showing maps and requiring representation of imprecise features or websites with routing functions needing to handle concepts as walking distance or closeby

4U2206+54 - an Unusual High Mass X-ray Binary with a 9.6 Day Orbital Period but No Strong Pulsations

Rossi X-ray Timing Explorer All-Sky Monitor observations of the X-ray source 4U2206+54, previously proposed to be a Be star system, show the X-ray flux to be modulated with a period of approximately 9.6 days. If the modulation is due to orbital variability then this would be one of the shortest orbital periods known for a Be star X-ray source. However, the X-ray luminosity is relatively modest whereas a high luminosity would be predicted if the system contains a neutron star accreting from the denser inner regions of a Be star envelope. Although a 392s pulse period was previously reported from EXOSAT observations, a reexamination of the EXOSAT light curves does not show this or any other periodicity. An analysis of archival RXTE Proportional Counter Array observations also fails to show any X-ray pulsations. We consider possible models that may explain the properties of this source including a neutron star with accretion halted at the magnetosphere and an accreting white dwarf.Comment: Accepted for publication in the Astrophysical Journa

Interplay Between Chaotic and Regular Motion in a Time-Dependent Barred Galaxy Model

We study the distinction and quantification of chaotic and regular motion in a time-dependent Hamiltonian barred galaxy model. Recently, a strong correlation was found between the strength of the bar and the presence of chaotic motion in this system, as models with relatively strong bars were shown to exhibit stronger chaotic behavior compared to those having a weaker bar component. Here, we attempt to further explore this connection by studying the interplay between chaotic and regular behavior of star orbits when the parameters of the model evolve in time. This happens for example when one introduces linear time dependence in the mass parameters of the model to mimic, in some general sense, the effect of self-consistent interactions of the actual N-body problem. We thus observe, in this simple time-dependent model also, that the increase of the bar's mass leads to an increase of the system's chaoticity. We propose a new way of using the Generalized Alignment Index (GALI) method as a reliable criterion to estimate the relative fraction of chaotic vs. regular orbits in such time-dependent potentials, which proves to be much more efficient than the computation of Lyapunov exponents. In particular, GALI is able to capture subtle changes in the nature of an orbit (or ensemble of orbits) even for relatively small time intervals, which makes it ideal for detecting dynamical transitions in time-dependent systems.Comment: 21 pages, 9 figures (minor typos fixed) to appear in J. Phys. A: Math. Theo

X-ray Variability in the Young Massive Triple theta2 Ori A

Massive stars rarely show intrinsic X-ray variability. The only O-stars credited to be intrinsically variable are theta1 Ori C due to effects from magnetic confinement of its wind, and theta2 Ori A suspected of similar activity. Early Chandra observations have shown that the most massive star system in the Orion Trapezium Cluster, theta2 Ori A, shows rapid variability on time scales of hours. We determine X-ray fluxes and find that the star shows very strong variability over the last 5 years. We observed a second large X-ray outburst in November 2004 with the high resolution transmission grating spectrometer on-board Chandra. In the low state X-ray emissivities indicate temperatures well above 25 MK. In the high state we find an extended emissivity distribution with high emissivities in the range from 3 MK to over 100 MK. The outburst event in stellar terms is one of the most powerful ever observed and the most energetic one in the ONC with a lower total energy limit of 1.5x10^37 ergs. The line diagnostics show that under the assumption that the line emitting regions in the low states are as close as within 1 -- 2 stellar radii from the O-star's photosphere, whereas the hard states suggest a distance of 3 -- 5 stellar radii. The two outbursts are very close to the periastron passage of the stars. We argue that the high X-ray states are possibly the result of reconnection events from magnetic interactions of the primary and secondary stars of the spectroscopic binary. Effects from wind collisions seem unlikely for this system. The low state emissivity and R-ratios strengthen the predicament that the X-ray emission is enhanced by magnetic confinement of the primary wind. We also detect Fe fluorescence indicative of the existence of substantial amounts of neutral Fe in the vicinity of the X-ray emission.Comment: 11 pages, 8 figures, accepted for publication in The Astrophysical Main Journa

Regular and chaotic vibration in a piezoelectric energy harvester

We examine regular and chaotic responses of a vibrational energy harvester composed of a vertical beam and a tip mass. The beam is excited horizontally by a harmonic inertial force while mechanical vibrational energy is converted to electrical power through a piezoelectric patch. The mechanical resonator can be described by single or double well potentials depending on the gravity force from the tip mass. By changing the tip mass we examine bifurcations from single well oscillations, to regular and chaotic vibrations between the potential wells. The appearance of chaotic responses in the energy harvesting system is illustrated by the bifurcation diagram, the corresponding Fourier spectra, the phase portraits, and is confirmed by the 0–1 test. The appearance of chaotic vibrations reduces the level of harvested energy

Spatiotemporally localized solitons in resonantly absorbing Bragg reflectors

We predict the existence of spatiotemporal solitons (``light bullets'') in two-dimensional self-induced transparency media embedded in a Bragg grating. The "bullets" are found in an approximate analytical form, their stability being confirmed by direct simulations. These findings suggest new possibilities for signal transmission control and self-trapping of light.Comment: RevTex, 3 pages, 2 figures, to be published in PR