A non-periodic two scale asymptotic method to take account of rough topographies for 2D elastic wave propagation

International audienceWe propose a two scale asymptotic method to compute the effective effect of a free surface topography varying much faster than the minimum wavelength for 2-D P-SV elastic wave propagation. The topography variation is assumed to be non-periodic but with a deterministic description and, in this paper, the elastic body below the topography is assumed to be ho- mogeneous. Two asymptotic expansions are used, one in the boundary layer close to the free surface and one in the volume. Both expansions are matched appropriately up to the order 1 to provide an effective topography and an effective boundary condition. We show that the effective topography is not the averaged topography but it is a smooth free surface lying below the fast variations of the real topography. Moreover, the free boundary condition has to be modified to take account of the inertial effects of the fast variations of the topography above the effective topography. In other words, the wave is not propagating in the fast topography but below it and is slowed down by the weight of the fast topography. We present an iterative scheme allowing to find this effective topography for a given minimum wavelength. We do not attempt any mathematical proof of the proposed scheme, nevertheless, numerical tests show good results

Magnetic and semi-conducting nano-composite films of spinel ferrite and cubic zinc oxide

Magnetic and semi-conducting nano-composite films have been prepared under bias polarization, by radio-frequency sputtering of a pure zinc ferrite target. These composite thin films are made of cubic Zn1 − yFeyO monoxide islands inside a spinel ferrite matrix. The relative proportion of each phase depends on the substrate polarization (i.e. bias power). When no bias is applied the films solely display the diffraction pattern of a spinel phase even if some islands inside the film can be observed by electron microscopy. When the bias power is increased, the spinel phase disappears progressively as enhanced formation of islands takes place in such a manner that the cubic Zn1 − yFeyO monoxide is solely revealed by X-ray diffraction for a bias power higher than 5 W. From bibliographical data and calculated phase diagrams, it can be inferred that these phases would require very low oxygen partial pressure, high temperature and mechanical pressure, to be obtained simultaneously by a conventional ceramic process. This underlines the strong potential of radio-frequency sputtering of oxide targets to prepare original oxides or composite materials

1-D non periodic homogenization for the seismic wave equation

International audienceWhen considering numerical acoustic or elastic wave propagation in media containing small heterogeneities with respect to the minimum wavelength of the wavefield, being able to upscale physical properties (or homogenize them) is valuable mainly for two reasons. First, replacing the original discontinuous and very heterogeneous medium by a smooth and more simple one, is a judicious alternative to the necessary fine and difficult meshing of the original medium required by many wave equation solvers. Second, it helps to understand what properties of a medium are really ‘seen' by the wavefield propagating through, which is an important aspect in an inverse problem approach. This paper is an attempt of a pedagogical introduction to non- periodic homogenization in 1-D, allowing to find the effective wave equation and effective physical properties, of the elastodynamics equation in a highly heterogeneous medium. It can be extrapolated from 1-D to a higher space dimensions. This development can be seen as an extension of the classical two-scale homogenization theory applied to the elastic wave equation in periodic media, with this limitation that it does not hold beyond order 1 in the asymptotic expansion involved in the classical theory

Elaboration and characterization of Fe1–xO thin films sputter deposited from magnetite target

Majority of the authors report elaboration of iron oxide thin films by reactive magnetron sputtering from an iron target with Ar–O2 gas mixture. Instead of using the reactive sputtering of a metallic target we report here the preparation of Fe1–xOthin films, directly sputtered froma magnetite target in a pure argon gas flow with a bias power applied. This oxide is generally obtained at very low partial oxygen pressure and high temperature.We showed that bias sputtering which can be controlled very easily can lead to reducing conditions during deposition of oxide thin film on simple glass substrates. The proportion of wustite was directly adjusted bymodifying the power of the substrate polarization. Atomic force microscopy was used to observe these nanostructured layers. Mössbauer measurements and electrical properties versus bias polarization and annealing temperature are also reported

Preparation of delafossite CuFeO2 thin films by rf-sputtering on conventional glass substrate

CuFeO2 CuFeO2 is a delafossite-type compound and is a well known p-type semiconductor. The growth of delafossite CuFeO2 thin films on conventional glass substrate by radio-frequency sputtering is reported. The deposition, performed at room temperature leads to an amorphous phase with extremely low roughness and high density. The films consisted of a well crystallized delafossite CuFeO2 after heat treatment at 450 °C in inert atmosphere. The electrical conductivity of the film was 1 mS/cm. The direct optical band gap was estimated to be 2 eV

2-D non-periodic homogenization of the elastic wave equation: SH case

International audienceIn the Earth, seismic waves propagate through 3-D heterogeneities characterized by a large variety of scales, some of them much smaller than their minimum wavelength. The costs of computing the wavefield in such media using purely numerical methods, are very high. To lower them, and also to obtain a better geodynamical interpretation of tomographic images, we aim at calculating appropriate effective properties of heterogeneous and discontinuous media, by deriving convenient upscaling rules for the material properties and for the wave equation. To progress towards this goal we extend our successful work from 1-D to 2-D. We first apply the so-called homogenization method (based on a two-scale asymptotic expansion of the field variables) to model antiplane wave propagation in 2-D periodic media. These latter are characterized by short-scale variations of elastic properties, compared to the smallest wavelength of the wavefield. Seismograms are obtained using the 0th-order term of this asymptotic expansion, plus a partial first-order correction. Away from boundaries, they are in excellent agreement with solutions calculated at a much higher computational cost, using spectral elements simulations in the reference media. We then extend the homogenization of the wave equation, to 2-D non-periodic, deterministic media

The Potential Of High-Resolution BAC-FISH In Banana Breeding

Abstract The genetic complexity in the genus Musa has been subject of study in many breeding programs worldwide. Parthenocarpy, female sterility, polyploidy in different cultivars and limited amount of genetic and genomic information make the production of new banana cultivars difficult and time consuming. In addition, it is known that part of the cultivars and related wild species in the genus contain numerous chromosomal rearrangements. In order to produce new cultivars more effectively breeders must better understand the genetic differences of the potential crossing parents for introgression hybridization, but extensive genetic information is lacking. As an alternative to achieve information on genetic collinearity we make use of modern chromosome map technology known as high-resolution fluorescent in situ hybridization (FISH). This article presents the technical aspects and applications of such a technology in Musa species. The technique deals with BAC clone positioning on pachytene chromosomes of Calcutta 4 (Musa acuminata ssp. burmanicoides, A genome group, section Eumusa) and M. velutina (section Rodochlamys). Pollen mother cells digestion with pectolytic enzymes and maceration with acetic acid were optimized for making cell spread preparations appropriate for FISH. As an example of this approach we chose BAC clones that contain markers to known resistance genes and hybridize them for establishing their relative positions on the two species. Technical challenges for adapting existing protocols to the banana cells are presented. We also discuss how this technique can be instrumental for validating collinearity between potential crossing parents and how the method can be helpful in future mapping initiatives, and how this method allows identification of chromosomal rearrangements between related Musa species and cultivar

Reliability of mantle tomography models assessed by spectral element simulation

Global tomographic models collected in the Seismic wave Propagation and Imaging in Complex (SPICE media: a European network) model library (http://www.spicertn.org/research/planetaryscale/tomography/) share a similar pattern of long, spatial wavelength heterogeneity, but are not consistent at shorter spatial wavelengths. Here, we assess the performance of global tomographic models by comparing how well they fit seismic waveform observations, in particular Love and Rayleigh wave overtones and fundamental modes. We first used the coupled spectral element method (CSEM) to calculate long-period (>100 s) synthetic seismograms for different global tomography models. The CSEM can incorporate the effect of three-dimensional (3-D) variations in velocity, anisotropy, density and attenuation with very little numerical dispersion. We then compared quantitatively synthetic seismograms and real data. To restrict ourselves to high-quality overtone data, and to minimize the effects of the finite extent of seismic sources and of crustal heterogeneity, we favour deep (>500 km) earthquakes of intermediate magnitude (Mw ∼ 7). Our comparisons reveal that: (1) The 3-D global tomographic models explain the data much better than the one-dimensional (1-D) anisotropic Preliminary Reference Earth Model (PREM). The current 3-D tomographic models have captured the large-scale features of upper-mantle heterogeneities, but there is still some room for the improvement of large-scale features of global tomographic models. (2) The average correlation coefficients for deep events are higher than those for shallow events, because crustal structure is too complex to be completely incorporated into CSEM simulations. (3) The average correlation coefficient (or the time lag) for the major-arc wave trains is lower (or higher) than that for the minor-arc wave trains. Therefore, the current tomographic models could be much improved by including the major-arc wave trains in the inversion. (4) The shallow-layer crustal correction has more effects on the fundamental surface waves than on the overtone

Spectral element modeling of three dimensional wave propagation in a self-gravitating Earth with an arbitrarily stratified outer core

This paper deals with the spectral element modeling of seismic wave propagation at the global scale. Two aspects relevant to low-frequency studies are particularly emphasized. First, the method is generalized beyond the Cowling approximation in order to fully account for the effects of self-gravitation. In particular, the perturbation of the gravity field outside the Earth is handled by a projection of the spectral element solution onto the basis of spherical harmonics. Second, we propose a new formulation inside the fluid which allows to account for an arbitrary density stratification. It is based upon a decomposition of the displacement into two scalar potentials, and results in a fully explicit fluid-solid coupling strategy. The implementation of the method is carefully detailed and its accuracy is demonstrated through a series of benchmark tests.Comment: Sent to Geophysical Journal International on July 29, 200

2-D non-periodic homogenization to upscale elastic media for P-SV waves

International audienceThe pur pose of this paper is to give an upscaling tool valid for the wave equation in general elastic media. This paper is focused on P–SV wave propagation in 2-D, but the methodology can be extended without any theoretical difficulty to the general 3-D case. No assumption on the heterogeneity spectrum is made and the medium can show rapid variations of its elastic properties in all spatial directions. The method used is based on the two-scale homogenization expansion, but extended to the non-periodic case. The scale separation is made using a spatial low-pass filter. The ratio of the filter wavelength cut-off and the minimum wavelength of the propagating wavefield defines a parameter ε0 with which the wavefield propagating in the homogenized medium converges to the reference wavefield. In the general case, this non- periodic extension of the homogenization technique is only valid up to the leading order and for the so-called first-order cor rector. We apply this non-periodic homogenization procedure to two kinds of heterogeneous media: a randomly generated, highly heterogeneous medium and the Marmousi2 geological model. The method is tested with the Spectral Element Method as a solver to the wave equation. Comparing computations in the homogenized media with those obtained in the original ones shows that convergence with ε0 is even better than expected. The effects of the leading order cor rection to the source and first cor rection at the receivers' location are shown