Global heat kernel bounds via desingularizing weights

We obtain global heat kernel bounds for semigroups which need not be ultracontractive by transferring them to appropriately chosen weighted spaces where they become ultracontractive. Our construction depends upon two assumptions: the classical Sobolev imbedding and a “desingularizing” (L¹,L¹) bound on the weighted semigroup.     

Analysis of transient wave scattering from an inclusion with an unilateral smoothly contact interface by BEM

Summary A 2D time-domain Boundary Element Method (BEM) is applied to solve the problem of transient scattering of plane waves by an inclusion with a unilateral smooth contact interface. The incident wave is assumed strong enough so that localized separations take place along the interface. The present problem is indeed a nonlinear boundary value problem since the mixed boundary conditions involve unknown intervals (separation and contact regions). In order to determine the unknown intervals, an iterative technique is developed. As an example, we consider the scattering of plane waves by the cross section of a circular cylinder embedded in an infinite solid. Numerical results for the near field solutions are presented. The distortion of the response waves and the variation of the interface states are discussed. The financial support by the China National Natural Science Foundation under Grant No. 19872001 and No. 59878004 is gratefully acknowledged. The second author is also grateful to the support of the National Science Fund for Distinguished Young Scholars under Grant No. 10025211.     

Formation of nanosystems under near-equilibrium copper condensation in an ultrapure inert medium

Mechanisms of the self-organization of nanosystems at the condensation of the extremely weak steady flows of copper vapors obtained in magnetron sputtering in an ultrapure argon are studied. It is shown that the free-energy minimization near equilibrium condensation creates prerequisites for the self-organization of statistically homogeneous layers of nanoclusters and determines the transition to the formation of nanosystems in the form of fractal networks. Original Russian Text ? V.I. Perekrestov, A.S. Kornyushchenko, Yu.A. Kosminskaya, 2007, published in Pis’ma v Zhurnal éksperimental’noĭ i Teoreticheskoĭ Fiziki, 2007, Vol. 86, No. 12, pp. 879–883.     

Stark structure of the Yb3+ ion levels in (YbxY1?x)2Ti2O7 and the crystal field in rare-earth titanates with a pyrochlore structure

The absorption spectra of Yb₂Ti₂O₇ single crystals and the luminescence and luminescence excitation spectra of Y₂Ti₂O₇: Yb (1%) polycrystals were studied in the temperature range 4.2–300 K. The spectra were analyzed in terms of the crystal-field theory and the exchange-charge model. Based on the set of crystal-field parameters found for Yb₂Ti₂O₇, analogous sets of parameters were determined for other rare-earth titanates and proved to be in reasonable agreement with all available experimental data. __________ Translated from Fizika Tverdogo Tela, Vol. 47, No. 8, 2005, pp. 1376–1380. Original Russian Text Copyright ? 2005 by Klimin, Popova, Chukalina, Malkin, Zakirov, Antic-Fidancev, Goldner, Aschehoug, Dhalenne.     

Separation of phenols, alcohols, and alkylbenzenes by gas chromatography on adsorption layers of copper and nickel alizarinates

The separation of mixtures of phenols, alcohols, and alkylbenzenes by gas chromatography on adsorption layers of nickel and copper alizarinates was investigated. The thermodynamic parameters were calculated. It was shown that the sorbates differ in strength of interaction with the copper and nickel ions in their alizarin complexes.     

Technology for producing adsorbents from petroleum residues

Advantage of use residue from thermal cracking and products of its condensation as components of the mixture for manufacturing mechanically rigid (93%) granulated and ground carbon sorbents with extended volume of micropores (up to 0.27 cm³/cm³), showing enhanced sorption activity (E is up to 25.6 kJ mol^?1) and high ability of separation various gas mixtures is demonstrated. As a carrier for medicine preparations these adsorbents show higher performance as compared with industrial samples. Solutions of the cracking residue can be used for impregnation of worked out zeolites for petroleum technology and for production of organomineral adsorbents with high adsorption capacity on extraction mercury from sewages.     

Evaluation of the capillary pressure in a liquid interlayer between the particles of a dispersed phase

The capillary pressure in a liquid interlayer between two spherical particles is calculated as a function of their sizes and the wetting properties of the liquid.