Multi-layer thin films/substrate system subjected to non-uniform misfit strains

Current methodologies used for the inference of thin film stress through curvature measurement are strictly restricted to stress and curvature states that are assumed to remain uniform over the entire film/substrate system. These methodologies have recently been extended to a single layer of thin film deposited on a substrate subjected to the non-uniform misfit strain in the thin film. Such methodologies are further extended to multi-layer thin films deposited on a substrate in the present study. Each thin film may have its own non-uniform misfit strain. We derive relations between the stresses in each thin film and the change of system curvatures due to the deposition of each thin film. The interface shear stresses between the adjacent films and between the thin film and the substrate are also obtained from the system curvatures. This provides the basis for the experimental determination of thin film stresses in multi-layer thin films on a substrate.     

Stress concentration and effective stiffness of aligned fiber reinforced composite with anisotropic constituents

The paper addresses the problem of calculation of the local stress field and effective elastic properties of a unidirectional fiber reinforced composite with anisotropic constituents. For this aim, the representative unit cell approach has been utilized. The micro geometry of the composite is modeled by a periodic structure with a unit cell containing multiple circular fibers. The number of fibers is sufficient to account for the micro structure statistics of composite. A new method based on the multipole expansion technique is developed to obtain the exact series solution for the micro stress field. The method combines the principle of superposition, technique of complex potentials and some new results in the theory of special functions. A proper choice of potentials and new results for their series expansions allow one to reduce the boundary-value problem for the multiple-connected domain to an ordinary, well-posed set of linear algebraic equations. This reduction provides high numerical efficiency of the developed method. Exact expressions for the components of the effective stiffness tensor have been obtained by analytical averaging of the strain and stress fields.     

Chlorination of aromatic substrates catalyzed by the phthalocyanine complexes

The chlorination of benzene, toluene, and o-xylene with molecular chlorine in the presence of the phthalocyanine complexes of different structures was studied. The transformations of the catalysts during the reaction were investigated. Published in Russian in Izvestiya Akademii Nauk. Seriya Khimicheskaya, No. 8, pp. 1644–1647, August, 2008.     

Influence of transition metal ions on the textural properties of alumina and aluminasilicates

Accelerated phase transformations and chemical reactions of metastable aluminas and kaolinite, doped with Cu^{2 +}, Mn^{3 +}/Mn^{2 +} and Fe^{3 +}/Fe^{2 +} ions, are accompanied with accelerated decrease of surface area and pore volume values. The phenomena in metal ion doped samples are explained by a catalytic mechanism, in terms of the Jahn-Teller effect. This revised version was published online in June 2006 with corrections to the Cover Date.     

Equivalence and Singularity of Gaussian Measures on the Conic Sigma-Field

The alternative: equivalence-singularity on the conic sigma-field is established for a pair of centered Gaussian distributions and a corresponding criterion is given. The behavior of the logarithmic variation is established for the Radon–Nikodym derivative on the conic sigma-subfield. Bibliography: 6 titles.     

Generalizations of the Nikodym boundedness and Vitali–Hahn–Saks theorems

Generalizations of the Nikodym boundedness and Vitali–Hahn–Saks theorems for scalar-valued measures on rings of sets that are in general not σ-rings are presented. As a consequence, the rings of subsets of N with density zero and uniform density zero are shown to have the Nikodym property. In addition, vector measure generalizations of the Vitali–Hahn–Saks theorem are given.