Mössbauer study of Martian regolith analogues

Terrestrial basalt rocks considered to be a good analogues of the Martian regolith were studied by using the Mössbauer spectroscopy and X-ray diffraction. The weathering of basalts was followed by the changes of the Fe²⁺/Fe³⁺ ratio. The basalt rock undergoes alteration from primary mineral composition (olivine+pyroxene+plagioclase) through smectite to kaolinite clay with oxides and hydroxides with the increase of the Fe²⁺/Fe³⁺ ratio.     

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.     

Spectral boundary controllability of networks of strings

In this Note we give a necessary and sufficient condition for the spectral controllability from one simple node of a general network of strings that undergoes transversal vibrations in a sufficiently large time. This condition asserts that no eigenfunction vanishes identically on the string that contains the controlled node. The proof combines the Beurling–Malliavin's theorem and an asymptotic formula for the eigenvalues of the network. The optimal control time may be characterized as twice the sum of the lengths of all the strings of the network. To cite this article: R. Dáger, E. Zuazua, C. R. Acad. Sci. Paris, Ser. I 334 (2002) 545–550.     

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)     

Improving the rate of convergence of Newton methods on Banach spaces with a convergence structure and applications

In this note, we use inexact Newton-like methods to find solutions of nonlinear operator equations on Banach spaces with a convergence structure. Our technique involves the introduction of a generalized norm as an operator from a linear space into a partially ordered Banach space. In this way, the metric properties of the examined problem can be analyzed more precisely. Moreover, this approach allows us to derive from the same theorem, on the one hand, semilocal results of Kantorovich-type, and on the other hand, global results based on monotonicity considerations. By imposing very general Lipschitz-like conditions on the operators involved, on the one hand, we cover a wider range of problems, and on the other hand, by choosing our operators appropriately, we can find sharper error bounds on the distances involved than before. Furthermore, we show that special cases of our results reduce to the corresponding ones already in the literature. Finally, several examples are being provided where our results compare favorably with earlier ones.