On Publications on the Brittle Fracture Mechanics of Prestressed Materials

The paper analyzes new publications on the brittle fracture mechanics of prestressed materials. It is found out that new scientific results published in the International Journal of Solids and Structures in 2002 are a particular case of the results obtained at the Institute of Mechanics 20 years ago     

Some functional equations originating from number theory

We will introduce new functional equations (3) and (4) which are strongly related to well-known formulae (1) and (2) of number theory, and investigate the solutions of the equations. Moreover, we will also study some stability problems of those equations.     

α-Fe2O3-In2O3 mixed oxide nanoparticles synthesized under hydrothermal supercritical conditions

α-Fe₂O₃-In₂O₃ mixed oxide nanoparticles system has been synthesized by hydrothermal supercritical and postannealing route, starting with (1−x)Fe(NO₃)₃·9H₂O·xIn(NO₃)₃·5H₂O aqueous solution (x=0-1). X-ray diffraction and Mössbauer spectroscopy have been used to study the phase structure and substitutions in the nanosized samples. The concentration regions for the existence of the solid solutions in the α-Fe₂O₃-In₂O₃ nanoparticle system together with the solubility limits of In³⁺ ions in the hematite lattice and of Fe³⁺ ions in the cubic In₂O₃ structure have been evidenced. In general, the substitution level is considerably lower than the nominal concentration x. A justification of the processes leading to the formation of iron and indium phases in the investigated supercritical hydrothermal system has been given.     

Bounds for non‐periodic mixtures of infinitely many materials

We prove bounds on the homogenized coefficients for general non‐periodic mixtures of an arbitrary number of isotropic materials, in the heat conduction framework. The component materials and their proportions are given through the Young measure associated to the sequence of coefficient functions. Upper and lower bounds inequalities are deduced in terms of algebraic relations between this Young measure and the eigenvalues of the H‐limit matrix. The proofs employ arguments of compensated compactness and fine properties of Young measures. When restricted to the periodic case, we recover known bounds. Copyright © 2005 John Wiley & Sons, Ltd.     

Almost automorphic solutions for abstract functional differential equations

For abstract linear functional differential equations with an almost automorphic forcing term, we establish a result on the existence of almost automorphic solutions, which extends the classical theorem due to Massera on the existence of periodic solutions for linear periodic ordinary differential equations.     

Statistical approach to light scattering from deformed textured heterogeneous polymer materials

A statistical theory of light scattering from deformed isotropic and textured heterogeneous polymer materials is formulated. Two types of textured structures are analyzed: assemblies of optically isotropic and anisotropic rods and a spatially anisotropic distribution of isotropic spherical inclusion centers. The small-angle H_v light-scattering patterns are calculated. The appearance of scattering from isotropic rods and spheres in deformed materials has been demonstrated. The changes of the H_v scattering patterns as a function of elongation and strucuture parameters are discussed. © 1993 John Wiley & Sons, Inc.     

Circularly polarized light-induced electrogyration in the Au nanoparticles on the ITO

We have found that the gold nanoparticles on the ITO substrates might be considered promising materials for circularly polarized light-induced linear electrogyration (EG). The maximal achieved value of the EG susceptibility described by third-order axial tensor caused by probe circularly polarized light at a wavelength of 1060 nm was equal to about 13 deg/mm at pulsed electric field strength 30.0 V/cm with a duration of about 1 ms. We have revealed that the maximal EG coefficient is achieved for the samples possessing maximal resistivity. The investigated composites possess long-lived EG grating which decreases by not more than 12% after 120 min of laser treatment. Applying a non-circular pump light leads to the diminishing of the observed EG.     

Characterisation of oxygen defects in calciumdifluoride

We study the aggregation of oxygen dipoles well dispersed in a CaF₂ crystal upon annealing at temperatures ranging from 370 to 420 K. The concentration of oxygen dipoles is monitored by measuring the intensity of the ionic thermocurrent peak as well as by absorption and luminescence spectroscopies. Results from three methods agree within experimental error and yield an activation energy of (1.2±0.1) eV for the diffusion of isolated oxygen centres in the crystal.     

Orbital-selective Mott-insulator transition in Ca 2 - x Sr x RuO 4

The electronic structures of the metallic and insulating phases of the alloy series Ca_2-xSr_xRuO₄ ( 0 ? x ? 2) are calculated using LDA, LDA+U and Dynamical Mean-Field Approximation methods. In the end members the groundstate respectively is an orbitally non-degenerate antiferromagnetic insulator (x = 0) and a good metal (x = 2). For x > 0.5 the observed Curie-Weiss paramagnetic metallic state which possesses a local moment with the unexpected spin S = 1/2, is explained by the coexistence of localized and itinerant Ru-4d-orbitals. For 0.2 < x < 0.5 we propose a state with partial orbital and spin ordering. An effective model for the localized orbital and spin degrees of freedom is discussed. The metal-insulator transition at x = 0.2 is attributed to a switch in the orbital occupation associated with a structural change of the crystal. Received 27 July 2001     

一类具无穷时滞泛函微分方程的周期解

讨论具有无穷时滞中立型泛函微分方程$ \frac{\rm d}{{\rm d}t}\left(x(t)-\int_{-\infty}^{0}g(s,x(t+s)){\rm d}s\right) =A(t,x(t))x(t)+f(t,x_t)$的周期解问题,利用重合度理论中的延拓定理得到了周期解的存在性和唯一性条件;特别地,当$g(s,x)\equiv 0, A(t,x)=A(t)$时, 给出了存在唯一稳定周期解的条件.