Mathematical modelling of the oxidation of nickel titanium alloys

A one-dimensional bulk reaction model for the oxidation of nickeltitanium is formulated, with preferential oxidation of titaniumbeing included. The modelling is directed at the better understandingof the dominant mechanisms involved in the oxidation processand their significance for the biocompatibility of the alloy.Two different regimes for the relative diffusivities of oxygenand the metals are investigated. By assuming fast bulk reactions,different asymptotic structures emerge in different parameterregimes and the resulting models take the form of moving boundaryproblems. Different profiles of nickel concentration are obtained:in particular a nickel-rich layer (observed in practice) ispresent below the oxide/metal interface for the case when oxygenand the metals diffuse at comparable rates.     

Entangled Bell states of two electrons in coupled quantum dots—phonon decoherence

We demonstrate coupling and entangling of quantum states in a pair of vertically aligned self assembled quantum dots by studying the dynamics of two interacting electrons driven by external electric field. The present entanglement involves the spatial degree of freedom for the two electrons system. We show that system of two interacting electrons initially delocalized (localized each in one dot) oscillate slowly in response to electric field, since the strong Coulomb repulsion makes them behaving so. We use an explicit formula for the entanglement of formation of two qubit in terms of the concurrence of the density operator. In ideal situations, entangled quantum states would not decohere during processing and transmission of quantum information. However, real quantum systems will inevitably be influenced by surrounding environments. We discuss the degree of entanglement of this system in which we introduce the decoherence effect caused by the acoustic phonon. In this entangled states proposal, the decohering time depends on the external parameters.     

Crystallographic report: A new polymorph for bis[bis(N,N‐dibenzyldithiocarbamato)cadmium(II)]

The title compound is a centrosymmetric dimer with each cadmium in a distorted CdS₅ square pyramidal geometry. The Cd–S bond distances range from 2.5626(11) to 2.8459(11) Å. Copyright © 2004 John Wiley & Sons, Ltd.     

Rank estimation in reduced-rank regression

Reduced rank regression assumes that the coefficient matrix in a multivariate regression model is not of full rank. The unknown rank is traditionally estimated under the assumption of normal responses. We derive an asymptotic test for the rank that only requires the response vector have finite second moments. The test is extended to the nonconstant covariance case. Linear combinations of the components of the predictor vector that are estimated to be significant for modelling the responses are obtained.     

Tomographic reconstruction using heuristic Monte Carlo methods

A tomographic reconstruction method based on Monte Carlo random searching guided by the information contained in the projections of radiographed objects is presented. In order to solve the optimization problem, a multiscale algorithm is proposed to reduce computation. The reconstruction is performed in a coarse-to-fine multigrid scale that initializes each resolution level with the reconstruction of the previous coarser level, which substantially improves the performance. The method was applied to a real case reconstructing the internal structure of a small metallic object with internal components, showing excellent results.     

Fabrication and characterization of a PbTe quantum dots multilayer structure

Multilayer PbTe quantum dots (QDs) and SiO₂ were grown by pulsed laser deposition (PLD) and Plasma enhanced chemical vapor deposition (PECVD) techniques. The crystalline structure, QD size and size dispersion were observed by high-resolution transmission electron microscopy (HRTEM) measurements. This technique allows one to grow PbTe QDs as small as 1.8 nm diameter and 0.6 nm size dispersion. The whole structure can be used in a Fabry–Perot cavity for an optical device operating at the mid-infrared region.     

The “corset effect” of spin-lattice relaxation in polymer melts confined in nanoporous media

Linear polyethylene oxides with molecular weightsM _w of 1665 and 10170 confined in pores with variable diameters in a solid methacrylate matrix were studied by proton field-cycling nuclear magnetic resonance relaxometry. The pore diameter was varied in the range of 9–57 nm. In all cases, the spin-lattice relaxation time shows a frequency dependence close toT ₁∞ v^3/4 in the range ofv=3·10^?1-2·10¹ MHz as predicted by the tube-reptation model. This protonT ₁ dispersion essentially reproduces that found in a previous deuteron study (R. Kimmich, R.-O. Seitter, U. Beginn, M. Möller, N. Fatkullin: Chem. Phys. Lett. 307, 147, 1999). As a feature particularly characteristic for reptation, this finding suggests that reptation is the dominating chain dynamics mechanism under pore confinement in the corresponding time range. The absolute values of the spin-lattice relaxation times indicate that the diameter of the effective tubes in which reptation occurs is much smaller than the pore diameters on the time scale of spin-lattice relaxation experimens. An estimation leads to a valued ^*～0.5 nm. The impenetrability of the solid pore walls, the uncrossability of polymer chains (“excluded volume”) and the low value of the compressibility in polymer melts create the “corset effect” which reduces the lateral motions of polymer chains to a microscopic scale of only a few tenths of a nanometer.     

Modelling and design of a travelling-wave electro-optic modulator on InP

Based on a rigorous vectorial analysis, a fast travelling-wave Mach–Zehnder modulator is modelled and designed. The cross-section of the semiconductor layer stack and the lossy electrodes are carefully modelled using the method of lines in order to investigate propagation characteristics, velocity and losses. This yields an accurate microwave and optical field distribution to explain the behaviour of the component. In order to enhance the modulation efficiency, design curves are derived and the cross-sectional dimensions for minimum microwave loss are determined. The loss of the optimized modulator agrees very well with small-signal measurements up to 40 GHz and HFSS simulations. The layerstack of the fabricated device is suitable for integration with InP multi-wavelength lasers.     

Förster energy transfer from poly(arylene–ethynylene)s to an erbium–porphyrin complex

We study the infrared emission at 1.54 μm of an organolanthanide complex, Er(III)-tetraphenylporphyrin [Er(TPP)acac], both as a result of direct optical excitation and via energy transfer from host π-conjugate polymers of type poly(arylene–ethynylene) [PAE]. In the first case, the emission of the neat complex is characterized in inert transparent materials and a value of the quantum yield at 1.54 μm φ_IR=4×10⁻⁴ is measured. Then, fluorescence resonance transfer is investigated in blends of Er(TPP)acac with PAEs by monitoring the quenching of the polymer fluorescence along with the enhancement of both the visible emission of the ligand and the near-infrared band of Er³⁺. These different procedures allow a detailed analysis of the transfer efficiency within a specific implementation of the Förster model for polymeric donors. The experimental values of the critical radius R₀, ranging from 1.3 to 2.5 nm for the different blends, are in good agreement with theory for a wide interval of the physical and spectroscopic parameters. This suggests that other mechanisms for excitation transfer do not play a significant role in these materials.