Convergence of optimal controls in some optimization problems

We consider the behavior of bundles of optimal controls when the initial state of the system goes to some given vector. We investigate three types of optimization problems: problems with fixed process length and a free right endpoint; problems with fixed process length and a fixed right endpoint; time-optimal problems. The article is a review of recent results obtained by the author. __________ Translated from Nelineinaya Dinamika i Upravlenie, No. 4, pp. 301–314, 2004.     

Molecular Structure of Bis(trimethylsilyl) Hypophosphite HP(OSiMe3)2 by Gas-Phase Electron Diffraction and Quantum Chemistry

Geometric parameters and conformation of the bis(trimethylsilyl)hypophosphite molecule were determined by gas-phase electron diffraction and quantum-chemical calculations. The molecule has an asymmetric structure, including an asymmetric P(OSiMe₃)₂ group. The principal geometric parameters are as follows: (r _a; in parentheses are standard deviations): bond lengths: P-O 1.616 and 1.633(1), Si-O 1.670(1), Si-C 1.892(1), C-H 1.097(3) Å; bond angles: OPO 100.8(8), POSi 133.3, and 138.4(3)°; torsion angles about P-O bonds 120(2) and 41.(3)°; and torsion angles about Si-O bonds are 145 and −178(4)°.__________Translated from Zhurnal Obshchei Khimii, Vol. 75, No. 6, 2005, pp. 897–902.Original Russian Text Copyright © 2005 by Naumov, Oberhammer, Tafipol’skii.     

Effect of cerium oxide on the activity of platinum catalysts of hydrogen and CO oxidation

Effective catalytic systems based on Pt/CeO₂-C were prepared. The use of a cerium oxide addition in the substrate stabilized the platinum catalysts against their poisoning with carbon monoxide at room temperature.     

Nonlinear theory of the compressible gas flows over a nonuniform boundary in the gravitational field in the shallow-water approximation

A set of equations is derived for the motion of a compressible ideal gas over a nonuniform boundary in the gravitational field in the shallow-water approximation. Classical simple waves are shown not to be the solutions to this set of equations. Generalized simple waves are found to exist only in the case of a linear underlying-surface profile. All continuous and discontinuous solutions are obtained in an explicit form for the case of the boundary in the form of an inclined plane, and an analytical solution is found for the problem of the decay of an arbitrary discontinuity. This solution consists of four wave configurations. Necessary and sufficient conditions are determined for the existence of each configuration.     

The dynamics of 180° domains in a ferroelectric in the process of polarization reversal and electron emission

A model is proposed to describe the evolution of 180° domains in a ferroelectric. Closed analytic expressions are obtained for the velocity of sideways motion of a 180° domain wall in an electric field and numerical calculations are performed. The connection between polarization reversal and electron emission is discussed.     

Noncollinear orientation of external magnetic field and flux lines penetrating an isotropic hard superconductor

Penetration by Abrikosov flux lines of an isotropic hard superconductor in the critical state induced by changes in the orientation of external magnetic field has been theoretically investigated. The analysis has been based on the microscopic nonlocal model taking into account forces of bulk and surface pinning, alongside magnetic forces of interaction of the row of penetrating vortices with existing flux lines, Meissner currents, and vortex images. New vortices penetrate a superconductor only when the angle through which the field is rotated is larger than a certain critical value. It has been determined that the alignment of entering vortices is essentially different from that of the applied magnetic field. The feasibility of detecting noncollinearity effects is discussed. Zh. éksp. Teor. Fiz. 114, 1804–1816 (November 1998)     

Absorption and scattering of high-power laser radiation in low-density porous media

We have experimentally investigated the interaction of high-power neodymium laser pulses in the intensity range 10¹³–10¹⁴ W/cm² with flat low-density (0.5–10 mg/cm³) agar-agar targets under conditions of interest for problems of inertial nuclear fusion. Optical and x-ray methods with high temporal and spatial resolution were used to examine the dependence of absorption and scattering of the incident beam on the initial mean density and thickness of the irradiated samples. We show that when a porous target is irradiated, a bulk absorption layer of high-temperature plasma is produced inside the target whose dimensions are determined by the initial density of the material. The time dependence and spectral composition of the harmonics 2ω ₀ and 3ω ₀/2 observed in the plasma-scattered radiation are measured. A theoretical model is developed that describes the interaction of high-power laser pulses with a porous medium. Predictions of the model, based on the hypothesis of two stages of homogenization of the target material—a fast stage (0.1–0.3 ns) and a slow stage (1–3 ns), are in good agreement with the experimental data. Zh. éksp. Teor. Fiz. 115, 805–818 (March 1999)     

Correlation reception of thermal acoustic radiation

Correlated signals of thermal acoustic radiation from heated sources extending in the transverse direction (a pair of narrow plasticine plates and a wide plasticine strip) are measured. The measurements are performed by multiplying together the signals that are shifted in time with respect to each other and detected by two piezoelectric transducers. The values of the correlated signals of thermal acoustic radiation are determined by the spatial variation of temperature in the medium under study.     

Dynamics of acoustoelectromagnetic solitons as a manifestation of higher nonlinearity

The acoustoelectromagnetic interaction is examined in a regime where three mechanisms must be taken into account simultaneously: photoelasticity, quadratic photoelasticity, and elastic nonlinearity. It is shown that beyond the critical conditions, acoustic solitary waves are formed at harmonic and subharmonic frequencies in a crystal. Including damping and nonideal reflection at the boundaries does not lead to the establishment of any sort of stationary state: a soliton spatial-temporal dynamic develops. Fiz. Tverd. Tela (St. Petersburg) 39, 1101–1104 (June 1997)     

Formation of semiconductor titanium disilicide

Nanostructured titanium disilicide powders with semiconductor properties are synthesized and studied. The optical and electrophysical properties of TiSi₂ are found to be controlled by its crystallite size.