Localization for a Matrix-valued Anderson Model

We study localization properties for a class of one-dimensional, matrix-valued, continuous, random Schrödinger operators, acting on $L^2(\mathbb R)\otimes \mathbb C^NWe study localization properties for a class of one-dimensional, matrix-valued, continuous, random Schr?dinger operators, acting on , for arbitrary N ≥ 1. We prove that, under suitable assumptions on the Fürstenberg group of these operators, valid on an interval , they exhibit localization properties on I, both in the spectral and dynamical sense. After looking at the regularity properties of the Lyapunov exponents and of the integrated density of states, we prove a Wegner estimate and apply a multiscale analysis scheme to prove localization for these operators. We also study an example in this class of operators, for which we can prove the required assumptions on the Fürstenberg group. This group being the one generated by the transfer matrices, we can use, to prove these assumptions, an algebraic result on generating dense Lie subgroups in semisimple real connected Lie groups, due to Breuillard and Gelander. The algebraic methods used here allow us to handle with singular distributions of the random parameters.      

Microchemical surface analysis of two Numidian coins

This work is a contribution to the microchemical surface analysis of two Numidian coins. Numidia was an ancient kingdom of northern Algeria during 2nd and 1st century BC. Investigations were performed with scanning electron microscopy (SEM) coupled with energy dispersive spectrometry (EDS), energy dispersive X-ray fluorescence spectrometry (EDXRF) and X-ray diffraction (XRD). The identification of the coins was done thanks to the name initials and effigy of King Massinissa. SEM observations of coins showed heterogeneous surfaces. SEM and EDXRF analyses showed an alloy structure with copper (65%), antimony (19%) and lead (16%). The XRD identified a metal structure and corrosion products which were on the coin surfaces: Litharge (PbO), Hydrocerussite (Pb₃(CO₃)₂(OH)₂), Bindheimite (Pb₂Sb₂O₇) and Bystromite (MgSb₂O₆).     

Supercuspidal Gelfand pairs

If G is a totally disconnected group and H is a closed subgroup then, according to the Gelfand-Kazhdan Lemma, if the double coset space H?G/H is preserved by an antiautomorphism of G of order two then (G,H) must be a Gelfand pair in the sense that Hom_H(π,1) has dimension at most one for each irreducible, admissible representation π of G. Under certain rather general restrictions, we show that if the symmetry property holds only for almost all double cosets, then (G,H) is a supercuspidal Gelfand pair in the sense that for all irreducible, supercuspidal representations π of G. There exist examples of supercuspidal Gelfand pairs which are not Gelfand pairs.     

Linear stability of scroll waves

A full linear stability of a straight scroll wave in an excitable medium is presented. The five eigenmode branches which correspond to deformation in the third dimension of the five main modes of two-dimensional (2D) spiral dynamics are found to play a dominant role. For untwisted scroll waves, modulations in the third dimension have stabilizing or destabilizing effects on the different modes depending on the parameter regimes, in partial agreement with previous predictions. The influence of twist on the different branches is investigated. In particular, the sproing instability is seen to arise from the twist-induced deformation of the translation branches above a threshold twist.     

Direct observation of macropore self-formation in hierarchically structured metal oxides

The current work presents an unprecedented direct observation of macropore formation in the spontaneous self-assembly process to obtain hierarchical meso/macroporous metal oxides made possible with the help of an unusual titanium alkoxide.     

Selective ion exchange separation of uranium from concomitant impurities in uranium materials and subsequent determination of the impurities by ICP-OES

An ion exchange method has been developed for the separation of uranium from trace level metallic impurities prior to their determination by inductively coupled plasma optical emission spectrometry (ICP-OES) in uranium materials. Selective separation of uranium from trace level metallic impurities consisting Cr, Co, Cu, Fe, Mn, Cd, Gd, Dy, Ni, and Ca was achieved on anion exchange resin Dowex 1 × 8 in sulphate medium. The resin (100–200 mesh, in chloride form) was packed in a small Teflon column (7.8 cm × 0.8 cm I.D.) and brought into sulphate form by passing 0.2 N ammonium sulphate solution. Optimum experimental conditions including pH and concentration of sulphate in the liquid phase were investigated for the effective uptake of uranium by the column. Uranium was selectively retained on the column as anionic complex with sulphate, while impurities were passed through the column. Post column solution was collected and analyzed by ICP-OES for the determination of metallic impurities. Up to 2,500 μg/mL of uranium was retained with >99% efficiency after passing 25 mL sample through the column at pH 3. Percentage recoveries obtained for most of the metallic impurities were >95% with relative standard deviations <5%. The method established was applied for the determination of gadolinium in urania–gadolinia (UO₂–Gd₂O₃) ceramic nuclear fuel and excellent results were achieved. Solvent extraction method using tributylphosphate (TBP) as extractant was also applied for the separation of uranium in urania–gadolinia nuclear fuel samples prior to the determination of gadolinium by ICP-OES. The results obtained with the present method were found very comparable with those of the solvent extraction method.     

Determination of nanolayer thickness and effective thermal conductivity of nanofluids

Nanofluids having high thermal conductivity enhancement relative to conventional pure fluids are fluids engineered by suspending solid nanoparticles into base fluids. In the present study, calculating the Van der Waals interaction energy between a nanoparticle and an ordered liquid nanolayer around it, the nanolayer thickness was determined, the average velocity of the Brownian motion of nanoparticles in a fluid was estimated, and by taking into account both the aggregation of nanoparticles and the presence of a nanolayer a new thermal conductivity model for nanofluids was proposed. It has been shown that the nanolayer thickness in nanofluids is independent on the radius of nanoparticles when the radius of the nanoparticles is much greater than the nanolayer thickness and determines by the specific interaction of the given liquid and solid nanoparticle through the Hamaker constant, the surface tension and the wetting angle. It was proved that the frequency of heat exchange by fluid molecules is two orders of magnitude higher than the frequency of heat transfer by nanoparticles, so that the contribution due to the Brownian motion of nanoparticles in the thermal conductivity of nanofluids can be neglected. The predictions of the proposed model of thermal conductivity were compared with the experimental data and a good correlation was achieved.     

Application of Liquid-Liquid Microextraction-High-Performance Thin-Layer Chromatography for Preconcentration and Determination of Phenolic Compounds in Aqueous Samples

JPC – Journal of Planar Chromatography – Modern TLC - A novel liquid-phase microextraction method coupled with high-performance thin-layer chromatography (HPTLC) for preconcentration,...