Solution of the 2D ising model on a triangular lattice by the method of auxiliaryq-deformed Grassmann fields

A representation in the form of a functional integral is obtained for the partition function of the inhomogeneous 2D Ising model on a triangular lattice where the coupling parameters are arbitrary functions of coordinates. The method for transforming the partition function into an integral uses an auxiliary six-component Grassmann field in which the Grassmann fields corresponding to one of the components commute with the others. Thus, one pair of components realizes a representation of the q-deformed group SL_q(2, R) with q=–1 and the other two pairs correspond to the usual Grassmann spinors (q=1). An explicit expression in terms of the modified Pfaffian is found for the Gaussian integral over these fields and its relation to the ordinary Grassmann functional integral is established.Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 109, No. 3, pp. 441–463, December, 1996.     

THE USE OF THERMOELASTICITY TO EVALUATE STRESS REDISTRIBUTION AND NOTCH SENSITIVITY IN CERAMIC MATRIX COMPOSITES

Thermoelastic stress analysis was used to document the effect of composite damage on the stress distribution in three ceramic matrix composites. Composite damage was found to significantly alter the thermoelastic response of each material, with the greatest effect noted in SiC/CAS. Thermoelastic imaging of these materials affords a more complete picture of how the various damage mechanisms affect the stress distribution. In particular, a stress concentration factor computed from thermoelastic images, serves as an indicator of stress redistribution. The stress concentration factors were computed by comparing notch root to far field temperatures, and monitored after the introduction of various amounts of damage. In each material, the stress concentration factor diminished as the damaging load approached the ultimate stress. Reduction in the stress concentration is associated with local changes in modulus, mechanistically arising from combinations of fiber, matrix and interface fracture. Stress redistribution occurs as a consequence of modulus changes, leading to lower notch sensitivity in each of the tested composites.     

The effect of complexing processes on energy transfer Tl+→Gd3+ and Tl+→Tb3+ in glass

T. Shevchenko Kiev University, 252022 Kiev, Pr. Akad. Glushakova, 6, Ukraine. Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 62, No. 3, pp. 192–196, May–June, 1995.     

Subthreshold ϕ-meson production and medium effects in proton-nucleus reactions

Within the spectral function approach, we study the direct production and decay via the dikaon (dimuon) channel of ϕ mesons in the interactions of 2.4-and 2.7-GeV protons with light and medium target nuclei. It is shown that the K ⁺ K ⁻ (μ⁺ μ⁻) invariant-mass distribution consists of the two components, which correspond to the ϕ decay “outside” and “inside” the target nucleus. The first (narrow) component has the free ϕ width, while the second (broad) component is distorted by the nuclear matter owing to resonance-nucleon scattering and a possible in-medium modification of the kaons and ρ meson at finite baryon density. The relative strength of the “inside” and “outside” components is analyzed in different scenarios for the ϕ width and momentum cut. It is demonstrated that the width of the resulting dimuon invariant-mass distribution on medium nuclei is larger than the free ϕ width by a factor of about 2 if the total ϕ in-medium width is used and the respective cutoff for the ϕ three-momentum is applied, whereas the resulting dikaon invariant-mass distribution has an insignificant sensitivity to the ϕ in-medium properties owing to the strong absorption of the K ⁻ in the surrounding nuclear matter. On the other hand, because of the distortion of the K ⁺ and K ⁻ on their way out of the target nucleus mainly due to the hadronic kaon potentials, the latter distribution is broadened and shifted to higher invariant masses, which means that the measurement of such broadening would give additional evidence for the modification of the kaon and antikaon properties in the nuclear medium. The text was submitted by the author in English.     

Nonlinear-optical and micro-Raman diagnostics of thin films and nanostructures of ABO3 ferroelectrics

Ferroelectric composite two-dimensional ferroelectric/aluminum oxide nanostructures were studied. A porous aluminum oxide matrix was used as a template into which a ferroelectric precursor was introduced, followed by annealing. The prepared nanostructures were studied using optical second harmonic generation and micro-Raman scattering.     

Metallic films forming on the surface of alkali-halide crystals during thermal diffusion of intracrystalline immpurities

It was detected for the first time that films consisting of a transition-metal-based structure form (via thermal diffusion of intracrystalline impurities) on the surface of alkali-halide (LiF, NaF) crystals activated by transition metals Co, Ni, or Mn. The thickness, density, and composition of the films are shown to be different, depending on the heat treatment conditions. The crystals were annealed at temperatures varying from 473 to 1073 K in vacuum and air. The surface structures forming upon annealing in vacuum exhibit magnetic properties. The films were studied by optical, x-ray fluorescence, and electron spectroscopy to reveal the mechanisms of transition-metal film formation during thermal annealing.     

Effect of oxygen exposure on the magnetic properties of ultrathin Co/Ge(1 1 1) films

Influences of oxygen exposure on the magnetic properties of Co/Ge(1 1 1) ultrathin films have been investigated by surface magneto-optic Kerr effect technique. As the oxygen exposure increases on Co/Ge(1 1 1) films, their magnetic properties could be modified. As an example for 15 ML Co/Ge(1 1 1) films, the coercivity increases from 730 to 920 Oe and the remanence Kerr intensity is reduced for 500 Langmuir (L) of oxygen exposure. Corresponding compositions analyzed by Auger electron spectroscopy measurement shows that the amount of oxygen on the surface layers increases with increasing the oxygen exposure time. Oxygen distributes on the topmost layers of the film. The adsorbed oxygen influences the electronic density of states of Co and results in the changes of the magnetic properties. Besides, the appearance of O/Co/Ge interface could modify the stress anisotropy, and as a result the coercivity of ultrathin Co/Ge(1 1 1) film is enhanced.     

Interpolation of positive operators

We study problems of interpolation of positive linear operators in couples of ordered Banach spaces. From this viewpoint, we study couples of noncommutative spaces L ₁, L _∞ associated with weights and traces on von Neumann algebras.