Application of the method of multiple scales to unravel energy exchange in nonlinear locally resonant metamaterials

In this paper, the effect of weak nonlinearities in 1D locally resonant metamaterials is investigated via the method of multiple scales. Commonly employed to the investigate the effect of weakly nonlinear interactions on the free wave propagation through a phononic structure or on the dynamic response of a Duffing oscillator, the method of multiple scales is here used to investigate the forced wave propagation through locally resonant metamaterials. The perturbation approach reveals that energy exchange may occur between propagative and evanescent waves induced by quadratic nonlinear local interaction

Fracture initiation in multi-phase materials: a systematic three-dimensional approach using a FFT-based solver

This paper studies a two-phase material with a microstructure composed of a hard brittle reinforcement phase embedded in a soft ductile matrix. It addresses the full three-dimensional nature of the microstructure and macroscopic deformation. A large ensemble of periodic microstructures is used, whereby the individual grains of the two phases are modeled using equi-sized cubes. A particular solution strategy relying on the Fast Fourier Transform is adopted, which has a high computational efficiency both in terms of speed and memory footprint, thus enabling a statistically meaningful analysis. This solution method naturally accompanies the regular microstructural model, as the Fast Fourier Transform relies on a regular grid. Using the many considered microstructures as an ensemble, the average arrangement of phases around fracture initiation sites is objectively identified by the correlation between microstructure and fracture initiation -- in three dimensions. The results show that fracture initiates where regions of the hard phase are interrupted by bands of the soft phase that are aligned with the direction of maximum shear. In such regions, the hard phase is arranged such that the area of the phase boundary perpendicular to the principal strain direction is maximum, leading to high hydrostatic tensile stresses, while not interrupting the shear bands that form in the soft phase. The local incompatibility that is present around the shear bands is responsible for a high plastic strain. By comparing the response to a two-dimensional microstructure it is observed that the response is qualitatively similar (both macroscopically and microscopically). One important difference is that the local strain partitioning between the two phases is over-predicted by the two-dimensional microstructure, leading to an overestimation of damage

Probing protoplanetary disks with silicate emission: Where is the silicate emission zone?

Recent results indicate that the grain size and crystallinity inferred from observations of silicate features may be correlated with the spectral type of the central star and/or disk geometry. In this paper, we show that grain size, as probed by the 10 μm silicate feature peak-to-continuum and 11.3 to 9.8 μm flux ratios, is inversely proportional to log Lsstarf. These trends can be understood using a simple two-layer disk model for passive irradiated flaring disks, CGPLUS. We find that the radius, R10, of the 10 μm silicate emission zone in the disk goes as (L*/L☉)^0.56, with slight variations depending on disk geometry (flaring angle and inner disk radius). The observed correlations, combined with simulated emission spectra of olivine and pyroxene mixtures, imply a dependence of grain size on luminosity. Combined with the fact that R10 is smaller for less luminous stars, this implies that the apparent grain size of the emitting dust is larger for low-luminosity sources. In contrast, our models suggest that the crystallinity is only marginally affected, because for increasing luminosity, the zone for thermal annealing (assumed to be at T > 800 K) is enlarged by roughly the same factor as the silicate emission zone. The observed crystallinity is affected by disk geometry, however, with increased crystallinity in flat disks. The apparent crystallinity may also increase with grain growth due to a corresponding increase in contrast between crystalline and amorphous silicate emission bands

Evidence for CO depletion in the inner regions of gas-rich protoplanetary disks

We investigate the physical properties and spatial distribution of Carbon Monoxide (CO) gas in the disks around the Herbig Ae/Be stars HD 97048 and HD 100546. Using high-spectral-resolution 4.588-4.715 $\mu$m spectra containing fundamental CO emission taken with CRIRES on the VLT, we probe the circumstellar gas and model the kinematics of the emission lines. By using spectro-astrometry on the spatially resolved targets, we constrain the physical size of the emitting regions in the disks. We resolve, spectrally and spatially, the emission of the $^{13}$CO v(1-0) vibrational band and the $^{12}$CO $v=1-0, v=2-1, v=3-2$ and $v=4-3$ vibrational bands in both targets, as well as the $^{12}$CO $v=5-4$ band in HD 100546. Modeling of the CO emission with a homogeneous disk in Keplerian motion, yields a best fit with an inner and outer radius of the CO emitting region of 11 and $\geq$ 100 AU for HD 97048. HD 100546 is not fit well with our model, but we derive a lower limit on the inner radius of 8 AU. The fact that gaseous [OI] emission was previously detected in both targets at significantly smaller radii suggests that CO may be effectively destroyed at small radii in the surface layers of these disksComment: v2: Letter format has been changed to Paper format; Change in the focus of the paper towards CO depletion; Major changes in text; Change of title. Submitted to A&A, 14/10/2008. Accepted by A&A, 17/04/200

The structure of the protoplanetary disk surrounding three young intermediate mass stars. II. Spatially resolved dust and gas distribution

[Abridged] We present the first direct comparison of the distribution of the gas, as traced by the [OI] 6300 AA emission, and the dust, as traced by the 10 micron emission, in the protoplanetary disk around three intermediate-mass stars: HD 101412, HD 135344 B and HD 179218. N-band visibilities were obtained with VLTI/MIDI. Simple geometrical models are used to compare the dust emission to high-resolution optical spectra in the 6300 AA [OI] line of the same targets. The disks around HD 101412 and HD 135344 B appear strongly flared in the gas, but self-shadowed in the dust beyond ~ 2 AU. In both systems, the 10 micron emission is rather compact (< 2 AU) while the [OI] brightness profile shows a double peaked structure. The inner peak is strongest and is consistent with the location of the dust, the outer peak is fainter and is located at 5-10 AU. Spatially extended PAH emission is found in both disks. The disk around HD 179218 is flared in the dust. The 10 micron emission emerges from a double ring-like structure with the first ring peaking at ~ 1 AU and the second at ~ 20 AU. No dust emission is detected between ~ 3 -- 15 AU. The oxygen emission seems also to come from a flared structure, however, the bulk of this emission is produced between ~ 1 -- 10 AU. This could indicate a lack of gas in the outer disk or could be due to chemical effects which reduce the abundance of OH -- the parent molecule of the observed [OI] emission -- further away from the star. The three systems, HD 179218, HD 135344 B and HD 101412, may form an evolutionary sequence: the disk initially flared becomes flat under the combined action of gas-dust decoupling, grain growth and dust settling.Comment: Accepted for publication in A&

Cold Disks: Spitzer Spectroscopy of Disks around Young Stars with Large Gaps

We have identified four circumstellar disks with a deficit of dust emission from their inner 15-50 AU. All four stars have F-G spectral type, and were uncovered as part of the Spitzer Space Telescope ``Cores to Disks'' Legacy Program Infrared Spectrograph (IRS) first look survey of ~100 pre-main sequence stars. Modeling of the spectral energy distributions indicates a reduction in dust density by factors of 100-1000 from disk radii between ~0.4 and 15-50 AU, but with massive gas-rich disks at larger radii. This large contrast between the inner and outer disk has led us to use the term `cold disks' to distinguish these unusual systems. However, hot dust [0.02-0.2 Mmoon] is still present close to the central star (R ~0.8 AU). We introduce the 30/13 micron, flux density ratio as a new diagnostic for identifying cold disks. The mechanisms for dust clearing over such large gaps are discussed. Though rare, cold disks are likely in transition from an optically thick to an optically thin state, and so offer excellent laboratories for the study of planet formation.Comment: 13 pages, 3 figures, accepted to ApJ

Vortex Motion Noise in Micrometre-Sized Thin Films of the Amorphous Nb0.7Ge0.3 Weak-Pinning Superconductor

We report high-resolution measurements of voltage (V) noise in the mixed state of micrometre-sized thin films of amorphous Nb0.7Ge0.3, which is a good representative of weak-pinning superconductors. There is a remarkable difference between the noise below and above the irreversibility field Birr. Below Birr, in the presence of measurable pinning, the noise at small applied currents resembles shot noise, and in the regime of flux flow at larger currents decreases with increasing voltage due to a progressive ordering of the vortex motion. At magnetic fields B between Birr and the upper critical field Bc2 flux flow is present already at vanishingly small currents. In this regime the noise scales with (1-B/Bc2)^2 V^2 and has a frequency (f) spectrum of 1/f type. We interpret this noise in terms of the properties of strongly driven depinned vortex systems at high vortex density.Comment: 8 pages, 5 figures, version accepted for publication in PR

C2D Spitzer-IRS spectra of disks around T Tauri stars: IV. Crystalline silicates

Aims. Dust grains in the planet-forming regions around young stars are expected to be heavily processed due to coagulation, fragmentation, and crystallization. This paper focuses on the crystalline silicate dust grains in protoplanetary disks for a statistically significant number of TTauri stars (96). Methods. As part of the cores to disks (c2d) legacy program, we obtained more than a hundred Spitzer/IRS spectra of TTauri stars, over a spectral range of 5-35 μm where many silicate amorphous and crystalline solid-state features are present. At these wavelengths, observations probe the upper layers of accretion disks up to distances of a dozen AU from the central object. Results. More than 3/4 of our objects show at least one crystalline silicate emission feature that can be essentially attributed to Mg-rich silicates. The Fe-rich crystalline silicates are largely absent in the c2d IRS spectra. The strength and detection frequency of the crystalline features seen at λ > 20 μm correlate with each other, while they are largely uncorrelated with the observational properties of the amorphous silicate 10 μm feature. This supports the idea that the IRS spectra essentially probe two independent disk regions: a warm zone (≤1 AU) emitting at ~ 10 μm and a much colder region emitting at λ > 20 μm (≤10 AU). We identify a crystallinity paradox, as the long-wavelength (λ > 20 m) crystalline silicate features are detected 3.5 times more frequently (~55% vs. ~15%) than the crystalline features arising from much warmer disk regions (λ ~ 10 μm). This suggests that the disk has an inhomogeneous dust composition within ~10 AU. The analysis of the shape and strength of both the amorphous 10 μm feature and the crystalline feature around 23 μm provides evidence for the prevalence of μm-sized (amorphous and crystalline) grains in upper layers of disks. Conclusions. The abundant crystalline silicates found far from their presumed formation regions suggest efficient outward radial transport mechanisms in the disks around TTauri stars. The presence of μm-sized grains in disk atmospheres, despite the short timescales for settling to the midplane, suggests efficient (turbulent) vertical diffusion, probably accompanied by grain-grain fragmentation to balance the expected efficient growth. In this scenario, the depletion of submicron-sized grains in the upper layers of the disks points toward removal mechanisms such as stellar winds or radiation pressure

Quantum Smoluchowski equation: Escape from a metastable state

We develop a quantum Smoluchowski equation in terms of a true probability distribution function to describe quantum Brownian motion in configuration space in large friction limit at arbitrary temperature and derive the rate of barrier crossing and tunneling within an unified scheme. The present treatment is independent of path integral formalism and is based on canonical quantization procedure.Comment: 10 pages, To appear in the Proceedings of Statphys - Kolkata I

Dissociation of the benzene molecule by UV and soft X-rays in circumstellar environment

Benzene molecules, present in the proto-planetary nebula CRL 618, are ionized and dissociated by UV and X-ray photons originated from the hot central star and by its fast wind. Ionic species and free radicals produced by these processes can lead to the formation of new organic molecules. The aim of this work is to study the photoionization and photodissociation processes of the benzene molecule, using synchrotron radiation and time of flight mass spectrometry. Mass spectra were recorded at different energies corresponding to the vacuum ultraviolet (21.21 eV) and soft X-ray (282-310 eV) spectral regions. The production of ions from the benzene dissociative photoionization is here quantified, indicating that C6H6 is more efficiently fragmented by soft X-ray than UV radiation, where 50% of the ionized benzene molecules survive to UV dissociation while only about 4% resist to X-rays. Partial ion yields of H+ and small hydrocarbons such as C2H2+, C3H3+ and C4H2+ are determined as a function of photon energy. Absolute photoionization and dissociative photoionization cross sections have also been determined. From these values, half-life of benzene molecule due to UV and X-ray photon fluxes in CRL 618 were obtained.Comment: The paper contains 8 pages, 9 figures and 4 tables. Accepted to be published on MNRAS on 2008 November 2