Water wave radiation by a sphere submerged in water with an ice-cover

Using the multipoles method, we formulate the problems of radiation (both heave and sway) of water waves by a submerged sphere in deep as well as in uniform finite depth water with an ice-cover, with the ice-cover being modelled as an elastic plate of very small thickness. In each case this leads to an infinite system of linear equations which are solved numerically by standard techniques. The added-mass and damping coefficients for a heaving and swaying sphere are obtained and depicted graphically against the wave number for various values of the radius of the submerged sphere and flexural rigidity of the ice-cover to show the effect of the presence of ice-cover on these quantities. When the flexural rigidity is taken to be zero, the numerical results for the added-mass and damping coefficient for water with a free surface are recovered.     

Numerical method and models for anti-plane strain of a system with a thin elastic wedge

The paper presents a general method to find asymptotics for a (multi-)wedge system containing a thin wedge. It employs separation of the symmetric and anti-symmetric parts of the boundary displacements and tractions of the wedge. The method is applicable when the angle of the thin wedge turns to zero. A physical interpretation of the derived equations is obtained by using power expansions of non-polynomial functions, which appear after the Mellin transform. We establish that the first term in the expansion of the symmetric part corresponds to shear, while the first term of the anti-symmetric part describes deflection of the wedge axis. Numerical experiments, performed by using a code developed on the basis of the theory, show that using only the first terms of the expansions insignificantly influence accuracy: the approximate results coincide with the exact values of roots to the third significant digit even for the wedge angle of 30°.     

A study of solid-state rhodium(III) sulfates

Solid-state rhodium(III) sulfates and their aqueous solutions were examined by IR and electronic absorption spectroscopy, thermogravimetry, X-ray powder diffraction analysis, and ¹⁰³Rh and ¹⁷O NMR spectroscopy. A study of the spontaneous aquation of freshly prepared solutions showed that this process results in an equilibrium between the subsystems of monomeric and oligomeric complexes. It was found that solid-state rhodium(III) sulfates vary in phase composition, basically consisting of dimeric and trimeric complexes.     

Synthesis and structure of unsymmetrical cross-conjugated dienones with thienyl substituents

By condensation of thiophenecarbaldehyde and m-nitrobenzaldehyde with furyl-, thienylmethylenecyclohexanones in basic medium 2-(het)arylmethylene-6-thienylmethylenecyclohexanones were prepared. Under the conditions of acid catalysis analogously built dienones were synthesized containing 5-nitrothiophene fragment. Based on the data of IR and ¹H NMR spectroscopy their E,E-configuration was established.     

Absorption of cnoidal electromagnetic waves by superlattice electrons in the process of impurity ionization

Absorption of cnoidal electromagnetic waves, which are the most general periodic solution to the sine-Gordon equation, by electrons of a one-dimensional quantum semiconductor superlattice in the process of impurity ionization is studied in terms of the semiclassical approximation. The dependence of the absorption coefficient on the electric field of an electromagnetic wave is found to be nonmonotone with a pronounced peak.     

Sound scattering by a body in a planar layered waveguide

In the framework of the theory of integral equations, the problem of sound diffraction by pressure-release and acoustically stiff inhomogeneities of an oceanic waveguide is considered. The iteration method is used to obtain recurrent relations for the surface currents. The relations describe the diffraction process as a sequence of interactions between the body and the waveguide boundaries (multiple reflections). The validity condition for the zero-order approximation, which ignores multiple reflections, is formulated and physically justified.     

Self-broadening of space-time spectra of few-cycle pulses in dielectric media

The nonparaxial dynamics of spectra of pulses comprising a few cycles of a light field is analyzed in transparent nonlinear media with dispersion. It is shown that the inhomogeneous self-broadening of the time spectrum of a pulse proceeds more effectively into the blue region at all spatial frequencies. A decrease in the energy in the central part of the time spectrum is realized mainly at high spatial frequencies.     

Luminescence of self-trapped excitons in calcium fluoride under pulsed electron irradiation

Time-resolved pulsed spectroscopy was used to measure the luminescence spectra of calcium fluoride. Characteristic features of the luminescence of self-trapped excitons are discussed. It is shown that various configurations of self-trapped excitons incorporating hole nuclei of a more complex structure, may be formed in CaF₂ crystals. Fiz. Tverd. Tela (St. Petersburg) 40, 1226–1227 (July 1998)     

Estimates of the rate of convergence of a dynamic reconstruction algorithm under incomplete information about the phase state

In this paper, we study a dynamic reconstruction algorithm which reconstructs the unknown unbounded input and all unobservable phase coordinates from the results of measurements of part of the coordinates. An upper and a lower bound for the accuracy of the reconstruction is obtained. We determine the class of inputs for which the upper bound is uniform. We give a condition for optimally matching the algorithm parameters, ensuring the highest order of the upper bound and equating the orders of the upper and lower bounds. Thus, we establish the sharpness of the upper bound.     

The contribution of the (t(τ)+N) component to the α-particle wave function from data on the reactions p(α,pp)t and p(α,pn)τ at incident α-particle momentum 5 GeV/c

The 2-meter liquid-hydrogen bubble chamber is exposed to a separated beam of α particles from the ITEP synchrotron. The momentum of the incident ⁴He nuclei, averaged over the fiducial volume of the chamber, is 5 GeV/c (the kinetic energy of initial protons in the nucleus rest frame is T _p =620 MeV). The spectral functions of decays α→tp and α→τn) are extracted in the 4π geometry (the latter is extracted for the first time) from the exclusive reactions αp→tpp and αp→τpn in the spectator momentum region 0<q<0.3 GeV/c. The pole dominance criteria are carefully checked. Extrapolation of the nuclear vertex function to the pole gives a lower bound on the nuclear vertex constant. Our experimental data are compared with the results of other studies and with theoretical calculations. Pis’ma Zh. éksp. Teor. Fiz. 66, No. 2, 69–74 (25 July 1997) Published in English in the original Russian journal. Edited by Steve Torstveit.