Dephasing times in closed quantum dots

Dephasing of one-particle states in closed quantum dots is analyzed within the framework of random matrix theory and the master equation. The combination of this analysis with recent experiments on the magnetoconductance allows, for the first time, the evaluation of the dephasing times of closed quantum dots. These dephasing times turn out to be dependent on the mean level spacing and significantly enhanced as compared with the case of open dots. Moreover, the experimental data available are consistent with the prediction that the dephasing of one-particle states in finite closed systems disappears at low enough energies and temperatures.     

Formation and structure of polyelectrolyte and nanoparticle multilayers: effect of particle characteristics

The formation and structure of multilayer films containing a cationic polyelectrolyte and anionic silica nanoparticles were studied by means of ellipsometry and atomic force microscopy. Three types of silica particles of different sizes were examined. The density and thickness of the films as well as the adsorption kinetics appear to be strongly dependent on the choice of particle; smaller particles favor the formation of smooth and dense films with a higher content of the inorganic component.     

Elastic and piezoelectric fields due to polyhedral inclusions

We derive explicit, closed-form expressions describing elastic and piezoelectric deformations due to polyhedral inclusions in uniform half-space and bi-materials. Our analysis is based on the linear elasticity theory and Green’s function method. The method involves evaluation of volume and surface integrals of harmonic and bi-harmonic potentials. In case of polyhedra, such integrals are expressed through algebraic functions. Our results generalize numerous studies on this subject, and they allow to obtain fully analytical solutions for a number of physical and engineering problems. In the limiting case of an infinite space, our relations have an essentially more compact form, than relations obtained by other authors. We present solutions to classical Mindlin and Cherruti problems. We describe the elastic relaxation of a misfitting polygonal quantum dot in bi-materials assuming isotropic and vertically isotropic properties. It is explained how to analyze non-hydrostatic and non-uniform inclusions. We also study piezoelectric fields induced by inclusions in materials with cubic and hexagonal lattices. Among other results, we have found that a cubic inclusion in an isotropic material reproduces fields of quantum dots in GaAs (0, 0, 1) and GaAs (1, 1, 1) depending on the orientation of the cube. This suggests that one can qualitatively model crystals with different lattices by choosing an appropriate inclusion shape.     

Asymptotics of eigenfrequencies and eigenmodes of non‐homogeneous inextensible filament with an end load

We consider a class of non‐selfadjoint operators generated by the equation and the boundary conditions, which govern small vibrations of an ideal filament with non‐conservative boundary conditions at one end and a heavy load at the other end. The filament has a non‐constant density and is subject to a viscous damping with a non‐constant damping coefficient. The boundary conditions contain two arbitrary complex parameters. We derive the spectral asymptotics for the aforementioned two‐parameter family of non‐selfadjoint operators. In the forthcoming papers, based on the asymptotical results of the present paper, we will prove the Riesz basis property of the eigenfunctions. The spectral results obtained in the aforementioned papers will allow us to solve boundary and/or distributed controllability problems for the filament using the spectral decomposition method. Copyright © 2001 John Wiley & Sons, Ltd.     

Detonation diffraction through different geometries

We performed the study of the diffraction of a self-sustained detonation from a cylindrical tube (of inner diameter d) through different geometric configurations in order to characterise the transmission processes and to quantify the transmission criteria to the reception chamber. For the diffraction from a tube to the open space the transmission criteria is expressed by d _c  = k _c ·λ (with λ the detonation cell size and k _c depending on the mixture and on the operture configuration, classically 13 for alkane mixtures with oxygen). The studied geometries are: (a) a sharp increase of diameter (D/d > 1) with and without a central obstacle in the diffracting section, (b) a conical divergent with a central obstacle in the diffracting section and (c) an inversed intermediate one end closed tube insuring a double reflection before a final diffraction between the initiator tube and the reception chamber. The results for case A show that the reinitiation process depends on the ratio d/λ. For ratios below k _c the re-ignition takes place at the receptor tube wall and at a fixed distance from the step, i.e. closely after the diffracted shock reflection shows a Mach stem configuration. For ratios below a limit ratio k _lim (which depends on D/d) the re-ignition distance increases with the decrease of d/λ. For both case A and B the introduction of a central obstacle (of blockage ratio BR = 0.5) at the exit of the initiator tube decreases the critical transmission ratio k _c by 50%. The results in configuration C show that the re-ignition process depends both on d/λ and the geometric conditions. Optimal configuration is found that provides the transmission through the two successive reflections (from d = 26 mm to D _ch = 200 mm) at as small d/λ as 2.2 whatever the intermediate diameter D is. This configuration provides a significant improvement in the detonation transmission conditions.

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This paper was based on work that was partly presented at the International Conference on Combustion and Detonation, Zel’dovich Memorial II, Moscow, Russia, 30 August–3 September 2004, and at the 20th International Colloquium on the Dynamics of Explosions and Reactive systems, Montreal, Canada, 31 July–5 August 2005.     

Syntheses of 2,4‐diaryl‐2,3‐dihydro‐1,5‐benzothiazepines

The condensation of α,β‐unsaturated ketones with substituted o‐aminothiophenols, obtained by reductive cleavage of the corresponding disulfides in the presence of triphenylphosphine, is an effective method for the synthesis of 2,4‐diaryl‐2,3‐dihydro‐1,5‐benzothiazepines under neutral conditions.     

The polyoxometallate [(CH3)4N]2[Mo4O10(OCH3)4Cl2]

The crystal and molecular structure of bis(tetra­methyl­ammonium) di­chloro­tetra‐μ₂‐methoxo‐di‐μ₂‐oxo‐octo­oxo­tetra­molybdate(VI), (C₄H₁₂N)₂[Mo₄O₁₀(OCH₃)₄Cl₂], has been determined from X‐ray diffraction data. The crystallographically centrosymmetric anion is built up of four edge‐sharing octahedra, two MoO₆ and two MoO₅Cl.     

Second-order variational analysis in second-order cone programming

Mathematical Programming - The paper conducts a second-order variational analysis for an important class of nonpolyhedral conic programs generated by the so-called second-order/Lorentz/ice-cream...