Flow near the rear end of a slender axisymmetric body

The steady flow of a viscous incompressible fluid at high Reynolds numbers near a body of revolution of finite length whose radius coincides in order of magnitude with the thickness of the boundary layer is considered. The structure of the boundary layer in the neighborhood of the rear end of the body is investigated on the assumption that it has a power-law shape with values of the exponent n 1/2. A solution is also obtained for the near wake.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 10–18, September–October, 1990.     

Femtosecond relaxation dynamics of surface plasmon-polaritons in the vicinity of fano-type resonance

Temporal modification of femtosecond laser pulses reflected from planar periodic metal nanostructures with resonant excitation of surface plasmon-polaritons is experimentally studied. Spectral time-resolved measurements of the second-order cross-correlation function performed with the pulse duration comparable with the surface plasmon-polariton relaxation time (about 100 fs) show the strong spectral dependence of the envelope of the reflected femtosecond pulse described by Fano-resonance parameters.     

Young Measures as Measurable Functions and Their Applications to Variational Problems

In this paper, we give a systematic exposition of our approach to the Young measure theory. This approach is based on characterzation of these objects as measurable functions into a compact metric space with a metric of integral form. We explain advantages of this approach in the study of the behavior of integral functionals on weakly convergent sequences. Bibliography: 38 titles. __________ Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 310, 2004, pp. 191–212.     

Flow in the neighborhood of the cusp of an axisymmetric cavity

The steady-state axisymmetric potential flow of an ideal incompressible fluid is considered. The structure of the singularity at the point where the free stream surface leaves the axis of symmetry is investigated.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 175–176, September–October, 1989.     

On Local Perturbations of a Three-Dimensional Boundary Layer

A high-Reynolds steady-state viscous incompressible fluid flow is investigated in the neighborhood of a small three-dimensional irregularity located on the smooth surface of a body and oriented almost along the skin-friction lines. The regime in which quasi-two-dimensional flow with a given pressure gradient is realized on the irregularity scale is studied in detail. The numerical solution of the corresponding boundary value problem for the boundary layer equations is obtained. It is shown that, as distinct from the plane case, this solution is unique.     

Asymptotic theory of vortex breakdown

Axisymmetric breakdown of a vortex in a steady flow of incompressible fluid is investigated by means of an asymptotic analys is of the Navier-Stokes equations for large Reynolds number (R). A criterion for vortex breakdownis formulated. The region of slow motion resulting from vortex breakdown is shown to be bounded by an ellipsoid with length of order R^–1/4 and thickness of the order R^–3/8.Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 3, pp. 78–90, May–June, 1993.     

The effect of simple electrolytes on coagulation of hydrosols of monodisperse negatively charged detonation nanodiamond

The influence of the concentration of potassium and barium chlorides on the aggregation stability of a hydrosol of monodisperse negatively charged detonation nanodiamond with particle sizes of 4?5 nm obtained by annealing of its agglomerates in air has been studied by turbidimetry. The experimental results have been discussed within the classical and generalized Derjaguin?Landau?Verwey?Overbeek theories. The analysis of the pair interaction potentials calculated for ultradispersed particles of detonation nanodiamond has led to the conclusion that the coagulation occurs by the barrier mechanism in the primary potential minimum. It has been assumed that the structural component of the interparticle interaction energy contributes to the total balance of the surface forces.     

Variational field theory from the point of view of direct methods

In this paper we show that the classical field theory ofWeierstrass–Hilbert can be strengthen on applying direct methods. Concretely, given a field of extremals and an extremal that is an element of the field, we can show that the latter gives minimum in the class of Lipschitz functions with the same boundary data and with the graphs in the set covered by the field. We suggest the two proofs: a modern one (exploiting Tonelli’s Theorem on lower semicontinuity of integral functionals with respect to the weak convergence of admissible functions in W ^1,1) and the one based only on arguments available already in the 19th century.     

Asymptotic theory of nonstationary separation

Nonstationary separation of a laminar boundary layer in a incompressible fluid is studied on the basis of asymptotic analysis of the Navier-Stokes equations at large Reynolds numbers. The case when the point of separation moves upstream is considered. It is shown that under certain restrictions on the acceleration with which the motion of the point of separation occurs the local solution depends on the time as on a parameter. As in the stationary case, the separation occurs spontaneously under the influence of the large local pressure gradient. An important difference is however that the mechanism of nonstationary separation is inviscid.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 21–32, November–December, 1979.I thank A. I. Ruban for great interest and assistance in the work, and also O. S. Ryzhov for a number of helpful comments.