Fractal dimension,attractors, and the boussinesq approximation in three dimensions

The Boussinesq approximation, where the viscosity depends polynomially on the shear rate, finds more and more frequent use in geological practice. In the paper, this modified Boussinesq approximation is investigated as a dynamical system for which the existence of a global attractor is proved. Finally, a new criterion for estimating the fractal dimension of invariant sets is formulated and its application to the problem under consideration is illustrated.     

Eliashberg theory for disordered superconductors. II. Tunneling into disordered two-dimensional Pb films

A series ofc-axis oriented YBa₂Cu₃O _x -films with different oxygen content were prepared by laser deposition. The oxygen contentx was determined by X-ray diffraction and by resonant Rutherford-back-scattering (RRBS) measurements. Thec-axis length in these films of YBa₂Cu₃O _x is about 0.5% larger compared to bulk values. We describe transport measurements in magnetic fields up to 7 Tesla between room temperature andT _c in samples with an oxygen content between the orthorhombic-to-tetragonal transition (x6.4) and full oxygenation (x7). The ratio /R _H was investigated with respect to the two-dimensional Luttinger liquid theory and the model of the two-dimensional ionic metal. We report on deviations from the expected quadratic temperature behaviour of /R _H , especially in films with high oxygen content.     

Excimer-laser-assisted RF glow-discharge deposition of amorphous and microcrystalline silicon thin films

We combine the deposition of Hydrogenated amorphous Silicon (a-Si:H) by rf glow discharge with XeCl-excimer laser irradiation of the growing surface in order to obtain different kinds of silicon films in the same deposition system. In-situ UV-visible ellipsometry allows us to measure the optical properties of the films as the laser fluence is increased from 0 up to 180 mJ/cm² in separate depositions. For fixed glow-discharge conditions and a substrate temperature of 250° C we observe dramatic changes in the film structure as the laser fluence is increased. With respect to a reference a-Si:H film (no laser irradiation) we observe at low laser fluences (15–60 mJ/cm²) that the film remains amorphous but demonstrates enchanced surface roughness and bulk porosity. At intermediate fluences (80–165 m/Jcm²), we obtain an amorphous film with an enhanced density with respect to the reference film. Finally, at high fluences (165–180 mJ/cm²), we obtain microcrystalline films. The in-situ ellipsometry measurements are complemented by ex-situ measurements of the dark conductivity, X-ray diffraction, and Elastic Recoil Detection Analysis (ERDA). Simulation of the temperature profiles for different film thicknesses and for three laser fluences indicates that crystallization occurs if the surface temperature reaches the melting point of a-Si:H ( 1420 K). The effects of laser treatment on the film properties are discussed by taking into account the photonic and thermal effects of laser irradiation.Presented at LASERION 93, Munich, June 21–23, 1993     

On a characterization of distributive lattices by the betweenness relation

We construct an example of a ternary structure satisfying certain conditions due to M. Kolibiar, which is not a betweenness relation of any lattice. This answers a question posed by J. Hedlíková and T. Katriák.Dedicated to the memory of Alan DayPresented by J. Sichler.Supported by GA SAV Grant 362/92.     

Combination of three analytical techniques for speciation of Al in environmental samples

An analytical scheme is proposed which combines three speciation techniques for determination of particular Al species in soil extracts and percolating waters. A cation-exchange fast protein liquid chromatography — inductively coupled plasma atomic emission spectrometry (FPLC-ICP-AES) procedure, a microcolumn chelating ion-exchange chromatography- atomic absorption spectrometry (MCC-ETAAS) technique and the 8-hydroxyquinoline spectrophotometric method (8HQ-spectrophotometry) were employed. The FPLC-ICP-AES procedure offers determination of Al³⁺ (retention time 4.5 min) and Al(OH)²⁺ species (retention time 4.0 min) which are separated from Al(OH)⁺ ₂ (retention time 1.5min). AlF²⁺ coelutes with Al(OH)²⁺ species, while Al(SO₄)⁺, AlF⁺ ₂ and negatively charged Al organic complexes coelute with Al(OH)⁺ ₂ species. The MCC-ETAAS technique enables determination of the sum of positively charged monomeric aqua- and hydroxy-Al species plus sulphate- and fluoro-Al complexes. Employing the 8HQ-spectrophotometry the sum of positively charged monomeric aqua- and hydroxy-Al species plus sulphato- and most of the labile organic Al species are determined. The sensitivities of these selected techniques were adequate for speciation of Al in the samples analyzed. On the basis of the specific selectivity of a particular technique various groups of Al species may be determined. Thus, the comparison of analytical data from complementary procedures provides more comprehensive information on Al species present in soil extracts and percolating waters.