Extension of the Vook–Witt and inverse Vook–Witt elastic grain-interaction models to general loading states

The recently developed Vook–Witt and inverse Vook–Witt elastic grain-interaction models have been employed for the calculation of mechanical elastic constants and diffraction (X-ray) stress factors of, in particular, thin films. However, their applicability is limited to a planar, rotationally symmetric state of macroscopic, mechanical stress. For such a loading state (and an, at least, transversely, elastically isotropic specimen), only two mechanical elastic constants are necessary to describe mechanical elastic behaviour and only the sum of two diffraction (X-ray) stress factors is needed to relate lattice strains to the one independent component of the mechanical stress tensor. The restriction to a planar, rotationally symmetric state of mechanical stress will be removed in this work. Calculation of the full stiffness tensor and all six diffraction (X-ray) stress factors then becomes possible. It was found previously that the Vook–Witt and inverse Vook–Witt models become (but only approximately) equivalent to the Eshelby–Kröner model for certain ideal grain-shape textures. For this reason, results of numerical calculations of mechanical elastic constants and diffraction (X-ray) stress factors, based on the Vook–Witt and inverse Vook–Witt models, will be presented and compared to corresponding results obtained from the Eshelby--Kröner grain-interaction model considering ideal grain-shape (‘morphological’) textures.     

In vitro analysis of immersed human tissues by Raman microspectroscopy

Raman microspectroscopy is a powerful tool for the analysis of tissue sections, providing a molecular map of the investigated samples. Nevertheless, data pre‐processing and, particularly, the removal of the broad background to the spectra remain problematic. Indeed, the physical origin of the background has not been satisfactorily determined. Using 785 nm as source in a confocal geometry, it is demonstrated for the example of the protein kappa‐elastin that the background and resulting quality of the recorded spectrum are dependent on the morphology of the sample. Whereas a fine powder yields a dominant broad background, compressed pellets and solution‐cast thin films produce, respectively, improved quality spectra and significantly reduced spectral background. As the chemical composition of the samples is identical, the background is ascribed to stray light due to diffuse scattering rather than an intrinsic photoluminescence. The recorded spectra from a tissue sample exhibit a large and spatially variable background, resulting in poorly defined spectral features. A significant reduction of the background signal as well as improvement of the spectral quality is achieved by immersion of the sample in water and measurement with an immersion objective. The significant improvement in signal to background is attributed to a reduction of the diffuse scattering due to a change in the effective morphology as a result of an improved index matching at the water/tissue interface compared to the air/tissue interface. Compared to sections measured in air, the background is reduced to that of the water, and pre‐processing is reduced to the subtraction of the substrate and water signal and correction for the instrument response, both of which are highly reproducible. Data pre‐processing is thus greatly simplified and the results significantly more reliable. Copyright © 2010 John Wiley & Sons, Ltd.     

Invariant Foliations and Decoupling of Non-autonomous Difference Equations

In this paper, we continue a previous study of the geometric properties of a certain prototype system of nonautonomous difference equations. In fact, we show that by means of the fundamental theorem on the existence of invariant fiber bundles two foliations of the extended state space can be found. This detailed information about the geometric structure of the underlying system is then used to construct transformations establishing the topological equivalence between a given coupled and a completely uncoupled system.     

Monotone Solutions of Neutral Difference Equations of Odd Order

A class of monotone sequences is introduced. A classification of all such monotone solutions of odd order neutral difference equation is established. Necessary and/or sufficient conditions are then derived for the existence of these solutions.     

XPS Study of a Cu-A1-O Compound Under H2/CO Mixture

Mixed copper aluminium oxide has been studied by XPS. It was shown that the reduction under hydrogen of the precursor oxide leads to the formation of cuprous ions located in the octahedral sites of the spinel matrix γ-A1₂0₃ and hydridic species stored in the solid. The use of the pre-reduced compound at 300°C before catalysis with H₂/CO is necessary to maintain almost intact the spinel phase despite the formation of metallic copper, whereas a strong modification of a surface composition was obseved when the solid is directly treated by H₂/CO mixture.

     

Some identities for Moore–Penrose inverses of matrix products

A group of identities are established for the Moore–Penrose inverses and the weighted Moore–Penrose inverses of matrix products AB and ABC. Some consequences and applications are also presented.     

On the Free Boundary Conditions for a Dynamic Shell Model Based on Intrinsic Differential Geometry

The mathematical theory behind the modeling of shells is a crucial issue in many engineering problems. Here, the authors derive the free boundary conditions and associated strong form of a dynamic shallow Kirchhoff shell model based on the intrinsic geometry methods of Michael Delfour and Jean-Paul Zolésio. This model relies on the oriented distance function which describes the geometry. This is an extension of the work done in [J. Cagnol, I. Lasiecka, C. Lebiedzik and J.-P. Zolésio (2002). Uniform stability in structural acoustic models with flexible curved walls. J. Differential Equation, 186(1), 88–121.], where the model was derived for clamped boundary conditions only. In the current article, manipulations with the model result in a cleaner form where the displacement of the shell and shell boundary is written explicitly in terms of standard tangential operators.