On the excitation of a closely spaced array by a line source

An infinite row of periodically spaced, identical rigid circularcylinders is excited by an acoustic line source which is parallelto the generators of the cylinders. A method for calculatingthe scattered field accurately and efficiently is presented.When the cylinders are sufficiently close together, Rayleigh–Blochsurface waves that propagate energy to infinity along the arrayare excited. An expression is derived which enables the amplitudesof these surface waves to be computed without requiring thesolution to the full scattering problem.     

Self-broadening in the millimeter-wave spectrum of ozone

Self broadened widths of seven lines of ozone between 75 and 120 GHz have been measured at room temperature. The variation with temperature of the self-broadening parameter for three of these lines has been studied in the range 245–292°K.     

Material tensor parameters of LiNbO3 relevant for electro- and elasto-optics

The complete set of self-consistent parameters of nominally undoped LiNbO₃ crystals of congruent composition that describe the electro-optic, piezoelectric, elasto-optic, elastic, and dielectric response has been determined by numerically evaluating available measurements. The parameters were determined at room temperature and consist of the low-frequency clamped dielectric constants ε^S _ij, elastic stiffness constants at constant electric field C^E _ijkl, piezoelectric stress coefficients e_ijk, elasto-optic constants at constant electric field p^E _ijkl, and clamped electro-optic coefficients r^S _ijk. It is shown that the complete set is required for calculating the effective electro-optic coefficients and dielectric constants in photorefractive applications of LiNbO₃. Received: 4 January 2002 / Revised version: 1 February 2002 / Published online: 14 March 2002     

Conditional Time Before Ruin of an Insurance Company

The statistical characteristics of conditional time before ruin of an insurance company, including the distribution function of conditional time and its moments are examined.     

A Symmetric-Impulse Approximation Applied to the Faddeev Theory on the Charge Transfer Amplitude

Off-the-shell anomalous factors of the two-body Coulomb transition matrices appear in the integral form of the Faddeev second-order nuclear-electronic amplitude, for proton-hydrogen charge transfer scattering in a typical nlm → n′l′m′ transition. A symmetric-impulse approximation (SIA) is applied to eliminate these factors and an induction method is proposed to analytically calculate the remaining integrals. The nuclear-electronic amplitude is derived for the general case, and for totally symmetric collisions, in terms of generalized hypergeometric functions of two variables, F ₄, and of one variable, ₃ F ₂, respectively. The angular distribution of the second-order nuclear-electronic charge transfer amplitude shows the Thomas mechanism as a peak or a hump for symmetric and asymmetric collisions. There also exists a peak in the forward angular distribution of the second-order nuclear-electronic amplitude, which partly cancels the kinematic peak in the angular distribution of the charge transfer differential cross sections.     

Phasing of three vircators simulated in terms of coupled van der Pol oscillators

Phase synchronization in a system of three virtual-cathode microwave oscillators (vircators) simulated by coupled van der Pol oscillators is studied. The phasing dynamics of the vircators is visualized with the phase portraits of the system in the triangular coordinates. Different phasing conditions are found.     

Fundamental aspects of initiated oxidation of tridecane and polyethylene in solutions

Specific features of the initiated oxidation of polyethylene and its low-molecular-weight analogue tridecane, associated with the occurrence of the process in the short-chain mode, were studied.     

Cosmic γ-ray bursts: Observations and modeling

It is now commonly accepted that cosmic γ-ray bursts (GRBs) are of cosmological origin. This conclusion is based on the statistical analysis of GRBs and the measurements of line redshifts in GRB optical afterglows, i.e., in the so-called long GRBs. In this review, the models of radiation and models of GRB sources are considered. In most of these models, if not in all of them, the isotropic radiation cannot provide the energy release necessary for the appearance of a cosmological GRB. No correlation is noted between the redshift, the GRB-spectrum shape, and the total detected energy. The comparison between data obtained in the Soviet experiment KONUS and the American experiment BATSE shows that they substantially differ in statistical properties and the detection of hard x-ray lines. The investigation of hard gamma (0.1–10 GeV) afterglows, the measurement of prompt optical spectra during the GRB detection, and the further investigation of hard x-ray lines is of obvious importance for gaining insight into the GRB origin. Observations of two bright optical GRB afterglows point to the fact that an initially bright optical flare is directly related to the GRB itself, and the subsequent weak and much more continuous optical radiation is of a different nature. The results of observations of optical GRB afterglows are discussed. They point to the fact that the GRBs originate in distant galaxies with a high matter density, where intense star formation takes place. The interaction of the cosmological GRB radiation with a dense surrounding molecular cloud results in the appearance of long-duration (up to 10 years) weak optical afterglows associated with the heating and reradiation of gas. Results of 2D numerical simulation of the heating and reradiation of gas in various variants of the relative disposition of GRB and molecular clouds are presented. In conclusion, the possible relation between the so-called short GRBs and recurrent sources of soft γ rays in our Galaxy, the so-called “soft gamma repeaters,” is discussed.