Attainment and relaxation results in special classes of deformations

In this paper we deal with the attainment and relaxation issues in variational problems of mathematical theory of elasticity. We consider minimization of energy functionals in certain classes of deformations which render the problem essentially scalar. It turns out that in those cases the relaxation theorem holds for integrands that are bounded from below by a power function, with power exceeding the dimension of the space of independent variables. The bound from below can be improved in the homogeneous case. The mathematical fact behind the results is that relaxation holds at those Sobolev functions that are a.e. differentiable in the classical sense, independently of growth of Carathéodory integrands. In the homogeneous case we can also indicate a condition which is both necessary and sufficient for solvability of all boundary value minimization problems of the Dirichlet type.Received: 16 June 2000, Accepted: 12 March 2003, Published online: 6 June 2003M. A. Sychev: This research was partially supported by the grant N 00-01-00912 of the Russian Foundation for Basic Research     

A condition on the value function both necessary and sufficient for full regularity of minimizers of one-dimensional variational problems

We study two-point Lagrange problems for integrands :

 

Under very weak regularity hypotheses [ is Hölder continuous and locally elliptic on each compact subset of ] we obtain, when is of superlinear growth in , a characterization of problems in which the minimizers of (P) are -regular for all boundary data. This characterization involves the behavior of the value function : defined by . Namely, all minimizers for (P) are -regular in neighborhoods of and if and only if is Lipschitz continuous at . Consequently problems (P) possessing no singular minimizers are characterized in cases where not even a weak form of the Euler-Lagrange equations is available for guidance. Full regularity results for problems where is nearly autonomous, nearly independent of , or jointly convex in are presented.

     

On asymptotic theory of separated flows past bodies

Symmetric two-dimensional steady flow past a body in a homogeneous incompressible fluid stream at high Reynolds numbers is considered. A slow motion in the reverse flow zone is investigated and the solution for the flow in the external region is obtained in the second approximation. Additional considerations of the fact that the flow in the closure region of the separation zone and in the wake behind this zone is turbulent are presented. The laminar-turbulent transition in the mixing layer is analyzed and an analogy between this process and the propagation of perturbations upstream of the boundary layer interaction regions is revealed.     

Influence of the initial pressure of polydisperse bubble media on characteristics of detonation waves

The influence of the initial pressure of polydisperse bubble media on the initiation conditions, structure, propagation velocity, and the pressure of detonation waves has been experimentally studied. It has been established that variations in the initial pressure of the bubble medium is an effective method of controlling the parameters of bubble detonation waves.     

Steady flow with separation past a thin airfoil at high Reynolds numbers

The results of calculating the steady separated flow of a viscous incompressible fluid past a 12% sinusoidal airfoil with and without a splitter plate are presented. The Navier—Stokes equations written in stream-function—vorticity variables are approximated in accordance with a central difference scheme and solved simultaneously by means of the direct method. The results obtained are analyzed from the standpoint of their consistency with the asymptotic theory based on the well-known three-deck scheme. Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No.2, pp. 155–160, March–April, 1994.     

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.     

The Tribo-Induced Effect of Shielding Action of Ethanolamines and Compounds of Cholesterol under the Dynamic Contact of Metals in Plastic Lubricants

Doklady Physics - The effect of the integrated shielding of plastic lubricants containing ethanolamines and liquid-crystalline cholesterol compounds induced during the frictional interaction of...     

Direct Methods in Variational Field Theory

Siberian Mathematical Journal - We show that the Weierstrass–Hilbert classical field theory can be strengthened. Namely, for each extremal field, it is true that if an extremal is an element...     

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.