Analyticity of smooth eigenfunctions and spectral analysis of the Gauss map

We provide a sufficient condition of analyticity of infinitely differentiable eigenfunctions of operators of the form Uf(x) = integral a(x, y) f(b( x, y)) mu(dy) acting on functions f: [u, v] --> C ( evolution operators of one-dimensional dynamical systems and Markov processes have this form). We estimate from below the region of analyticity of the eigenfunctions and apply these results for studying the spectral properties of the Frobenius-Perron operator of the continuous fraction Gauss map. We prove that any infinitely differentiable eigenfunction f of this Frobenius-Perron operator, corresponding to a non-zero eigenvalue admits a (unique) analytic extension to the set C\(-infinity, 1]. Analyzing the spectrum of the Frobenius Perron operator in spaces of smooth functions, we extend significantly the domain of validity of the Mayer and Ropstorff asymptotic formula for the decay of correlations of the Gauss map.

Retrospective assessment of dryland soil stability in relation to grazing and climate change

Accelerated soil erosion is an aspect of dryland degradation that is affected by repeated intense drought events and land management activities such as commercial livestock grazing. A soil stability index (SSI) that detects the erosion status and susceptibility of a landscape at the pixel level, i.e., stable, erosional, or depositional pixels, was derived from the spectral properties of an archived time series (from 1972 to 1997) of Landsat satellite data of a commercial ranch in northeastern Utah. The SSI was retrospectively validated with contemporary field measures of soil organic matter and erosion status that was surveyed by US federal land management agencies. Catastrophe theory provided the conceptual framework for retrospective assessment of the impact of commercial grazing and soil water availability on the SSI. The overall SSI trend was from an eroding landscape in the early drier 1970s towards stable conditions in the wetter mid-1980s and late 1990s. The landscape catastrophically shifted towards an extreme eroding state that was coincident with the “The Great North American Drought of 1988”. Periods of landscape stability and trajectories toward stability were coincident with extremely wet El Niño events. Commercial grazing had less correlation with soil stability than drought conditions. However, the landscape became more susceptible to erosion events under multiple droughts and grazing. Land managers now have nearly a year warning of El Niño and La Niña events and can adjust their management decisions according to predicted landscape erosion conditions.

Resonances of the cusp family

We study a family of chaotic maps with limit cases-the tent map and the cusp map (the cusp family). We discuss the spectral properties of the corresponding Frobenius-Perron operator in different function spaces including spaces of analytical functions and study numerically the eigenvalues and eigenfunctions.

Facile synthesis of two diastereomeric indolizidines corresponding to the postulated structure of alkaloid 5,9E-259B from a Bufonid toad (Melanophryniscus)

A short synthesis of the postulated structure for indolizidine alkaloid 259B with the hydrogens at C5 and C9 entgegen has been achieved with complete control of stereochemistry at C5. Both diastereoisomers at C8 were obtained, but neither proved to be the natural product. The comparison of the mass and FTIR spectral properties of the synthetic compounds to those of the natural material strongly suggest that the gross structure is correct and that the difference may be a branch in the C5 alkyl side-chain. The GC-retention times of the two synthetic compounds were markedly longer than that of the natural 5,9E-259B.

Multiple major outbursts from a restless luminous blue variable in NGC 3432

We present new photometric and spectroscopic observations of an unusual luminous blue variable (LBV) in NGC 3432, covering three major outbursts in 2008 October, 2009 April and 2009 November. Previously, this star experienced an outburst also in 2000 (known as SN 2000ch). During outbursts the star reached an absolute magnitude between -12.1 and -12.8. Its spectrum showed H, He I and Fe II lines with P-Cygni profiles during and soon after the eruptive phases, while only intermediate-width lines in pure emission (including He II lambda 4686) were visible during quiescence. The fast-evolving light curve soon after the outbursts, the quasi-modulated light curve, the peak magnitude and the overall spectral properties are consistent with multiple episodes of variability of an extremely active LBV. However, the widths of the spectral lines indicate unusually high wind velocities (1500-2800 km s-1), similar to those observed in Wolf-Rayet stars. Although modulated light curves are typical of LBVs during the S-Dor variability phase, the luminous maxima and the high frequency of outbursts are unexpected in S-Dor variables. Such extreme variability may be associated with repeated ejection episodes during a giant eruption of an LBV. Alternatively, it may be indicative of a high level of instability shortly preceding the core-collapse or due to interaction with a massive, binary companion. In this context, the variable in NGC 3432 shares some similarities with the famous stellar system HD 5980 in the Small Magellanic Cloud, which includes an erupting LBV and an early Wolf-Rayet star.

The VLT-FLAMES Tarantula Survey I. Introduction and observational overview

The VLT-FLAMES Tarantula Survey (VFTS) is an ESO Large Programme that has obtained multi-epoch optical spectroscopy of over 800 massive stars in the 30 Doradus region of the Large Magellanic Cloud (LMC). Here we introduce our scientific motivations and give an overview of the survey targets, including optical and near-infrared photometry and comprehensive details of the data reduction. One of the principal objectives was to detect massive binary systems via variations in their radial velocities, thus shaping the multi-epoch observing strategy. Spectral classifications are given for the massive emission-line stars observed by the survey, including the discovery of a new Wolf-Rayet star (VFTS 682, classified as WN5h), 2' to the northeast of R136. To illustrate the diversity of objects encompassed by the survey, we investigate the spectral properties of sixteen targets identified by Gruendl & Chu from Spitzer photometry as candidate young stellar objects or stars with notable mid-infrared excesses. Detailed spectral classification and quantitative analysis of the O- and B-type stars in the VFTS sample, paying particular attention to the effects of rotational mixing and binarity, will be presented in a series of future articles to address fundamental questions in both stellar and cluster evolution.

From perfect to fractal transmission in spin chains

Perfect state transfer is possible in modulated spin chains [Phys. Rev. Lett. 92, 187902 (2004)], imperfections, however, are likely to corrupt the state transfer. We study the robustness of this quantum communication protocol in the presence of disorder both in the exchange couplings between the spins and in the local magnetic field. The degradation of the fidelity can be suitably expressed, as a function of the level of imperfection and the length of the chain, in a scaling form. In addition the time signal of fidelity becomes fractal. We further characterize the state transfer by analyzing the spectral properties of the Hamiltonian of the spin chain.

Photon Production from the Vacuum Close to the Superradiant Transition: Linking the Dynamical Casimir Effect to the Kibble-Zurek Mechanism

The dynamical Casimir effect (DCE) predicts the generation of photons from the vacuum due to the parametric amplification of the quantum fluctuations of an electromagnetic field. The verification of such an effect is still elusive in optical systems due to the very demanding requirements of its experimental implementation. We show that an ensemble of two-level atoms collectively coupled to the electromagnetic field of a cavity, driven at low frequencies and close to a quantum phase transition, stimulates the production of photons from the vacuum. This paves the way to an effective simulation of the DCE through a mechanism that has recently found experimental demonstration. The spectral properties of the emitted radiation reflect the critical nature of the system and allow us to link the detection of the DCE to the Kibble-Zurek mechanism for the production of defects when crossing a continuous phase transition.

GIANT LOBES OF CENTAURUS A RADIO GALAXY OBSERVED WITH THE SUZAKU X-RAY SATELLITE

We report on Suzaku observations of selected regions within the southern giant lobe of the radio galaxy Centaurus A. In our analysis we focus on distinct X-ray features detected with the X-ray Imaging Spectrometer within the range 0.5-10 keV, some of which are likely associated with fine structure of the lobe revealed by recent high-quality radio intensity and polarization maps. With the available photon statistics, we find that the spectral properties of the detected X-ray features are equally consistent with thermal emission from hot gas with temperatures kT > 1 keV, or with a power-law radiation continuum characterized by photon indices Gamma similar to 2.0 +/- 0.5. However, the plasma parameters implied by these different models favor a synchrotron origin for the analyzed X-ray spots, indicating that a very efficient acceleration of electrons up to greater than or similar to 10 TeV energies is taking place within the giant structure of Centaurus A, albeit only in isolated and compact regions associated with extended and highly polarized radio filaments. We also present a detailed analysis of the diffuse X-ray emission filling the whole field of view of the instrument, resulting in a tentative detection of a soft excess component best fitted by a thermal model with a temperature of kT similar to 0.5 keV. The exact origin of the observed excess remains uncertain, although energetic considerations point to thermal gas filling the bulk of the volume of the lobe and mixed with the non-thermal plasma, rather than to the alternative scenario involving a condensation of the hot intergalactic medium around the edges of the expanding radio structure. If correct, this would be the first detection of the thermal content of the extended lobes of a radio galaxy in X-rays. The corresponding number density of the thermal gas in such a case is n(g) similar to 10(-4) cm(-3), while its pressure appears to be in almost exact equipartition with the volume-averaged non-thermal pressure provided by the radio-emitting electrons and the lobes' magnetic field. A prominent large-scale fluctuation of the Galactic foreground emission, resulting in excess foreground X-ray emission aligned with the lobe, cannot be ruled out. Although tentative, our findings potentially imply that the structure of the extended lobes in active galaxies is likely to be highly inhomogeneous and non-uniform, with magnetic reconnection and turbulent acceleration processes continuously converting magnetic energy to internal energy of the plasma particles, leading to possibly significant spatial and temporal variations in the plasma beta parameter around the volume-averaged equilibrium condition beta similar to 1.

When Casimir meets Kibble-Zurek

Verification of the dynamical Casimir effect (DCE) in optical systems is still elusive due to the very demanding requirements for its experimental implementation. This typically requires very fast changes in the boundary conditions of the problem. We show that an ensemble of two-level atoms collectively coupled to the electromagnetic field of a cavity, driven at low frequencies and close to a quantum phase transition, stimulates the production of photons from the vacuum. This paves the way for an effective simulation of the DCE through a mechanism that has recently found experimental demonstration. The spectral properties of the emitted radiation reflect the critical nature of the system and allow us to link the detection of DCE to the Kibble-Zurek mechanism for the production of defects when crossing a continuous phase transition.

Xheal: A localized self-healing algorithm using expanders

We consider the problem of self-healing in reconfigurable networks e.g., peer-to-peer and wireless mesh networks. For such networks under repeated attack by an omniscient adversary, we propose a fully distributed algorithm, Xheal, that maintains good expansion and spectral properties of the network, while keeping the network connected. Moreover, Xheal does this while allowing only low stretch and degree increase per node. The algorithm heals global properties like expansion and stretch while only doing local changes and using only local information. We also provide bounds on the second smallest eigenvalue of the Laplacian which captures key properties such as mixing time, conductance, congestion in routing etc. Xheal has low amortized latency and bandwidth requirements. Our work improves over the self-healing algorithms Forgiving tree [PODC 2008] andForgiving graph [PODC 2009] in that we are able to give guarantees on degree and stretch, while at the same time preserving the expansion and spectral properties of the network.

Growth and properties of gold and nickel nanorods in thin film alumina

Arrays of nickel and gold nanorods have been grown on glass and silicon substrates using porous alumina templates of less than 500 nm thickness. A method is demonstrated for varying the diameter of the nanorods whilst keeping the spacing constant. Optical extinction spectra for the gold nanorods show two distinct maxima associated with the transverse and longitudinal axes of the rods. Adding small quantities of oxygen to the aluminium before anodization is found to improve the sharpness of the extinction peaks. The spectral position of the longitudinal peak is shown to be sensitive to the nanorod diameter for constant length and spacing. For the nickel nanorods it is shown that the magnetic properties are governed by both interactions between the wires and shape anisotropy.

Joined Spectral Trees for Scalable SPIHT-Based Multispectral Image Compression

In this paper, the compression of multispectral images is addressed. Such 3-D data are characterized by a high correlation across the spectral components. The efficiency of the state-of-the-art wavelet-based coder 3-D SPIHT is considered. Although the 3-D SPIHT algorithm provides the obvious way to process a multispectral image as a volumetric block and, consequently, maintain the attractive properties exhibited in 2-D (excellent performance, low complexity, and embeddedness of the bit-stream), its 3-D trees structure is shown to be not adequately suited for 3-D wavelet transformed (DWT) multispectral images. The fact that each parent has eight children in the 3-D structure considerably increases the list of insignificant sets (LIS) and the list of insignificant pixels (LIP) since the partitioning of any set produces eight subsets which will be processed similarly during the sorting pass. Thus, a significant portion from the overall bit-budget is wastedly spent to sort insignificant information. Through an investigation based on results analysis, we demonstrate that a straightforward 2-D SPIHT technique, when suitably adjusted to maintain the rate scalability and carried out in the 3-D DWT domain, overcomes this weakness. In addition, a new SPIHT-based scalable multispectral image compression algorithm is used in the initial iterations to exploit the redundancies within each group of two consecutive spectral bands. Numerical experiments on a number of multispectral images have shown that the proposed scheme provides significant improvements over related works.