The Generalized Maxwell Garnett Approximation for Textured Matrix Composites with Coated Inclusions

Doklady Physics - A generalization of the Maxwell Garnett approximation for a textured matrix composite consisting of ellipsoidal inclusions with a shell is proposed; using it, an expression for an...     

Photochromism and the spectral properties of bispiroanthro-bis-oxazine

The spectral and photochromic properties of bispiroanthro-bis-oxazine (bis-SAO) in toluene, DMF, and polystyrene films were investigated in the 77–300 K interval. It is shown that the long-wave part of the absorption spectrum of the starting form of the molecule is formed by three-electron transitions localized in the anthro-bis-oxazine fragment. The directions of the oscillators of these transitions relative to the nuclear. backbone of the molecule are proposed on the basis of luminescence polarization data. It is proposed that the photochromic properties of the solutions are determined by the existence of bis-SAO molecules in dimer form.N. N. Semenov Institute of Chemical Physics, Russian Academy of Sciences, 117977 Moscow. Institute of Solid State and Semiconductor Physics, Academy of Sciences of Belarus, 210023 Vitebsk. Translated fromIzvestiya Akademii Nauk, Seriya Khimicheskaya, No. 12, pp. 2718–2725, December, 1992.     

Association of evaluation methods of the effective permittivity of heterogeneous media on the basis of a generalized singular approximation

Various methods for evaluation of the effective permittivity of heterogeneous media, namely, the effective medium approximation (Bruggeman’s approximation), the Maxwell-Garnett approximation, Wiener’s bounds, and the Hashin-Shtrikman variational bounds (for effective static characteristics) are combined on the basis of a generalized singular approximation.     

Multiphoton optical breakdown in water under picosecond laser pulses

The phenomenon of optical breakdown in highly purified (free of external impurities and bubstons) water under picosecond laser excitation was experimentally investigated. Narrow-band UV flashes were revealed. This effectmakes it possible to distinguish themodes of optical breakdown occurring either through multiphoton ionization of water molecules or via impact ionization at heterogeneous seeds.     

Pathological solutions to the Euler–Lagrange equation and existence/regularity of minimizers in one-dimensional variational problems

In this paper, we prove that if $L(x,u,v)\in C^3(R^3\to R)$, $L_{vv}>0$ and $L\ge \alpha |v|+\beta$, $\alpha >0$, then all problems (1), (2) admit solutions in the class $W^{1,1}[a,b]$, which are in fact $C^3$-regular provided there are no pathological solutions to the Euler equation (5). Here $u\in C^3[c,d[$ is called a pathological solution to equation (5) if the equation holds in $[c,d[$, $|\dot{u}(x)|\to \infty$ as $x\to d$, and ${6u6}_{C[c,d]}<\infty$. We also prove that the lack of pathological solutions to the Euler equation results in the lack of the Lavrentiev phenomenon, see Theorem 9; no growth assumptions from below are required in this result.     

Lower semicontinuity and relaxation for integral functionals with <Emphasis Type="Italic">p</Emphasis>(<Emphasis Type="Italic">x</Emphasis>)- and <Emphasis Type="Italic">p</Emphasis>(<Emphasis Type="Italic">x,u</Emphasis>)-growth

We consider the questions of lower semicontinuity and relaxation for the integral functionals satisfying the p(x)- and p(x, u)-growth conditions. Presently these functionals are actively studied in the theory of elliptic and parabolic problems and in the framework of the calculus of variations. The theory we present rests on the following results: the remarkable result of Kristensen on the characterization of homogeneous p-gradient Young measures by their summability; the earlier result of Zhang on approximating gradient Young measures with compact support; the result of Zhikov on the density in energy of regular functions for integrands with p(x)-growth; on the author’s approach to Young measures as measurable functions with values in a metric space whose metric has integral representation.     

Efficient calculation of the packing density of the crystal lattice of perovskite

The methodology of efficient macroscopic calculation of parameters of the cubic crystal lattice based on the use of the coefficient of structured packing of its elementary cell is considered. The possibility of precision theoretical determination of the numerical values of interatomic distances in crystals of the type under consideration is shown.