Dynamics of interacting edge defects in copolymer lamellae

It is known that terraces at the air-polymer interface of lamella forming diblock copolymers do not make discontinuous jumps in height. Despite the underlying discretized structure, the height profiles are smoothly varying. The width of a transition region of a terrace edge in isolation is typically several hundreds of nanometres, resulting from a balance between surface tension, chain stretching penalties, and the enthalpy of mixing. What is less well known in these systems is what happens when two transition regions interact with one another. In this study, we investigate the dynamics of the interactions between copolymer lamellar edges. We find that the data can be well described by a model that assumes a repulsion between adjacent edges. While the model is simplistic, and does not include molecular level details, its agreement with the data suggest that some of the the underlying assumptions provide insight into the complex interplay between defects.

Some numerical experiments on the effect of the variation of static stability in two-layer quasi-geostrophic models

A method to solve a quasi-geostrophic two-layer model including the variation of static stability is presented. The divergent part of the wind is incorporated by means of an iterative procedure. The procedure is rather fast and the time of computation is only 60–70% longer than for the usual two-layer model. The method of solution is justified by the conservation of the difference between the gross static stability and the kinetic energy. To eliminate the side-boundary conditions the experiments have been performed on a zonal channel model. The investigation falls mainly into three parts: The first part (section 5) contains a discussion of the significance of some physically inconsistent approximations. It is shown that physical inconsistencies are rather serious and for these inconsistent models which were studied the total kinetic energy increased faster than the gross static stability. In the next part (section 6) we are studying the effect of a Jacobian difference operator which conserves the total kinetic energy. The use of this operator in two-layer models will give a slight improvement but probably does not have any practical use in short periodic forecasts. It is also shown that the energy-conservative operator will change the wave-speed in an erroneous way if the wave-number or the grid-length is large in the meridional direction. In the final part (section 7) we investigate the behaviour of baroclinic waves for some different initial states and for two energy-consistent models, one with constant and one with variable static stability. According to the linear theory the waves adjust rather rapidly in such a way that the temperature wave will lag behind the pressure wave independent of the initial configuration. Thus, both models give rise to a baroclinic development even if the initial state is quasi-barotropic. The effect of the variation of static stability is very small, qualitative differences in the development are only observed during the first 12 hours. For an amplifying wave we will get a stabilization over the troughs and an instabilization over the ridges.

Scattering of electromagnetic waves by rough interfaces and inhomogeneous layers

We consider a two-dimensional problem of scattering of a time-harmonic electromagnetic plane wave by an infinite inhomogeneous conducting or dielectric layer at the interface between semi-infinite homogeneous dielectric half-spaces. The magnetic permeability is assumed to be a fixed positive constant. The material properties of the media are characterized completely by an index of refraction, which is a bounded measurable function in the layer and takes positive constant values above and below the layer, corresponding to the homogeneous dielectric media. In this paper, we examine only the transverse magnetic (TM) polarization case. A radiation condition appropriate for scattering by infinite rough surfaces is introduced, a generalization of the Rayleigh expansion condition for diffraction gratings. With the help of the radiation condition the problem is reformulated as an equivalent mixed system of boundary and domain integral equations, consisting of second-kind integral equations over the layer and interfaces within the layer. Assumptions on the variation of the index of refraction in the layer are then imposed which prove to be sufficient, together with the radiation condition, to prove uniqueness of solution and nonexistence of guided wave modes. Recent, general results on the solvability of systems of second kind integral equations on unbounded domains establish existence of solution and continuous dependence in a weighted norm of the solution on the given data. The results obtained apply to the case of scattering by a rough interface between two dielectric media and to many other practical configurations.

Commodity risks and the cross-section of equity returns

The article examines whether commodity risk is priced in the cross-section of global equity returns. We employ a long-only equally-weighted portfolio of commodity futures and a term structure portfolio that captures phases of backwardation and contango as mimicking portfolios for commodity risk. We find that equity-sorted portfolios with greater sensitivities to the excess returns of the backwardation and contango portfolio command higher average excess returns, suggesting that when measured appropriately, commodity risk is pervasive in stocks. Our conclusions are robust to the addition to the pricing model of financial, macroeconomic and business cycle-based risk factors.

An integral equation method for a boundary value problem arising in unsteady water wave problems

In this paper we consider the 2D Dirichlet boundary value problem for Laplace’s equation in a non-locally perturbed half-plane, with data in the space of bounded and continuous functions. We show uniqueness of solution, using standard Phragmen-Lindelof arguments. The main result is to propose a boundary integral equation formulation, to prove equivalence with the boundary value problem, and to show that the integral equation is well posed by applying a recent partial generalisation of the Fredholm alternative in Arens et al [J. Int. Equ. Appl. 15 (2003) pp. 1-35]. This then leads to an existence proof for the boundary value problem. Keywords. Boundary integral equation method, Water waves, Laplace’s

Variable step-size LMS blind CDMA multiuser detectors

Adaptive least mean square (LMS) filters with or without training sequences, which are known as training-based and blind detectors respectively, have been formulated to counter interference in CDMA systems. The convergence characteristics of these two LMS detectors are analyzed and compared in this paper. We show that the blind detector is superior to the training-based detector with respect to convergence rate. On the other hand, the training-based detector performs better in the steady state, giving a lower excess mean-square error (MSE) for a given adaptation step size. A novel decision-directed LMS detector which achieves the low excess MSE of the training-based detector and the superior convergence performance of the blind detector is proposed.

Improved process topology for membrane distillation

In membrane distillation in a conventional membrane module, the enthalpies of vaporisation and condensation are supplied and removed by changes in the temperatures of the feed and permeate streams, respectively. Less than 5% of the feed can be distilled in a single pass, because the potential changes in the enthalpies of the liquid streams are much smaller than the enthalpy of vaporisation. Furthermore, the driving force for mass transfer reduces as the feed stream temperature and vapour pressure fall during distillation. These restrictions can be avoided if the enthalpy of vaporisation is uncoupled from the heat capacities of the feed and permeate streams. A specified distillation can then be effected continuously in a single module. Calculations are presented which estimate the performance of a flat plate unit in which the enthalpy of distillation is supplied and removed by the condensing and boiling of thermal fluids in separate circuits, and the imposed temperature difference is independent of position. Because the mass flux through the membrane is dependent on vapour pressure, membrane distillation is suited to applications with a high membrane temperature. The maximum mass flux in the proposed module geometry is predicted to be 30 kg/m2 per h at atmospheric pressure when the membrane temperature is 65°C. Operation at higher membrane temperatures is predicted to raise the mass flux, for example to 85 kg/m2 per h at a membrane temperature of 100°C. This would require pressurisation to 20 bar to prevent boiling at the heating plate of the feed channel. Pre-pressurisation of the membrane pores and control of the dissolved gas concentrations in the feed and the recyled permeate should be investigated as a means to achieve high temperature membrane distillation without pore penetration and wetting.

Scattering by infinite one-dimensional rough surfaces

We consider the Dirichlet boundary-value problem for the Helmholtz equation in a non-locally perturbed half-plane. This problem models time-harmonic electromagnetic scattering by a one-dimensional, infinite, rough, perfectly conducting surface; the same problem arises in acoustic scattering by a sound-soft surface. ChandlerWilde & Zhang have suggested a radiation condition for this problem, a generalization of the Rayleigh expansion condition for diffraction gratings, and uniqueness of solution has been established. Recently, an integral equation formulation of the problem has also been proposed and, in the special case when the whole boundary is both Lyapunov and a small perturbation of a flat boundary, the unique solvability of this integral equation has been shown by Chandler-Wilde & Ross by operator perturbation arguments. In this paper we study the general case, with no limit on surface amplitudes or slopes, and show that the same integral equation has exactly one solution in the space of bounded and continuous functions for all wavenumbers. As an important corollary we prove that, for a variety of incident fields including the incident plane wave, the Dirichlet boundary-value problem for the scattered field has a unique solution.

A uniqueness result for scattering by infinite rough surfaces

Consider the Dirichlet boundary value problem for the Helmholtz equation in a non-locally perturbed half-plane with an unbounded, piecewise Lyapunov boundary. This problem models time-harmonic electromagnetic scattering in transverse magnetic polarization by one-dimensional rough, perfectly conducting surfaces. A radiation condition is introduced for the problem, which is a generalization of the usual one used in the study of diffraction by gratings when the solution is quasi-periodic, and allows a variety of incident fields including an incident plane wave to be included in the results obtained. We show in this paper that the boundary value problem for the scattered field has at most one solution. For the case when the whole boundary is Lyapunov and is a small perturbation of a flat boundary we also prove existence of solution and show a limiting absorption principle.

Acoustic scattering by an inhomogeneous layer on a rigid plate

The problem of scattering of time-harmonic acoustic waves by an inhomogeneous fluid layer on a rigid plate in R2 is considered. The density is assumed to be unity in the media: within the layer the sound speed is assumed to be an arbitrary bounded measurable function. The problem is modelled by the reduced wave equation with variable wavenumber in the layer and a Neumann condition on the plate. To formulate the problem and prove uniqueness of solution a radiation condition appropriate for scattering by infinite rough surfaces is introduced, a generalization of the Rayleigh expansion condition for diffraction gratings. With the help of the radiation condition the problem is reformulated as a system of two second kind integral equations over the layer and the plate. Under additional assumptions on the wavenumber in the layer, uniqueness of solution is proved and the nonexistence of guided wave solutions of the homogeneous problem established. General results on the solvability of systems of integral equations on unbounded domains are used to establish existence and continuous dependence in a weighted norm of the solution on the given data.

The impedance boundary value problem for the Helmholtz equation in a half-plane

We prove unique existence of solution for the impedance (or third) boundary value problem for the Helmholtz equation in a half-plane with arbitrary L∞ boundary data. This problem is of interest as a model of outdoor sound propagation over inhomogeneous flat terrain and as a model of rough surface scattering. To formulate the problem and prove uniqueness of solution we introduce a novel radiation condition, a generalization of that used in plane wave scattering by one-dimensional diffraction gratings. To prove existence of solution and a limiting absorption principle we first reformulate the problem as an equivalent second kind boundary integral equation to which we apply a form of Fredholm alternative, utilizing recent results on the solvability of integral equations on the real line in [5].

Electronic charge transfer between ceria surfaces and gold adatoms: a GGA+U investigation

We use density functional theory calculations with Hubbard corrections (DFT+U) to investigate electronic aspects of the interaction between ceria surfaces and gold atoms. Our results show that Au adatoms at the (111) surface of ceria can adopt Au0, Au+ or Au� electronic configurations depending on the adsorption site. The strongest adsorption sites are on top of the surface oxygen and in a bridge position between two surface oxygen atoms, and in both cases charge transfer from the gold atom to one of the Ce cations at the surface is involved. Adsorption at other sites, including the hollow sites of the surface, and an O–Ce bridging site, is weaker and does not involve charge transfer. Adsorption at an oxygen vacancy site is very strong and involves the formation of an Au� anion. We argue that the ability of gold atoms to stabilise oxygen vacancies at the ceria surface by moving into the vacancy site and attracting the excess electrons of the defect could be responsible for the enhanced reducibility of ceria surfaces in the presence of gold. Finally, we rationalise the differences in charge transfer behaviour from site to site in terms of the electrostatic potential at the surface and the coordination of the species.

Enthalpy-driven ring-opening polymerization of highly strained macrocyclic biaryl-ether-ketones

Highly strained macrocyclic ether-ketones obtained by nickel-catalyzed cyclization of linear precursor oligomers undergo ring-opening polyinerization via ether exchange in the presence of nucleophilic initiators such as fluoride or phenoxide anions. Strain enthapies of these macrocycles, from DSC analyses of their exothermic ring-opening polymerization are in the range 50-90 kJ mol(-1). Melt-phase polymerization generally affords slightly cross-linked materials, but solution-phase polymerization at high macrocycle concentrations gives fully soluble, high molar mass polymers with inherent viscosities of up to 1.78 dL g(-1). Sequence-analysis of the resulting polymers by C-13 NMR shows that alternating or random monomer sequences may be obtained, depending on whether one or both aromatic rings adjacent to the ether linkages are activated toward nucleophilic attack.

Solvent extraction of Am(III) and Eu(III) from nitrate solution using synergistic mixtures of n-tridentate heterocycles and chlorinated cobalt dicarbollide

The separation by solvent extraction of Am-241(III) from Eu-152(III), in 1 M NaNO3 weakly acidic (pH 4) aqueous solutions, into dilute (ca. 10(-2) M) solutions of triazinylbipyridine derivatives (diethylhemi-BTP or di(benzyloxyphenyl) hemi-BTP) and chlorinated cobalt dicarbollide (COSAN) in 1-octanol or nitrobenzene has been studied. The N-tridentate heterocyclic ligands, which are selective for Am(III) over Eu(III), secured efficient separation of the two metal ions, while COSAN, strongly hydrophobic and fully dissociated in polar diluents, enhanced the extraction of the metal ions by ion-pair formation. Molecular interactions between the two co-extractants, observed at higher concentrations, led to the precipitation of their 1: 1 molecular adduct. In spite of that, efficient separations of Am and Eu ions were attained, with high separation factors, SFAm/Eu of 40 and even 60, provided the concentration of hemi-BTP was significantly greater than that of COSAN. Excess COSAN concentrations caused an antagonistic effect, decreasing both the distribution ratio of the metal ions and their separation factor.

Synthesis, structure and solution chemistry of quaternary oxovanadium(V) complexes incorporating hydrazone ligands

[VIVO(acac)(2)] reacts with an equimolar amount of benzoyl hydrazone of 2-hydroxyacetophenone (H2L1) or 5-chloro-2-hydroxyacetophenone (H2L2) in the presence of excess pyridine (py) in methanol to produce the quaternary [(VO)-O-V(L-1)(OCH3)(py)] (1) and [(VO)-O-V(L-2)(OCH3)(py)] (2) complexes, respectively, while under similar condition, the benzoyl hydrazones of 2-hydroxy-5-methylacetophenone (H2L3) and 2-hydroxy-5-methoxyacetophenone (H2L4) afforded only the methoxy bridged dimeric [(VO)-O-V(L-3/L-4)(OCH3)](2) complexes. The X-ray structural analysis of 1 and 2 indicates that the geometry around the metal is distorted octahedral where the three equatorial positions are occupied by the phenolate-O, enolate-O and the imine-N of the fully deprotonated hydrazone ligand in its enolic form and the fourth one by a methoxide-O atom. An oxo-O and a pyridine-N atom occupy two axial positions. Quaternary complexes exhibit one quasi-reversible one-electron reduction peak near 0.25 V versus SCE in CH2Cl2 and they decompose appreciably to the corresponding methoxy bridged dimeric complex in CDCl3 solution as indicated by their H-1 NMR spectra. These quaternary VO3+ complexes are converted to the corresponding V2O34+-complexes simply on refluxing them in acetone and to the VO2+-complexes on reaction with KOH in methanol. An equimolar amount of 8-hydroxyquinoline (Hhq) converts these quaternary complexes to the ternary [(VO)-O-V(L)(hq)] complexes in CHCl3. (C) 2009 Elsevier B. V. All rights reserved.