Peripheral spectrum of positive quasi-compact operators onC 0(X)

LetX be a locally compact space, andT, a quasi-compact positive operator onC ₀(X), with positive spectral radius,r. Then the peripheral spectrum ofT is a finite set of poles containingr, and the residue of the resolvent ofT at each peripheral pole is of finite rank. Using the concept of closed absorbing set, we develop an iterative process that gives the order,p, ofr, some special bases of the algebraic eigenspaces ker(T-r) ^p and ker(T ^*-r) ^p , and finally the dimension of the algebraic eigenspace associated to each peripheral pole.     

A local hermitian RBF meshless numerical method for the solution of multi‐zone problems

The local Hermitian interpolation (LHI) method is a strong‐form meshless numerical technique in which the solution domain is covered by a series of small and heavily overlapping radial basis function (RBF) interpolation systems. Aside from its meshless nature and the ability to work on very large scattered datasets, the main strength of the LHI method lies in the formation of local interpolations, which themselves satisfy both boundary and governing PDE operators, leading to an accurate and stable reconstruction of partial derivatives without the need for artificial upwinding or adaptive stencil selection. In this work, an extension is proposed to the LHI formulation which allows the accurate capture of solution profiles across discontinuities in governing equation parameters. Continuity of solution value and mass flux is enforced between otherwise disconnected interpolation systems, at the location of the discontinuity. In contrast to other local meshless methods, due to the robustness of the Hermite RBF formulation, it is possible to impose both matching conditions simultaneously at the interface nodes. The procedure is demonstrated for 1D and 3D convection–diffusion problems, both steady and unsteady, with discontinuities in various PDE properties. The analytical solution profiles for these problems, which experience discontinuities in their first derivatives, are replicated to a high degree of accuracy. The technique has been developed as a tool for solving flow and transport problems around geological layers, as experienced in groundwater flow problems. The accuracy of the captured solution profiles, in scenarios where the local convective velocities exceed those typically encountered in such Darcy flow problems, suggests that the technique is indeed suitable for modeling discontinuities in porous media properties. © 2010 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 27: 1201–1230, 2011     

Backscatter factor and absorption ratio of fibrous zirconia media in the visible

Fibrous thermal insulations are widely used to conserve energy in ambient to high temperature applications including buildings, solar collectors, heat exchangers, furnaces and thermal protection systems of reusable launch vehicles. It has long been recognised that zirconia has the lowest thermal conductivity of commercial refractories. The thermal conductivity of a zirconia fibrous medium is strongly dependent of its bulk density; high bulk densities of zirconia fibers provide the most effective insulation at high temperatures. Lee's theory for radiative transfer through fibrous media is used in this paper. The two-flux model is applied to determine the backward and forward parameters of a medium of zirconia fibers oriented in parallel planes. Theoretical calculations of the backscatter factor and absorption ratio of this medium are carried out in the visible spectrum for different size parameters of the fibers and for three different temperatures. Our results show that the backscatter factor of zirconia fibrous insulations is maximum, and therefore the heat transfer by the fibrous medium is the lowest, for a size parameter of 0.45 for all the temperatures studied. We also observed that the backscatter factor decreases with increasing temperature.     

Ordered and disordered patterns in two-phase flows in microchannels

We show that wetting properties crucially control the patterns in two-phase flows of immiscible fluids in microchannels. Ordered patterns, continuously entrained by the flow, are obtained when one phase completely wets the walls, while disordered patterns, intermittently adhering to the channel walls, are unavoidably produced when wetting is partial. A lower limit for the channel sizes capable of generating well structured objects (drops, pears, pearl necklaces, ...) is presented.     

Simplicial elimination schemes,extremal lattices and maximal antichain lattices

Fix a partial order P=(X, <). We first show that bipartite orders are sufficient to study structural properties of the lattice of maximal antichains. We show that all orders having the same lattice of maximal antichains can be reduced to one representative order (called the poset of irreducibles by Markowsky [14]). We then define the strong simplicial elimination scheme to characterize orders which have distributive lattice of maximal antichains. The notion of simplicial elimination corresponds to the decomposition process described in [14] for extremal lattices. This notion leads to simple greedy algorithms for distributivity checking, lattice recognition and jump number computation. In the last section, we give several algorithms for lattices and orders.     

Spontaneous formation of liquid crystalline phases and phase transitions in highly concentrated plasmid DNA

The liquid crystalline (LC) properties of two supercoiled plasmid DNA samples, pBSK (2958 bp) and pGEM (3000 bp), have been studied using polarised light microscopy (PLM), circular dichroism (CD) and UV–Vis spectroscopy. The influence of methods of isolation on plasmid LC behaviour is described, and using PLM we have demonstrated the spontaneous formation of cholesteric fingerprint-like textures. Preliminary studies of LC phase transitions in pGEM show the irreversibility of LC phase formation, as a consequence of changes in the tertiary structure of supercoiled plasmids. Using UV–Vis spectroscopy a hyperchromic effect was observed with increasing temperature. The CD spectra clearly showed structural changes, and probably mismatching of DNA bases, during cooling. Finally, we have observed an irreversible phase transition in plasmid DNA which is very different from that previously reported in linear DNA.     

Structural properties of ultra-small thorium and uranium dioxide nanoparticles embedded in a covalent organic framework

We report the structural properties of ultra-small ThO₂ and UO₂ nanoparticles (NPs), which were synthesized without strong binding surface ligands by employing a covalent organic framework (COF-5) as an inert template. The resultant NPs were used to observe how structural properties are affected by decreasing grain size within bulk actinide oxides, which has implications for understanding the behavior of nuclear fuel materials. Through a comprehensive characterization strategy, we gain insight regarding how structure at the NP surface differs from the interior. Characterization using electron microscopy and small-angle X-ray scattering indicates that growth of the ThO₂ and UO₂ NPs was confined by the pores of the COF template, resulting in sub-3 nm particles. X-ray absorption fine structure spectroscopy results indicate that the NPs are best described as ThO₂ and UO₂ materials with unpassivated surfaces. The surface layers of these particles compensate for high surface energy by exhibiting a broader distribution of Th–O and U–O bond distances despite retaining average bond lengths that are characteristic of bulk ThO₂ and UO₂. The combined synthesis and physical characterization efforts provide a detailed picture of actinide oxide structure at the nanoscale, which remains highly underexplored compared to transition metal counterparts.

ThO₂ and UO₂ nanoparticles synthesized using a COF-5 template exhibit unpassivated surfaces and provide insight into nanoscale properties of actinides.     

Characterisation of ethoxylated fatty chains of anionic surfactants and determination of residual ethoxylated fatty alcohols

Bachus et al. [1] recently described a new derivatisation method using 2-furoyl chloride for the characterisation of mixtures of polyethoxylated alcohols and their corresponding sulfates. This paper deals with the control of the derivatisation steps; hydrolysis and extraction conditions were optimised. The method is extended to the characterisation of alkyl sulfosuccinates, alkyl sulfoacetates and alkyl phosphates and to the analysis of residual polyethoxylated alcohols in surfactants. Extraction of non-ionic compounds using solid-phase extraction cartridges was performed before derivatisation. Residual amounts of alcohol were determined in five commercial anionic surfactants. Moreover, direct derivatisation without preliminary SPE in the same anionic surfactants proved to be efficient for dry samples.     

Multiplexed binding determination of seven glycoconjugates for Pseudomonas aeruginosa lectin I (PA-IL) using a DNA-based carbohydrate microarray

The binding of seven multivalent glycoconjugates displaying linear or antenna-like structures and different electronic environments were evaluated towards PA-IL on a DNA-based carbohydrate microarray. The affinity can be modulated by the charge and the topology of the galactosylated derivatives.     

Polymer-nanoparticle complexes: from dilute solution to solid state

We report on the formation and the structural properties of "supermicellar" aggregates made from mineral nanoparticles and polyelectrolyte-neutral block copolymers in aqueous solutions. The mineral particles put under scrutiny are ultrafine and positively charged yttrium hydroxyacetate nanoparticles. Combining light, neutron, and X-ray scattering experiments, we have characterized the sizes and the aggregation numbers of the organic-inorganic complexes. We have found that the hybrid aggregates have typical sizes in the range of 100 nm and exhibit a remarkable colloidal stability with respect to ionic strength and concentration variations. Solid films with thicknesses up to several hundreds of micrometers were cast from solutions, resulting in a bulk polymer matrix in which nanoparticle clusters are dispersed and immobilized. It was found in addition that the structure of the complexes remains practically unchanged during film casting.