Gas dynamics of a rocket plume in the upper atmosphere

We study the expansion of a rocket exhaust plume in the direction perpendicular to the rocket motion. We compare numerical calculations with a self-similar approximation for a strong cylindrically symmetric explosion and show that, if the rocket velocity V _∞ is high enough and exceeds the sum of the exhaust gas velocity V _e and the sound velocity V _s (V _∞ > V _e + V _s ), a gasdynamic hole may be formed for a short time around the rocket flight trajectory in the upper atmosphere, where the plume-gas concentration is less than the ambient-gas concentration at a given altitude. We calculate the density and temperature profiles of the transversal plume expansion.     

Thermodynamic study of characteristics of the converter with separated supply of hydrocarbon fuel for thermo-oxidative and steam reforming

Thermodynamic studies of the converter characteristics were performed to produce hydrogen-containing syngas from hydrocarbon fuel (kerosene) with its separated supply for thermo-oxidative and steam reforming. It is demonstrated that the optimal conditions of the converter performance correlate with the oxidant ratio of α > 0.5 at the heattransfer wall temperature of 1200 K. Hydrogen content in the final syngas reaches 60 % by volume, free carbon (soot) deposition in reforming products is excluded, and there is no need to apply walls water cooling in the converter.     

Refinement of the K0.96Ti0.96Nb0.04OPO4 structure

The structure of a K_0.96Ti_0.96Nb_0.04OPO₄ single crystal was established by the methods of the X-ray diffraction analysis. Additional positions of K atoms were established. In the superionic state, these atoms provide ionic transport in the crystals.     

The interaction of punches on the face of an elastic wedge

The interaction of two punches, which are elliptic in plan, on the face of an elastic wedge is investigated in a three-dimensional formulation for different types of boundary conditions on the other face. The wedge material is assumed to be incompressible. An asymptotic solution is obtained for punches which are relatively distant from one another and from the edge of the wedge. For the case when the punches are arranged relatively close to the edge of the wedge (or reach the edge, the contact area is unknown) the numerical method of boundary integral equations is used. The mutual effect of the punches is estimated by means of calculations. The asymptotic solution of the generalized Galin problem, concerning the effect of a concentrated force applied on the edge of the three-dimensional wedge on the contact pressure distribution under a circular punch relatively far from the edge, is obtained.     

Preparation and characterization of modified aluminum oxide catalysts

The formation of individual and modified high-purity aluminum oxides (γ-Al₂O₃) prepared from aluminum alcoholates was studied. In the study of the hydrolysis of aluminum alcoholates and modified (Zr, Ti, and Si) aluminum alcoholates, it was found that an increase in the chain length of the alkoxy group and an increase in the aging temperature or aging time in mother liquor resulted in a decrease in the concentration of an amorphous phase, an increase in the concentration of a pseudoboehmite phase, and an improvement in its crystal structure. Hydrolysis in alkaline (a 0.5 wt % solution of ammonia) or neutral solutions made it possible to obtain samples with an almost 100% pseudoboehmite content. At the same time, the samples prepared by hydrolysis in an acidic solution (a 0.1 M solution of HCl) contained a considerable amount of an amorphous phase. It was found that the specific rate of dehydration of n-butanol on the modified aluminum oxide samples linearly decreased with the concentration of donor sites and linearly increased with the concentration of acceptor sites, whose concentration was measured using the spin probe method.     

Polar Decomposition of Scale-Homogeneous Measures with Application to Lévy Measures of Strictly Stable Laws

A scaling on some space is a measurable action of the group of positive real numbers. A measure on a measurable space equipped with a scaling is said to be \(\alpha \)-homogeneous for some nonzero real number \(\alpha \) if the mass of any measurable set scaled by any factor \(t > 0\) is the multiple \(t^{-\alpha }\) of the set’s original mass. It is shown rather generally that given an \(\alpha \)-homogeneous measure on a measurable space there is a measurable bijection between the space and the Cartesian product of a subset of the space and the positive real numbers (that is, a “system of polar coordinates”) such that the push-forward of the \(\alpha \)-homogeneous measure by this bijection is the product of a probability measure on the first component (that is, on the “angular” component) and an \(\alpha \)-homogeneous measure on the positive half line (that is, on the “radial” component). This result is applied to the intensity measures of Poisson processes that arise in Lévy-Khinchin-Itô-like representations of infinitely divisible random elements. It is established that if a strictly stable random element in a convex cone admits a series representation as the sum of points of a Poisson process, then it necessarily has a LePage representation as the sum of i.i.d. random elements of the cone scaled by the successive points of an independent unit-intensity Poisson process on the positive half line each raised to the power \(-\frac{1}{\alpha }\).     

Entropic Moments and Domains of Attraction on Countable Alphabets

Modern information theory is largely developed in connection with random elements residing in large, complex, and discrete data spaces, or alphabets. Lacking natural metrization and hence moments, the associated probability and statistics theory must rely on information measures in the form of various entropies, for example, Shannon’s entropy, mutual information and Kullback–Leibler divergence, which are functions of an entropic basis in the form of a sequence of entropic moments of varying order. The entropicmoments collectively characterize the underlying probability distribution on the alphabet, and hence provide an opportunity to develop statistical procedures for their estimation. As such statistical development becomes an increasingly important line of research in modern data science, the relationship between the underlying distribution and the asymptotic behavior of the entropic moments, as the order increases, becomes a technical issue of fundamental importance. This paper offers a general methodology to capture the relationship between the rates of divergence of the entropic moments and the types of underlying distributions, for a special class of distributions. As an application of the established results, it is demonstrated that the asymptotic normality of the remarkable Turing’s formula for missing probabilities holds under distributions with much thinner tails than those previously known.     

Shape resonances in slow electron scattering by aromatic molecules. I. Anthraquinone derivatives

A series of anthraquinone (C(14)O(2)H(8)) derivatives has been studied by means of electron capture negative ion mass spectrometry (ECNI-MS), photoelectron spectroscopy (PES), and AM1 quantum chemical calculations. Mean lifetimes of molecular negative ions M(-.) (MNI) have been measured. The mechanism of long-lived MNI formation in the epithermal energy region of incident electrons has been investigated. A simple model of a molecule (a spherical potential well with the repulsive centrifugal term) has been applied for the analysis of the energy dependence of cross sections at the first stage of the electron capture process. It has been shown that a temporary resonance of MNI at the energy approximately 0.5 eV corresponds to a shape resonance with lifetime 1-2.10(-13) s in the f-partial wave (l = 3) of the incident electron. The next resonant state of MNI at the energy approximately 1.7 eV has been associated with the electron excited Feshbach resonance (whose parent state is a triplet npi* transition). In all cases the initial electron state of the MNI relaxes into the ground state by means of a radiationless transition, and the final state of the MNI is a nuclear excited resonance with a lifetime measurable on the mass spectrometry timescale. Copyright 1999 John Wiley & Sons, Ltd.     

Temperature effect on the viscoelastic properties of solutions of cylindrical mixed micelles of zwitterionic and anionic surfactants

The viscoelastic properties of semidilute mixed aqueous solutions of oleyl amidopropylbetaine and sodium dodecylbenzene sulfonate are studied in the temperature range of 20–40°C. It is shown that, at 20°C, the solution viscosity can be as high as 390 (Pa s), which is related to the formation of a network of entanglements of long cylindrical micelles of surfactants. It is revealed that, upon heating, the viscosity and relaxation time of the system decrease, while the contour length of cylindrical micelles decreases consider-ably. It is shown that this susceptibility of viscoelastic surfactant solutions to temperature is due to the low energy of break, which is much lower than the energy of covalent bonds.     

Canonical and Boundary Representations on the Lobachevsky Plane

Canonical representations on Hermitian symmetric spaces G/K were introduced by Vershik, Gelfand and Graev and Berezin. They are unitary. We study canonical representations in a wider sense. In this paper we restrict ourselves to a crucial example – the Lobachevsky plane: G=SU(1,1), K=U(1). Canonical representations are labelled by the complex parameter (Vershik–Gelfand–Graev's representations correspond to –3/2<<0). We decompose the canonical representations into irreducible components. The decomposition includes boundary representations generated by the canonical representations. So we study these boundary representations themselves. The decomposition of boundary representations is closely connected with the meromorphic structure of Poisson and Fourier transforms associated with canonical representations. In particular, second-order poles give second-order Jordan blocks. Finally, we give a full decomposition of the Berezin transform using generalized powers (Pochhammer symbols) instead of usual powers of .