Functional a posteriori error estimates for incremental models in elasto-plasticity

We consider incremental problem arising in elasto-plastic models with isotropic hardening. Our goal is to derive computable and guaranteed bounds of the difference between the exact solution and any function in the admissible (energy) class of the problem considered. Such estimates are obtained by an advanced version of the variational approach earlier used for linear boundary-value problems and nonlinear variational problems with convex functionals [24, 30]. They do no contain mesh-dependent constants and are valid for any conforming approximations regardless of the method used for their derivation. It is shown that the structure of error majorant reflects properties of the exact solution so that the majorant vanishes only if an approximate solution coincides with the exact one. Moreover, it possesses necessary continuity properties, so that any sequence of approximations converging to the exact solution in the energy space generates a sequence of positive numbers (explicitly computable by the majorant functional) that tends to zero.      

Feature of the magnetotransport of a quasi-one-dimensional electrons on the superfluid helium

The magnetotransport in a nondegenerate quasi-one-dimensional (Q1D) electron system over superfluid helium has been investigated experimentally. The measurements are performed in the presence of a perpendicular magnetic field B up to 2.6 T in the temperature range T=0.48–2.05 K in the system of conducting channels of 100–400 nm width. It is shown that the value of longitudinal magnetoresistance ρ_xx increases with B. In the electron-gas scattering region (T>0.9 ), the behaviour of ρ_xx agrees with classical Drude law. In the quantum transport regime, the self-consistent Born approximation (SCBA) theory for a 2D electron system over liquid helium describes the experimental data qualitatively. The deviation due to the difference of the experimentally studied Q1D system of the electrons in a parabolic potential well differs from theoretically analysed one. The experimental data agree with the theoretical calculation for the Q1D electron system at the weak magnetic field and the low temperature.

The negative magnetoresistance of the conducting channels has been observed in both the gas- and the ripplon-scattering region. These effects have been explained by weak carrier localization on the gas atoms at high temperature and by display of the quantum magnetotransport features in a mesoscopic system at low temperature.     

Reactivity of the Cu2O(1 0 0) surface: Insights from first principles calculations

We present a summary of results of systematic first principles calculations of the electronic and geometric structures of the Cu₂O(1 0 0) surface and the process of CO oxidation on this surface (energetics and pathways of adsorption, diffusion and reactions of CO and O₂ on the surface). The (p, T) phase diagram of the Cu₂O(1 0 0) in equilibrium of with gas phase O₂ built using the ab initio thermodynamics approach suggests that the O-terminated surface is preferred over the Cu-terminated one within the entire ranges of pressures and temperatures in which the compound exists. Metastable Cu-terminated Cu₂O(1 0 0) is found to undergo a surface reconstruction in agreement with experiment. We find CO to oxidize spontaneously on the O-terminated Cu₂O(1 0 0) surface by consuming surface O atoms. Our calculations also show that the surface O-vacancies left in the course of the CO oxidation can be easily filled with dissociative adsorption of the gas phase O₂ molecules, which are usually present in reaction environment.     

Diffuse scattering and lattice dynamics of superionic copper chalcogenides

The energy-resolved neutron diffraction and inelastic neutron scattering study of diffuse scattering in copper chalcogenides was performed in order to clarify the role of static disorder versus low-energy phonons. Neutron diffraction patterns taken from Cu_1.75Se, Cu_1.98Se and Ag_0.25Cu_1.75Se powders in superionic phase show a broad maximum related to diffuse scattering. This diffuse background is suppressed in the energy-resolved experiment which indicates a strong contribution from inelastic scattering coming from correlated thermal displacements of the ions in the superionic phase. Diffraction experiments on a single crystal of α-Cu_1.8Se have revealed an ordered structure with superstructure reflections at the G ± 1/2 <111> and G ± 1/3 <220> positions of reciprocal space at room temperature. In addition to superstructure spots, diffuse scattering was observed along the <111> direction which is considered as a possible diffusion path of mobile Cu ions. In inelastic neutron scattering measurements with this single crystal sample strong inelastic scattering was observed along <111>. This shows that the diffuse scattering found in conventional diffraction experiment is mainly inelastic and most probably comes from low-energy phonons.     

Global and exponential attractors for 3‐D wave equations with displacement dependent damping

A weakly damped wave equation in the three‐dimensional (3‐D) space with a damping coefficient depending on the displacement is studied. This equation is shown to generate a dissipative semigroup in the energy phase space, which possesses finite‐dimensional global and exponential attractors in a slightly weaker topology. Copyright © 2006 John Wiley & Sons, Ltd.     

Polycapillary‐optics‐based micro‐XANES and micro‐EXAFS at a third‐generation bending‐magnet beamline

A focusing system based on a polycapillary half‐lens optic has been successfully tested for transmission and fluorescence µ‐X‐ray absorption spectroscopy at a third‐generation bending‐magnet beamline equipped with a non‐fixed‐exit Si(111) monochromator. The vertical positional variations of the X‐ray beam owing to the use of a non‐fixed‐exit monochromator were shown to pose only a limited problem by using the polycapillary optic. The expected height variation for an EXAFS scan around the Fe K‐edge is approximately 200 µm on the lens input side and this was reduced to ～1 µm for the focused beam. Beam sizes (FWHM) of 12–16 µm, transmission efficiencies of 25–45% and intensity gain factors, compared with the non‐focused beam, of about 2000 were obtained in the 7–14 keV energy range for an incoming beam of 0.5 × 2 mm (vertical × horizontal). As a practical application, an As K‐edge µ‐XANES study of cucumber root and hypocotyl was performed to determine the As oxidation state in the different plant parts and to identify a possible metabolic conversion by the plant.     

Carbon-nanotube-based saturable absorbers for near infrared solid state lasers

We demonstrate the passive mode-locking of a diode-pumped Nd⁺³:YAG (central wavelength: 1.32 μm; pulse duration: 50 ps; output energy: up to 70 μJ) laser using a polymer film containing single-wall carbon nanotubes. The mode-locking regime is stable at a pump repetition rate of up to 1 kHz. We also investigate the temporal evolution of the light-induced absorption change of the polymer film containing carbon nanotubes in the spectral range of 1.3–1.5 μm by femtosecond time-resolved pump-probe measurements. The measurements reveal that light-induced transmission exhibits fast and slow components that last 280 fs and more than 10 ps, respectively. The third-order susceptibility of the polymer film containing single wall carbon nanotubes is as high as 10⁻¹¹ esu.     

Cosmological perturbations in SFT inspired non-local scalar field models

We clearly and consistently supersymmetrize the celebrated horizontality condition to derive the off-shell nilpotent and absolutely anticommuting Becchi?CRouet?CStora?CTyutin (BRST) and anti-BRST symmetry transformations for the supersymmetric system of a free spinning relativistic particle within the framework of superfield approach to BRST formalism. For the precise determination of the proper (anti-)BRST symmetry transformations for all the bosonic and fermionic dynamical variables of our system, we consider the present theory on a (1,2)-dimensional supermanifold parameterized by an even (bosonic) variable (??) and a pair of odd (fermionic) variables ?? and $\bar{\theta}$ (with $\theta^{2} = \bar{\theta}^{2} = 0$ , $\theta\bar{\theta}+ \bar{\theta}\theta= 0$ ) of the Grassmann algebra. One of the most important and novel features of our present investigation is the derivation of (anti-)BRST invariant Curci?CFerrari type restriction which turns out to be responsible for the absolute anticommutativity of the (anti-)BRST transformations and existence of the coupled (but equivalent) Lagrangians for the present theory of a supersymmetric system. These observations are completely new results for this model.