Global Analysis of the Flows of Fluids with Pressure-Dependent Viscosities

 To describe the flows of fluids over a wide range of pressures, it is necessary to take into account the fact that the viscosity of the fluid depends on the pressure. That the viscosity depends on the pressure has been verified by numerous careful experiments. While the existence of solutions local-in-time to the equations governing the flows of such fluids are available for small, special data and rather unrealistic dependence of the viscosity on the pressure, no global existence results are in place. Our interest here is to establish the existence of weak solutions for spatially periodic three-dimensional flows that are global in time, for a large class of physically meaningful viscosity-pressure relationships. (Accepted May 1, 2002) Published online November 15, 2002 Communicated by S. S. ANTMAN     

Spin correlations in the resonance reactionsāa→ Ψ(Z) → bb

A study is made of the processes of annihilation of an arbitrarily polarized e^–e⁺ pair into a pair of particles of spin 0, 1/2, 1, and 3/2 in the (Z)-resonance region.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 10, pp. 53–59, October, 1978.     

Optimum ion implantation and annealing conditions for stimulating secondary negative ion emission

The type, energy, ion dose, and heating temperature required to ensure a stable minimum work function of a surface in one experimental cycle (at least 2–3 min) are determined. Secondary ion mass spectrograms are recorded using Cs⁺, Ba⁺, and Ar⁺ ions. Cu, Al, and Mo samples are studied. The optimum ion implantation conditions and the activation temperature that provide a stable minimum work function of the sample surfaces are found. The samples implanted by Ba⁺ ions withstand higher temperature and current loads than the samples implanted by Cs⁺ ions. However, the work function in the case of Cs⁺ ions decreases stronger (to 1.9 eV). It is shown that neutral sputtered particles do not leave the surface at eφ ≤ 1.85–1.90 eV.     

The processes of ordering and formation of two-dimensional glasses at metal surfaces

Using the experimental results obtained for the Dy-Mo(1 1 2) system, we discuss the possibilities and mechanisms of formation of two-dimensional (2D) glasses on metal surfaces. It has been found that in the coverage range 0.07 < θ < 0.58, ordered Dy superstructures formed and observed at T < 400 K are irreversibly destroyed by annealing to higher temperatures and turn into an amorphous (glass) structure on cooling. It is supposed that this conversion is caused by the formation, at T > 400 K, of a Dy-Mo surface alloy in which the rate of Dy surface diffusion is strongly reduced in comparison with its value in the absence of alloying. As a result, the mobility of Dy adatoms becomes too low at the temperatures corresponding to the ordered equilibrium state of the surface, and this state cannot be achieved in reasonable relaxation time. This interpretation is corroborated by the experimental data on substantial suppression of surface diffusion in some coadsorbed layers. Since surface glasses contact with ordered (crystalline) substrates, their structure may have a peculiar character different from that of “conventional” metal glasses. Surface glasses can find a number of applications as rather stable systems that combine low dimensionality, specific electronic structure of their constituents and extremely high density of defects.     

Some Spectral Properties of One Sturm-Liouville Type Problem with Discontinuous Weight

We consider a discontinuous weight Sturm-Liouville equation together with eigenparameter dependent boundary conditions and two supplementary transmission conditions at the point of discontinuity. We extend and generalize some approaches and results of the classic regular Sturm-Liouville problems to the similar problems with discontinuities. In particular, we introduce a special Hilbert space formulation in such a way that the problem under consideration can be interpreted as an eigenvalue problem for a suitable selfadjoint operator, construct the Green’s function and resolvent operator, and derive asymptotic formulas for eigenvalues and normalized eigenfunctions.Original Russian Text Copyright © 2005 Mukhtarov O. Sh. and Kadakal M.__________Translated from Sibirskii Matematicheskii Zhurnal, Vol. 46, No. 4, pp. 860–875, July–August, 2005.     

Guided modes of integrated optical guides. A mathematical study

A waveguide in integrated optics is defined by its refractiveindex. The guide is assumed to be invariant in the propagationdirection while in the transverse direction it is supposed tobe a compact perturbation of an unbounded stratified medium.We are interested in the modes guided by this device, whichare waves with a transverse energy confined in a neighbourhoodof the perturbation. Our goal is to analyse the existence of such guided modes. Underthe assumptions of weak guidance the problem reduces to a two-dimensionaleigenvalue problem for a scalar field. The associated operatoris unbounded, selfadjoint, and bounded from below. Its spectrumconsists of the discrete spectrum corresponding to the guidedmodes and of the essential spectrum corresponding to the radiationmodes. We present existence results of guided modes and an asymptoticstudy at high frequencies, which shows that contrarily to thecase of optical fibers, the number of guided modes can remainbounded. The major tools are the min-max principle and comparisonof results between different eigenvalue problems. The originalityof the present study lies in the stratified character of theunbounded reference medium.