Decay spectrum and decay subspace of normal operators

Let A be a self-adjoint operator on a Hilbert space. It is well known that A admits a unique decomposition into a direct sum of three self-adjoint operators A(p), A(ac) and A(sc) such that there exists an orthonormal basis of eigenvectors for the operator A(p) the operator A(ac) has purely absolutely continuous spectrum and the operator A(sc) has purely singular continuous spectrum. We show the existence of a natural further decomposition of the singular continuous component A c into a direct sum of two self-adjoint operators A(sc)(D) and A(sc)(ND). The corresponding subspaces and spectra are called decaying and purely non-decaying singular subspaces and spectra. Similar decompositions are also shown for unitary operators and for general normal operators.

Electroreduction of N-methylphthalimide in room temperature ionic liquids under insonated and silent conditions

The selective electroreduction N-methylphthalimide to 3-hydroxy-2-methyl-isoindolin-1-one has been performed in ionic liquids using phenol as a proton donor under silent and ultrasonic conditions. A significant increase in the rate of electroreduction is shown using ultrasonic activation and in addition high current efficiencies were observed. Some decomposition of the ionic liquid was found to have occurred under exposure to ultrasound. © 2004 Elsevier B.V. All rights reserved.

Sulfur-tolerant NOx storage traps: an infrared and thermodynamic study of the reactions of alkali and alkaline-earth metal sulfates

The sulfur tolerance of a barium-containing NOx storage/reduction trap was investigated using infrared analysis. It was confirmed that barium carbonate could be replaced by barium sulfate by reaction with low concentrations of sulfur dioxide (50 ppm) in the presence of large concentrations of carbon dioxide (10%) at temperatures up to 700 degreesC. These sulfates could at least be partially removed by switching to hydrogen-rich conditions at elevated temperatures. Thermodynamic calculations were used to evaluate the effects of gas composition and temperature on the various reactions of barium sulfate and carbonate under oxidizing and reducing conditions. These calculations clearly showed that if, under a hydrogen-rich atmosphere, carbon dioxide is included as a reactant and barium carbonate as a product then barium sulfate can be removed by reaction with carbon dioxide at a much lower temperature than is possible by decomposition to barium oxide. It was also found that if hydrogen sulfide was included as a product of decomposition of barium sulfate instead of sulfur dioxide then the temperature of reaction could be significantly lowered. Similar calculations were conducted using a selection of other alkaline-earth and alkali metals. In this case calculations were simulated in a gas mixture containing carbon monoxide, hydrogen and carbon dioxide with partial pressures similar to those encountered in real exhausts during switches to rich conditions. The results indicated that there are metals such as lithium and strontium with less stable sulfates than barium, which may also possess sufficient NOx storage capacity to give sulfur-tolerant NOx traps.

Atomistic studies of interactions between the dominant lattice dislocations and γ/γ-lamellar boundaries in lamellar γ-TiAl

This paper reports on atomistic simulations of the interactions between the dominant lattice dislocations in ?-TiAl (<1 0 1] superdislocations) with all three kinds of ?/?-lamellar boundaries in polysynthetically twinned (PST) TiAl. The purpose of this study is to clarify the early stage of lamellar boundary controlled plastic deformation in PST TiAl. The interatomic interactions in our simulations are described by a bond order potential for L10-TiAl which provides a proper quantum mechanical description of the bonding. We are interested in the dislocation core geometries that the lattice produces in proximity to lamellar boundaries and the way in which these cores are affected by the elastic and atomistic effects of dislocation-lamellar boundary interaction. We study the way in which the interfaces affect the activation of ordinary dislocation and superdislocation slip inside the ?-lamellae and transfer of plastic deformation across lamellar boundaries. We find three new phenomena in the atomic-scale plasticity of PST TiAl, particularly due to elastic and atomic mismatch associated with the 60° and 120° ?/?-interfaces: (i) two new roles of the ?/?-interfaces, i.e. decomposition of superdislocations within 120° and 60° interfaces and subsequent detachment of a single ordinary dislocation and (ii) blocking of ordinary dislocations by 60° and 120° interfaces resulting in the emission of a twinning dislocation.

Green synthesis of ZnO nanoparticles in a room-temperature ionic liquid 1-ethyl-3-methylimidazolium bis(trifluoromethylsulfonyl)imide

Nanoparticles of ZnO with the wurtzite structure have been successfully synthesized via a microwave through the decomposition of zinc acetate dihydrate in an ionic liquid, 1-ethyl-3-methylimidazolium bis(trifluoromethylsulfonyl)imide, as a solvent. Fundamental characterizations including X-ray diffraction (XRD), scanning electron microscopy (SEM), and transmission electron microscopy (TEM) were conducted for the ZnO nanostructures.

The main-sequence rotation-colour relation in the Coma Berenices open cluster

We present the results of a photometric survey of rotation rates in the Coma Berenices (Melotte 111) open cluster, using data obtained as part of the SuperWASP exoplanetary transit-search programme. The goal of the Coma survey was to measure precise rotation periods for main-sequence F, G and K dwarfs in this intermediate-age (~600 Myr) cluster, and to determine the extent to which magnetic braking has caused the stellar spin periods to converge. We find a tight, almost linear relationship between rotation period and J - K colour with an rms scatter of only 2 per cent. The relation is similar to that seen among F, G and K stars in the Hyades. Such strong convergence can only be explained if angular momentum is not at present being transferred from a reservoir in the deep stellar interiors to the surface layers. We conclude that the coupling time-scale for angular momentum transport from a rapidly spinning radiative core to the outer convective zone must be substantially shorter than the cluster age, and that from the age of Coma onwards stars rotate effectively as solid bodies. The existence of a tight relationship between stellar mass and rotation period at a given age supports the use of stellar rotation period as an age indicator in F, G and K stars of Hyades age and older. We demonstrate that individual stellar ages can be determined within the Coma population with an internal precision of the order of 9 per cent (rms), using a standard magnetic braking law in which rotation period increases with the square root of stellar age. We find that a slight modification to the magnetic-braking power law, P ~ t0.56, yields rotational and asteroseismological ages in good agreement for the Sun and other stars of solar age for which p-mode studies and photometric rotation periods have been published.

Determining Propeller Erosion at the Stern of a Berthing Ship

This paper presents the findings from an experimental investigation in to the nature and extent of the scouring that occurs when a ship berths in front of a perpendicular quay wall within the confines of a harbor. It examines the interaction between the relative position of the quay wall to the central axis of the ship and the influence of angle of the vessel's rudder on the magnitude of the scouring produced. The experimental programme covered a range of sediment sizes, propeller diameters and speeds of rotation and rudder angles. Also, methods for calculating the depth of expected scour are presented in terms of initial semi-empirical equations for the data range under investigation.

Asymmetric rhodium carbene insertion into the Si-H bond: identification of new dirhodium(II) carboxylate catalysts using parallel synthesis techniques

Decomposition of methyl 2-diazophenylacetate in the presence of silanes and a chiral dirhodium(11) catalyst results in Si-H insertion of the intermediate carbenoid with varying degrees of enantioselectivity. New chiral dirhodium(11) carboxylate catalysts were identified using solution phase parallel synthesis techniques. (C) 2003 Elsevier Science Ltd. All rights reserved.

Nonlinear Dynamics of Rotating Multi-Component Pair Plasmas and e-p-i Plasmas

The propagation of small amplitude stationary profile nonlinear electrostatic excitations in a pair plasma is investigated, mainly drawing inspiration from experiments on fullerene pair-ion plasmas. Two distinct pair ion species are considered of opposite polarity and same mass, in addition to a massive charged background species, which is assumed to be stationary, given the frequency scale of interest. In the pair-ion context, the third species is thought of as a background defect (e.g. charged dust) component. On the other hand, the model also applies formally to electron-positron-ion (e-p-i) plasmas, if one neglects electron-positron annihilation. A two-fluid plasma model is employed, incorporating both Lorentz and Coriolis forces, thus taking into account the interplay between the gyroscopic (Larmor) frequency ?c and the (intrinsic) plasma rotation frequency O0. By employing a multi-dimensional reductive perturbation technique, a Zakharov-Kuznetsov (ZK) type equation is derived for the evolution of the electric potential perturbation. Assuming an arbitrary direction of propagation, with respect to the magnetic field, we derive the exact form of nonlinear solutions, and study their characteristics. A parametric analysis is carried out, as regards the effect of the dusty plasma composition (background number density), species temperature(s) and the relative strength of rotation to Larmor frequencies. It is shown that the Larmor and mechanical rotation affect the pulse dynamics via a parallel-to-transverse mode coupling diffusion term, which in fact diverges at ?c ? ±2O0. Pulses collapse at this limit, as nonlinearity fails to balance dispersion. The analysis is complemented by investigating critical plasma compositions, in fact near-symmetric (T- ˜ T+) “pure” (n- ˜ n+) pair plasmas, i.e. when the concentration of the 3rd background species is negligible, case in which the (quadratic) nonlinearity vanishes, so one needs to resort to higher order nonlinear theory. A modified ZK equation is derived and analyzed. Our results are of relevance in pair-ion (fullerene) experiments and also potentially in astrophysical environments, e.g. in pulsars.

In situ study of ozone and hybrid plasma Ag-Al catalysts for the oxidation of toluene: Evidence of the nature of the active sites

Silver colloids have been prepared by reducing AgNO3 in aqueous solution and embeded in alumina following a sol-gel procedure in the presence of Pluronic 84 ((EO)(19)(PO)(39)(EO)(19)), as surfactant. Plasma-catalytic experiments aimed at the mineralization of toluene showed that the selectivity to CO2 was significantly increased in the presence of Ag catalysts compared with results obtained using the plasma alone. In-situ studies of the ozone interaction with catalysts provide an insight into the nature of the active sites of supported silver colloids for mineralization reactions. It is noticeable that when ozone is chemisorbed on embedded Ag colloidal catalysts no change in the silver oxidation state or size is found. The population of the chemisorbed species is higher at lower temperatures, where the non-selective decomposition of ozone is smaller. The catalysts exhibit high stability, preserving the structural and textural properties after the catalytic tests, that is indeed very important in the presence of ozone. (C) 2011 Elsevier B.V. All rights reserved.

Abatement of nitrous oxide over natural and iron modified natural zeolites

The natural zeolite obtained from the Sivas-Yavu region in Turkey and iron modified forms were studied for the decomposition of N2O and selective catalytic reduction of N2O with NH3. The natural and iron modified zeolites were characterised by XRD, SEM, H-2-TPR, NH3-TPD and low temperature nitrogen sorption. The effect iron loading, precursor and valency on the catalytic performance of catalysts were studied. The catalytic activity of the zeolites increased up to about 7.0 wt.% Fe. Above this value, the activity decreased as a result of a reduction in the surface area and pore volume of the zeolite. The highest catalytic activity was observed using catalysts prepared with FeCl2 due to the formation of more reducible iron species in the zeolites. When FeSO4 was used as the iron precursor, sulphate remained on the surface even after extensive washing resulting in a decrease in the N2O decomposition activity and a shift the N2O reduction temperature to higher values. Since the natural and iron exchanged natural zeolites prepared using FeCl2 have comparable activity with synthetic zeolites, the offer a promising alternative catalyst for the abatement of N2O, particularly for the selective reduction of N2O with NH3. (C) 2011 Elsevier B.V. All rights reserved.

Photodecomposition of ozone sensitised by a film of titanium dioxide on glass

High levels of ozone (typically 850 ppm) are readily decomposed by semiconductor photocatalysis, using a thin film of the semiconductor titanium dioxide (Degussa P25 TiO2) cast on a glass tube, and UVA light, i.e. light of energy greater than that of the bandgap of the semiconductor (ultra-bandgap light); in the absence of this light the thermal decomposition of ozone is relatively slow. The semiconductor films show no evidence of chemical or photochemical wear with repeated use. At high levels of ozone, i.e. 100 ppm less than or equal to [O-3] less than or equal to 1400 ppm, the initial rate of ozone decomposition by semiconductor photocatalysis is independent of [O-3], whereas, at lower ozone concentrations, i.e. 5 ppm less than or equal to [O-3] less than or equal to 100 ppm, the initial rate of ozone photodestruction decreases in a smooth, but non-linear, manner with decreasing [O-3]. The kinetics of ozone photodecomposition fit a Langmuir-Hinshelwood type kinetic equation and the possible mechanistic implications of these results are briefly discussed. (C) 2002 Elsevier Science B.V. All rights reserved.

Fatigue Damage of Composite Structures Applying a Micromechanical Approach

Fatigue damage calculations of unidirectional polymer composites is presented applying micromechanics theory. An orthotropic micromechanical damage model is integrated with an isotropic fatigue evolution model to predict the micromechanical fatigue damage of the composite structure. The orthotropic micromechanical damage model is used to predict the orthotropic damage evolution within a single cycle. The isotropic fatigue model is used to predict the magnitude of fatigue damage accumulated as a function of the number of cycles. The advantage of using this approach is the cheap determination of model parameters since the orthotropic damage model parameters can be determined using available data from quasi-static loading tests. Decomposition of the state variables down to the constituent scale is accomplished by micromechanics theory. Phenomenological damage evolution models are then postulated for each constituent and for interphase among them. Comparison between model predictions and experimental data is presented.

A micromechanics approach for damage modeling of polymer matrix composites

A new model for damage evolution in polymer matrix composites is presented. The model is based on a combination of two constituent-level models and an interphase model. This approach reduces the number of empirical parameters since the two constituent- level models are formulated for isotropic materials, namely fiber and matrix. Decomposition of the state variables down to the micro-scale is accomplished by micromechanics. Phenomenological damage evolution models are then postulated for each constituent. Determination of material parameters is made from available experimental data. The required experimental data can be obtained with standard tests. Comparison between model predictions and additional experimental data is presented.

A micro-mechanics damage approach for fatigue of composite materials

A new model for fatigue damage evolution of polymer matrix composites (PMC) is presented. The model is based on a combination of an orthotropic damage model and an isotropic fatigue evolution model. The orthotropic damage model is used to predict the orthotropic damage evolution within a single cycle. The isotropic fatigue model is used to predict the magnitude of fatigue damage accumulated as a function of the number of cycles. This approach facilitates the determination of model parameters since the orthotropic damage model parameters can be determined from available data from quasi-static-loading tests. Then, limited amount of fatigue data is needed to adjust the fatigue evolution model. The combination of these two models provides a compromise between efficiency and accuracy. Decomposition of the state variables down to the constituent scale is accomplished by micro-mechanics. Phenomenological damage evolution models are then postulated for each constituent and for the micro-structural interaction among them. Model parameters are determined from available experimental data. Comparison between model predictions and additional experimental data is presented.