Paraelectric resonance of centers with icosahedral symmetry

The paraelectric resonance spectrum of non-central impurity ions situated in crystal fields of icosahedral symmetry is predicted. A multiwell potential is considered that corresponds to the displacement of the ions from the center of symmetry toward the vertices of the icosahedron, the faces of a dodecahedron, and the pentagonal faces of a fullerene molecule. The effective Hamiltonian of endohedral complexes in external electric fields with arbitrary orientation is obtained, its eigenvalues are found, and the line intensities of different transitions between the tunnelling levels are calculated. Fiz. Tverd. Tela (St. Petersburg) 39, 1693–1698 (September 1997)     

Mechanism of detachment of particles from the surface of high-temperature superconducting targets absorbing laser pulses

A cluster mechanism is considered for the detachment of particles when the surface of a high-temperature superconducting target absorbs laser pulses. By proposing a fractal nature for the surface, one can model it as an assembly of a large number of nonlinear oscillators (clusters). Utilizing the method of sudden perturbations, a calculation was made of the probability of dissociation of these oscillators, i.e., of the detachment of clusters from the surface. The calculated probability decreases rapidly as the power density of the laser radiation is reduced to some limiting value. This is in agreement with experiments. State Institute of Sensory Microelectronics. Siberian Branch of the Russian Academy of Sciences. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 6, pp. 73–77, June, 1997.     

Flow in a waterfall with large Froude number

An approximate method is developed to solve the full nonlinear equations governing two-dimensional irrotational flow in a free waterfall, falling under the influence of gravity, at high Froude number based on conditions far upstream. Schwarz—Christoffel transformation is used to map the region, in the complex potential-plane, onto the upper half-plane. The Hilbert transformation as well as the perturbation technique, for large Froude number, are used as a basis for the approximate solution of the problem. A complete solution, up to second-order approximation, for the downstream free-surfaces profiles, for different Froude number, is discussed and illustrated. The obtained approximate solutions are compared with those of other authors. Favourable agreement with other results suggests that this method is effective in dealing with flow problems strongly influenced by gravity and high Froude number. The results obtained by this method are sufficiently accurate for practical purposes.     

Mutual coupling of elements in finite microstrip antennas

The mutual coupling of the radiating elements in microstrip antennas is studied using a rigorous electrodynamic approach in which the field singularities at the radiator edges are taken into account with analytic accuracy. A spectral method is employed in combination with a method of semi-inversion by extraction of the Green-function singularity. The degree of interaction of the elements of microstrip structures at the fundamental and higher current harmonicsis determined, and the applicability of various approximations is assessed.Radio-Astronomy Institute, Academy of Sciences of Ukraine. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 35, No. 8, pp. 688–701, August, 1992.     

Minimax estimators of spectral intensities of acoustic sources

We investigate some issues of minimax estimation of spectral intensity of acoustic sources in cases when the noise and the spectral amplitudes satisfy quadratic constraints. Recursive minimax filters are obtained.Translated from Vychislitel'naya i Prikladnaya Matematika, No. 58, pp. 116–119, 1986.     

Cylindrical solitons in a Gödel Universe and their stability

Exact cylindrically symmetric solutions are obtained for a class of interacting scalar and vector fields in a rotating Godel Universe. We select those with the properties of solitons with smooth decrease of the fields to asymptotics and those with sharp boundaries (droplets). It is shown that only some of the droplets are stable with respect to perturbations that preserve cylindrical symmetry.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 5, pp. 24–27, May, 1991.     

Research problem

This section appears from time to time. Contributions are invited, and should be submitted to R C. Thompson, Mathematics Department. University of California, Santa Barbara, CA93106-3080, USA.     

Direction of magnetization and domain wall mobility in (Dy,Y)Fe2

Magnetization measurements in the (Dy _x Y_1−x )Fe₂ intermetallic compounds show evidence of blocking of domain wall motion. This effect is a function of concentrationx. The direction of magnetization is also dependent on the Dy concentration. We have used the Mossbauer spectroscopy of⁵⁷Fe to verify the direction of magnetization in the series as a function ofx and temperature. The results show that this change in easy direction occurs at higher temperatures than those where the blocking is detected through DC magnetization measurements. supported by RHAE/SCT.     

Excitation of middle-IR range hollow metallic waveguides

The results of the efficiency of low-mode excitation of a parallel-plate hollow metallic waveguides (HMW) as a function of beam and waveguide parameters are represented. Coupling of two waveguides is also discussed.