Localization for a matrix-valued Anderson model

We study localization properties for a class of one-dimensional, matrix-valued, continuous, random Schr\"odinger operators, acting on L^2(\R)\otimes \C^N, for arbitrary $N\geq 1$. We prove that, under suitable assumptions on the F\"urstenberg group of these operators, valid on an interval $I\subset \R$, they exhibit localization properties on $I$, both in the spectral and dynamical sense. After looking at the regularity properties of the Lyapunov exponents and of the integrated density of states, we prove a Wegner estimate and apply a multiscale analysis scheme to prove localization for these operators. We also study an example in this class of operators, for which we can prove the required assumptions on the F\"urstenberg group. This group being the one generated by the transfer matrices, we can use, to prove these assumptions, an algebraic result on generating dense Lie subgroups in semisimple real connected Lie groups, due to Breuillard and Gelander. The algebraic methods used here allow us to handle with singular distributions of the random parameters

The effect of the natural raw barite and the dolomite material on borate glass formation

No Abstract

Numerical investigation of damage protective oxide mechanisms in thermal barrier system for aeronautical turbine blade.

The choice of a material for a given application requires insuring a good durability in its conditions of employment, in particular environmental. It is especially true for the systems destined to work in corrosive hot atmospheres. For it, the knowledge and the understanding of the corrosion phenomena, oxidization, ageing and damage are indispensable in order to anticipate the life period of the structures and to propose the adapted protective solutions. The study of the corrosion in high temperature is therefore a greatly interdisciplinary topic, into the interface of the physico-chemistry, metallic and ceramic materials and mechanics.We propose in this work a finite element method for the simulation of EBPVD TBCs spallation. Our studies concern one of several systems that we call thermal barrier coatings, which are a Composite materials deposited in layers on the hot components to isolate them chemically and thermally at high temperatures. This is the last operational technology adapted on aircraft engines but it is still studied and not fully exploited.This comprehensive article describes the systems currently used and the problem of interaction between mechanical and environment in the turbine. 

Positivity of Lyapunov exponents for a continuous matrix-valued Anderson model

We study a continuous matrix-valued Anderson-type model. Both leading Lyapunov exponents of this model are proved to be positive and distinct for all ernergies in $(2,+\infty)$ except those in a discrete set, which leads to absence of absolutely continuous spectrum in $(2,+\infty)$. This result is an improvement of a previous result with Stolz. The methods, based upon a result by Breuillard and Gelander on dense subgroups in semisimple Lie groups, and a criterion by Goldsheid and Margulis, allow for singular Bernoulli distributions

Localization Properties of the Chalker-Coddington Model

The Chalker Coddington quantum network percolation model is numerically pertinent to the understanding of the delocalization transition of the quantum Hall effect. We study the model restricted to a cylinder of perimeter 2M. We prove firstly that the Lyapunov exponents are simple and in particular that the localization length is finite; secondly that this implies spectral localization. Thirdly we prove a Thouless formula and compute the mean Lyapunov exponent which is independent of M.Comment: 29 pages, 1 figure. New section added in which simplicity of the Lyapunov spectrum and finiteness of the localization length are proven. To appear in Annales Henri Poincar

XPS, FTIR, EDX, and XRD analysis of Al₂O₃ scales grown on PM2000 alloy

This work is an original example to compare the results obtained after calcination of Al2O3 hydroxides and oxidation of alumino-formers alloys. FTIR and XPS signatures were obtained for various oxidation temperatures and compared with those known from the literature about calcination of Al2O3 precursors. The aim of this work is to evaluate the use of IR spectroscopy and XPS analysis to probe the structural varieties of Al2O3. For this objective, a study of the PM2000 oxidation at various temperatures was conducted by means of XRD, IR spectroscopy, XPS analysis, EDX analysis, and SEM observations. This allowed us to clearly differentiate the transition Al2O3 from the α-Al2O3 and, amongst the transition Al2O3, to differentiate the characteristic of the IR spectrum of γ-δ phases from that of the θ phase

Nitrogen deficiency increases basal branching and modifies visual quality of the rose bushes

Rosebush architecture resulting from the spatial organisation of the plant axes induces plant shape and consequently within ornamental horticulture context, its visual quality and commercial value. This architecture can be modulated by environmental conditions, particularly in the horticulture context in which the possibilities to control growing conditions are numerous. The objectives of the study were to determine, in young rose bushes, (1) whether short periods of nitrogen deficiency affect branching and (2) whether this effect is sufficient to modify the visual quality of the plant in a sustainable manner. Between vegetative bud burst and the petal colour visible stage of the generated primary branch, young rooted cuttings of bush rose (cv Radrazz) were subjected to one of three nitrogen regimes: (1) no nitrogen deficiency, (2) continuous nitrogen deficiency, i.e. 35 days of N deficiency, and (3) nitrogen deficiency restricted to the flowering stages, i.e. 18 days of N deficiency. After the petal colour visible stage, all three groups of plants were supplied continuously with nitrogen. We observed the morphology of the axes and the kinetics of axillary bud burst. Twelve weeks after the petal colour visible stage, the visual quality of the rose bushes was evaluated by an expert jury. We found that nitrogen deficiencies (1) increased bud burst ratios in the medial and basal zones of the primary branch, (2) delayed the bud burst in the apical zone of the primary branch and (3) had long-term effects on plant visual quality. The continuous nitrogen deficiency regime produced flatter, more asymmetric and less vigorous rose bushes than the no nitrogen deficiency regime. By contrast, nitrogen deficiency during the flowering stages only resulted in more symmetric, taller and more vigorous rose bushes than the no nitrogen deficiency regime. Based on these results, the role of nitrogen on bud burst was discussed and candidate processes at the origin of the visual quality modification were suggested. This new approach combining ecophysiology and sensory assessment of ornamental plants enabled the identification of some early architecture components to be correlated with later visual quality characteristics and then to better target the physiological processes of interest

Fatigue Life Prediction of Welded Box Structures

The objective of this study is to predict fatigue life of metal welded boxes. Experimental results of fatigue life are satisfactory predicted using an analytical scheme based on the volumetric approach.Проведено прогнозирование усталостной долговечности сварных коробчатых конструкций. Результаты расчета усталостной долговечности с использованием аналитической схемы, базирующейся на объемном методе, хорошо согласуются с соответствующими экспериментальными данными.Проведено прогнозування довговічності зварних коробчастих конструкцій від утомленості. Результати розрахунку довговічності від утомленості з використанням аналітичної схеми, що базується на об’ємному методі, добре узгоджуються з відповідними експериментальними даними

Experimental and ab initio infrared study of χ-, κ- and α-aluminas formed from gibbsite

χ-, κ- and α-alumina phases formed by dehydration of micro-grained gibbsite between 773 and 1573 K are studied using infrared spectroscopy (IR). The structural transitions evidenced by X-ray diffraction (XRD) were interpreted by comparing IR measurements with ab initio simulations (except for the χ form whose complexity does not allow a reliable simulation). For each phase, IR spectrum presents specific bands corresponding to transverse optical (TO) modes of Al-O stretching and bending under 900 cm-1. The very complex χ phase, obtained at 773 K, provides a distinctive XRD pattern in contrast with the IR absorbance appearing as a broad structure extending between 200 and 900 cm-1 resembling the equivalent spectra for γ-alumina phase. κ-alumina is forming at 1173 K and its rich IR spectrum is in good qualitative agreement with ab initio simulations. This complexity reflects the large number of atoms in the κ-alumina unit cell and the wide range of internuclear distances as well as the various coordinances of both Al and O atoms. Ab initio simulations suggest that this form of transition alumina demonstrates a strong departure from the simple pattern observed for other transition alumina. At 1573 K, the stable α-Αl2Ο3 develops. Its IR spectra extends in a narrower energy range as compared to transition alumina and presents characteristics features similar to model α-Αl2Ο3{dot operator} Ab initio calculations show again a very good general agreement with the observed IR spectra for this phase. In addition, for both κ- and α-Αl2Ο3, extra modes, measured at high energy (above 790 cm-1 for κ and above 650 cm-1 for α), can originate from either remnant χ-alumina or from surface mode