We show a result on propagation of the anisotropic Gabor wave front set for linear operators with a tempered distribution Schwartz kernel. The anisotropic Gabor wave front set is parametrized by a positive parameter relating the space and frequency variables. The anisotropic Gabor wave front set of the Schwartz kernel is assumed to satisfy a graph type criterion. The result is applied to a class of evolution equations that generalizes the Schrödinger equation for the free particle. The Laplacian is replaced by any partial differential operator with constant coefficients, real symbol and order at least two.

Anisotropy in clay-rich sedimentary rocks is receiving increasing attention. Seismic anisotropy is essential in the prospecting for petroleum deposits. Anisotropy of diffusion has become relevant for environmental contaminants, including nuclear waste. In both cases, the orientation of component minerals is a critical ingredient and, largely because of small grain size and poor crystallinity, the orientation distribution of clay minerals has been difficult to quantify. A method is demonstrated that relies on hard synchrotron X-rays to obtain diffraction images of shales and applies the crystallographic Rietveld method to deconvolute the images and extract quantitative information about phase fractions and preferred orientation that can then be used to model macroscopic physical properties. The method is applied to shales from European studies which investigate the suitability of shales as potential nuclear waste repositories (Meuse/Haute-Marne Underground Research Laboratory near Bure, France, and Benken borehole and Mont Terri Rock Laboratory, Switzerland). A Callovo-Oxfordian shale from Meuse/Haute-Marne shows a relatively weak alignment of clay minerals and a random distribution for calcite. Opalinus shales from Benken and Mont Terri show strong alignment of illite-smectite, kaolinite, chlorite, and calcite. This intrinsic contribution to anisotropy is consistent with macroscopic physical properties where anisotropy is caused both by the orientation distribution of crystallites and high-aspect-ratio pores. Polycrystal elastic properties are obtained by averaging single crystal properties over the orientation distribution and polyphase properties by averaging over all phases. From elastic properties we obtain anisotropies for p waves ranging from 7 to 22%.

Laser-assisted atom probe tomography (APT) is a relatively new, powerful technique for sub-nanometric mineral and biomineral analysis. However, the laser-assisted APT analysis of highly anisotropic and chemically diverse minerals, such as phyllosilicates, may prove especially challenging due to the complex interaction between the crystal structure and the laser pulse upon applying a high electric field. Micas are a representative group of nonswelling clay minerals of relevance to a number of scientific and technological fields. In this study, a Mg-rich biotite was analyzed by APT to generate preliminary data on nonisotropic minerals and to investigate the effect of the crystallographic orientation on mica chemical composition and structure estimation. The difference in results obtained for specimens extracted from the (001) and (hk0) mica surfaces indicate the importance of both experimental parameters and the crystallography. Anisotropy of mica has a strong influence on the physicochemical properties of the mineral during field evaporation and the interpretation of APT data. The promising results obtained in the present study open the way to future innovative APT applications on mica and clay minerals and contribute to the general discussion on the challenges for the analysis of geomaterials by atom probe tomography.

Carbon fiber technology drives significant development in lightweight and multifunctional applications. However, the microstructure of carbon fibers is not completely understood. A big challenge is to obtain the distribution of heteroatoms, for instance nitrogen, with high spatial resolution in three dimensions. Atom probe tomography (APT) has the potential to meet this challenge, but APT of carbon fibers is still relatively unexplored. We performed APT on three types of carbon fibers, including one high modulus type and two intermediate modulus types. Here, we present the methods to interpret the complex mass spectra of carbon fibers, enhance the mass resolution, and increase the obtained analysis volume. Finally, the origin of multiple hit events and possible methods to mitigate multiple hit events are also discussed. This paper provides guidance for future APT studies on carbon fibers, and thus leads the way to a deeper understanding of the microstructure, and consequently advancements in wide applications of carbon fibers.

As characterization and modeling of complex materials by phenomenological models remains challenging, data-driven computing that performs physical simulations directly from material data has attracted considerable attention. Data-driven computing is a general computational mechanics framework that consists of a physical solver and a material solver, based on which data-driven solutions are obtained through minimization procedures. This work develops a new material solver built upon the local convexity-preserving reconstruction scheme by He and Chen (2020) A physics-constrained data-driven approach based on locally convex reconstruction for noisy database. Computer Methods in Applied Mechanics and Engineering 363, 112791 to model anisotropic nonlinear elastic solids. In this approach, a two-level local data search algorithm for material anisotropy is introduced into the material solver in online data-driven computing. A material anisotropic state characterizing the underlying material orientation is used for the manifold learning projection in the material solver. The performance of the proposed data-driven framework with noiseless and noisy material data is validated by solving two benchmark problems with synthetic material data. The data-driven solutions are compared with the constitutive model-based reference solutions to demonstrate the effectiveness of the proposed methods.

Under suitable assumptions on the family of anisotropies, we prove the existence of a weak global 1/(n+1)-Hölder continuous in time mean curvature flow with mobilities of a bounded anisotropic partition in any dimension using the method of minimizing movements. The result is extended to the case when suitable driving forces are present. We improve the Hölder exponent to 1/2 in the case of partitions with the same anisotropy and the same mobility and provide a weak comparison result in this setting for a weak anisotropic mean curvature flow of a partition and an anisotropic mean curvature two-phase flow.

Diffusion tensor imaging (DTI) is a magnetic resonance imaging technique that is increasingly being used for the non-invasive evaluation of brain white matter abnormalities. In this review, we discuss the basic principles of DTI, its roots and the contribution of European centres in its development, and we review the findings from DTI studies in schizophrenia. We searched EMBASE, PubMed, PsychInfo, and Medline from February 1998 to December 2006 using as keywords ‘schizophrenia’, ‘diffusion’, ‘tensor’, and ‘DTI’. Forty studies fulfilling the inclusion criteria of this review were included and systematically reviewed. White matter abnormalities in many diverse brain regions were identified in schizophrenia. Although the findings are not completely consistent, frontal and temporal white matter seems to be more commonly affected. Limitations and future directions of this method are discussed.

Propagation of harmonic Lamb waves in plates made of functionally graded materials (FGM) with transverse inhomogeneity is studied by combination of the Cauchy six-dimensional formalism and matrix exponential mapping. For arbitrary transverse inhomogeneity a closed form implicit solution for dispersion equation is derived and analyzed. Both the dispersion equation and the corresponding solution resemble ones obtained for stratified media. The dispersion equation and the corresponding solution are applicable to media with arbitrary elastic (monoclinic) anisotropy.

In this study, we investigated the elastic constants, moduli, hardness, and electronic structures of Ti–Al intermetallic compounds (TiAl, Ti3Al, and TiAl3) using first-principles calculations. The cohesive energy and formation enthalpy of these compounds are negative, which indicates that they are thermodynamically stable. We calculated the elastic constants and moduli using the stress–strain method and Voigt–Reuss–Hill approximation, respectively. We evaluated the mechanical anisotropy of these compounds using the anisotropic index and found that the results are in good agreement with other experimental and theoretical data. We evaluated the chemical bonding of these compounds by calculating their density of states, the results of which revealed that the bonding behavior of all Ti–Al intermetallic compounds involved a mixture of metallic and covalent bonds. We also estimated the Debye temperature and sound velocities of these Ti–Al intermetallic compounds.