Investigation of the layer-by-layer transition near the bulk smectic-A-crystal-B transition in thick free-standing films

Highly sensitive optical reflectivity measurements are used to investigate the layer-by-layer transition in extremely thin and thick N-(4-n-hexyloxybenzylidene)-4-n-hexylaniline (6O.6) films. The simple power-law form, N=N ₀ t ^−1/3, for the penetration of the crystal-B order is found to describe the transitions only near the surface. A deviation from the power law is observed for the interior layers. Pis’ma Zh. éksp. Teor. Fiz. 63, No. 4, 266–269 (25 February 1996) Published in English in the original Russian journal. Edited by Steve Torstveit.     

Enlargement of the Wiener filtration by an absolutely continuous random variable via Malliavin’s calculus

Summary. The analytic treatment of problems related to the asymptotic behaviour of random dynamical systems generated by stochastic differential equations suffers from the presence of non-adapted random invariant measures. Semimartingale theory becomes accessible if the underlying Wiener filtration is enlarged by the information carried by the orthogonal projectors on the Oseledets spaces of the (linearized) system. We study the corresponding problem of preservation of the semimartingale property and the validity of a priori inequalities between the norms of stochastic integrals in the enlarged filtration and norms of their quadratic variations in case the random element F enlarging the filtration is real valued and possesses an absolutely continuous law. Applying the tools of Malliavin’s calculus, we give smoothness conditions on F under which the semimartingale property is preserved and a priori martingale inequalities are valid. Received: 12 April 1995 / In revised form: 7 March 1996     

Searching for losers

We investigate the following process: N people select b losers by flipping coins. The 0-party continues until there are less than b losers; then the 1-party has to find the other losers by the same process. The average time for this process is about long₂ N, but this result requires rather advanced methods. Furthermore, the average size of a binary tree associated to this process and the average number of coin flippings are computed. The method used in this article can be used to give asympotical solutions of a special type of bivariate recurrences. © 1993 John Wiley & Sons, Inc.     

Electromagnetic field singularities

An integral transform based method is given for determining information about the locating and properties of singularities of electromagnetic fields associated with axially symmetric radiating sources.     

Antiferromagnetic and superconducting states in the three-band two-dimensional repulsive Hubbard model

The three-band two-dimensional repulsive Hubbard model in the formalism of the temperature Green function is investigated. The applicability of the weak coupling approach at the values of the dimensionless coupling constant U/t≈10–11 is justified. The normal state, the antiferromagnetic state with Neel magnetic ordering on the “copper” sublattice, and the superconducting state with nontrivial Cooper pairing in channels with odd angular momenta are studied. The possibility of other magnetic states in the model is discussed. Bibliography: 20 titles. Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 209, 1994, pp. 194–228. Translated by K. Malyshev.     

Normalization and averaging on compact lie groups in nonlinear mechanics

We consider the method of normal forms, the Bogolyubov averaging method, and the method of asymptotic decomposition proposed by Yu. A. Mitropol’skii and the author of this paper. Under certain assumptions about group-theoretic properties of a system of zero approximation, the results obtained by the method of asymptotic decomposition coincide with the results obtained by the method of normal forms or the Bogolyubov averaging method. We develop a new algorithm of asymptotic decomposition by a part of the variables and its partial case — the algorithm of averaging on a compact Lie group. For the first time, it became possible to consider asymptotic expansions of solutions of differential equations on noncommutative compact groups.     

Temperature and field dependences of photo-induced changes in the magnetization in yttrium iron garnet

The changes in the magnetization of yttrium iron garnet (YIG) when irradiated by a pulsed neodymium laser beam with wavelength λ=1.06 μm are investigated. Measurements are performed in the temperature range from 100 K to 600 K in various external magnetic fields. YIG single crystals grown along the crystallographic (100), (110), and (111) directions are chosen so that the external anisotropy of the indicated processes can be determined. Characteristic temperature intervals dominated by different mechanisms of variation of the magnetization under the influence of a laser pulse are discussed. Fiz. Tverd. Tela (St. Petersburg) 39, 1263–1266 (July 1997)     

Temperature and frequency dependence of the spin-lattice relaxation times of E′1 centers in neutron-irradiated quartz glass

Results are reported for measurements of the spin-lattice relaxation times of E′₁ centers in quartz glass, produced by neutron irradiation, with the measurements made at two frequencies 9.25 and 24.0 GHz over a wide temperature interval 1.5–300 K. The experimental data are interpreted on the basis of interaction mechanisms of the spins with two-level systems with excitation energies ∼6, ∼26, and ∼420 cm⁻¹. A small modification of the existing theory allows us to explain a number of features of the observed temperature and frequency dependence of the relaxation rate. The results are compared with the data available in the literature on spin-lattice relaxation of irradiation centers in crystalline quartz and quartz glass. Fiz. Tverd. Tela (St. Petersburg) 39, 1335–1337 (August 1997)