Numerical solution of some nonlocal, nonlinear dispersive wave equations

We use a spectral method to solve numerically two nonlocal, nonlinear, dispersive, integrable wave equations, the Benjamin-Ono and the Intermediate Long Wave equations. The proposed numerical method is able to capture well the dynamics of the solutions; we use it to investigate the behaviour of solitary wave solutions of the equations with special attention to those, among the properties usually connected with integrability, for which there is at present no analytic proof. Thus we study in particular the resolution property of arbitrary initial profiles into sequences of solitary waves for both equations and clean interaction of Benjamin-Ono solitary waves. We also verify numerically that the behaviour of the solution of the Intermediate Long Wave equation as the model parameter tends to the infinite depth limit is the one predicted by the theory.

The demand for a healthy diet: estimating the almost ideal demand system with infrequency of purchase

A Bayesian method of estimating multivariate sample selection models is introduced and applied to the estimation of a demand system for food in the UK to account for censoring arising from infrequency of purchase. We show how it is possible to impose identifying restrictions on the sample selection equations and that, unlike a maximum likelihood framework, the imposition of adding up at both latent and observed levels is straightforward. Our results emphasise the role played by low incomes and socio-economic circumstances in leading to poor diets and also indicate that the presence of children in a household has a negative impact on dietary quality.

Overseas trained teachers: part of a problem or part of a solution?

Overseas trained teachers (OTTs) have grown in numbers during the past decade, particularly in London and the South East of England. In this recruitment explosion many OTTs have experienced difficulties. In professional literature as well as press coverage OTTs often become part of a deficit discourse. A small-scale pilot investigation of OTT experience has begun to suggest why OTTs have been successful as well as the principal challenges they have faced. An important factor in their success was felt to be the quality of support in school from others on the staff. Major challenges included the complexity of the primary curriculum. The argument that globalisation leads to brain-drain may be exaggerated. Suggestions for further research are made, which might indicate the positive benefits OTTs can bring to a school.

SARS coronavirus unique domain: three-domain molecular architecture in solution and RNA binding

Nonstructural protein 3 of the severe acute respiratory syndrome (SARS) coronavirus includes a "SARS-unique domain" (SUD) consisting of three globular domains separated by short linker peptide segments. This work reports NMR structure determinations of the C-terminal domain (SUD-C) and a two-domain construct (SUD-MC) containing the middle domain (SUD-M) and the C-terminal domain, and NMR data on the conformational states of the N-terminal domain (SUD-N) and the SUD-NM two-domain construct. Both SUD-N and SUD-NM are monomeric and globular in solution; in SUD-NM, there is high mobility in the two-residue interdomain linking sequence, with no preferred relative orientation of the two domains. SUD-C adopts a frataxin like fold and has structural similarity to DNA-binding domains of DNA-modifying enzymes. The structures of both SUD-M (previously determined) and SUD-C (from the present study) are maintained in SUD-MC, where the two domains are flexibly linked. Gel-shift experiments showed that both SUD-C and SUD-MC bind to single-stranded RNA and recognize purine bases more strongly than pyrimidine bases, whereby SUD-MC binds to a more restricted set of purine-containing RNA sequences than SUD-M. NMR chemical shift perturbation experiments with observations of (15)N-labeled proteins further resulted in delineation of RNA binding sites (i.e., in SUD-M, a positively charged surface area with a pronounced cavity, and in SUD-C, several residues of an anti-parallel beta-sheet). Overall, the present data provide evidence for molecular mechanisms involving the concerted actions of SUD-M and SUD-C, which result in specific RNA binding that might be unique to the SUD and, thus, to the SARS coronavirus.

Multiple sol-gel transitions of PEG-PCL-PEG triblock copolymer aqueous solution

An aqueous solution of a poly(ethylene glycol)-polycaprolactone-poly(ethylene glycol) (PEG-PCL-PEG) with a composition of EG13CL23EG13 undergoes multiple transitions, from sol-to-gel (hard gel)-to-sol-to-gel (soft gel)-to-sol, in the concentration range 20.0∼35.0 wt.-%. Through dynamic mechanical analysis, UV-vis spectrophotometry, small angle X-ray scattering, differential scanning calorimetry, microcalorimetry and 13C NMR spectroscopy, the mechanism of these transitions was investigated. The hard gel and soft gel are distinguished by the crystalline and amorphous state of the PCL. The extent of PEG dehydration and the molecular motion of each block also played a critical role in the multiple transitions. This paper suggests a new mechanism for these multiple transitions driven by temperature changes.

Unusually high differential attenuation at C band: Results from a two-year analysis of the French Trappes polarimetric radar data

The differential phase (ΦDP) measured by polarimetric radars is recognized to be a very good indicator of the path integrated by rain. Moreover, if a linear relationship is assumed between the specific differential phase (KDP) and the specific attenuation (AH) and specific differential attenuation (ADP), then attenuation can easily be corrected. The coefficients of proportionality, γH and γDP, are, however, known to be dependent in rain upon drop temperature, drop shapes, drop size distribution, and the presence of large drops causing Mie scattering. In this paper, the authors extensively apply a physically based method, often referred to as the “Smyth and Illingworth constraint,” which uses the constraint that the value of the differential reflectivity ZDR on the far side of the storm should be low to retrieve the γDP coefficient. More than 30 convective episodes observed by the French operational C-band polarimetric Trappes radar during two summers (2005 and 2006) are used to document the variability of γDP with respect to the intrinsic three-dimensional characteristics of the attenuating cells. The Smyth and Illingworth constraint could be applied to only 20% of all attenuated rays of the 2-yr dataset so it cannot be considered the unique solution for attenuation correction in an operational setting but is useful for characterizing the properties of the strongly attenuating cells. The range of variation of γDP is shown to be extremely large, with minimal, maximal, and mean values being, respectively, equal to 0.01, 0.11, and 0.025 dB °−1. Coefficient γDP appears to be almost linearly correlated with the horizontal reflectivity (ZH), differential reflectivity (ZDR), and specific differential phase (KDP) and correlation coefficient (ρHV) of the attenuating cells. The temperature effect is negligible with respect to that of the microphysical properties of the attenuating cells. Unusually large values of γDP, above 0.06 dB °−1, often referred to as “hot spots,” are reported for 15%—a nonnegligible figure—of the rays presenting a significant total differential phase shift (ΔϕDP > 30°). The corresponding strongly attenuating cells are shown to have extremely high ZDR (above 4 dB) and ZH (above 55 dBZ), very low ρHV (below 0.94), and high KDP (above 4° km−1). Analysis of 4 yr of observed raindrop spectra does not reproduce such low values of ρHV, suggesting that (wet) ice is likely to be present in the precipitation medium and responsible for the attenuation and high phase shifts. Furthermore, if melting ice is responsible for the high phase shifts, this suggests that KDP may not be uniquely related to rainfall rate but can result from the presence of wet ice. This hypothesis is supported by the analysis of the vertical profiles of horizontal reflectivity and the values of conventional probability of hail indexes.

A moving-mesh finite element method and its application to the numerical solution of phase-change problems

A distributed Lagrangian moving-mesh finite element method is applied to problems involving changes of phase. The algorithm uses a distributed conservation principle to determine nodal mesh velocities, which are then used to move the nodes. The nodal values are obtained from an ALE (Arbitrary Lagrangian-Eulerian) equation, which represents a generalization of the original algorithm presented in Applied Numerical Mathematics, 54:450--469 (2005). Having described the details of the generalized algorithm it is validated on two test cases from the original paper and is then applied to one-phase and, for the first time, two-phase Stefan problems in one and two space dimensions, paying particular attention to the implementation of the interface boundary conditions. Results are presented to demonstrate the accuracy and the effectiveness of the method, including comparisons against analytical solutions where available.

A new approach for the solution of the optimal set-point tracking problem for nonlinear systems

In this paper, a discrete time dynamic integrated system optimisation and parameter estimation algorithm is applied to the solution of the nonlinear tracking optimal control problem. A version of the algorithm with a linear-quadratic model-based problem is developed and implemented in software. The algorithm implemented is tested with simulation examples.

Dimorphosim of a dimethoxy bridged oxovanadium(v)-hydrazone complex

A monoclinic variety with C2/c space group of the title complex [(VO)-O-V(L)(OCH3)](2), incorporating the doubly deprotonated benzoyl hydrazone of 2-hydroxy-5-methylacetophenone (H2L) was synthesized from the decomposition of [(VO)-O-IV(L)(bipy)] (where bipy representing the 2,2'-bipyridine) in methanol which has been reported very recently from our laboratory In this paper we report another monoclinic variety of this complex with P2(1)/n space group that showed some differences in bonding patterns in the solid state (but in solution they are almost identical) prepared by different synthetic method viz, from the equimolar reaction of [(VO)-O-IV(acac)(2)], H2L and imidazole in CH3OH.

Synthesis, structure and solution chemistry of dioxidovanadium(V) complexes with a family of hydrazone ligands. Evidence of formation of centrosymmetric dimers via H-bonds in the solid state

[(VO)-O-IV(acac) 2] reacts with the methanol solution of tridentate ONO donor hydrazone ligands (H2L1-4, general abbreviation H2L; are derived from the condensation of benzoyl hydrazine with 2-hydroxyacetophenone and its 5-substituted derivatives) in presence of neutral monodentate alkyl amine bases having stronger basicity than pyridine e. g., ethylamine, diethylamine, triethylamine and piperidine (general abbreviation B) to produce BH+[VO2L] (1-16) complexes. Five of these sixteen complexes are structurally characterized revealing that the vanadium is present in the anionic part of the molecule, [VO2L] in a distorted square pyramidal environment. The complexes 5, 6, 15 and 16 containing two H-atoms associated with the amine-N atom in their cationic part (e. g., diethylammonium and piperidinium ion) are involved in H-bonding with a neighboring molecule resulting in the formation of centrosymmetric dimers while the complex 12 (containing only one hydrogen atom in the cationic part) exhibits normal H-bonding. The nature of the H-bonds in each of the four centrosymmetric dimeric complexes is different. These complexes have potential catalytic activity in the aerial oxidation of L-ascorbic acid and are converted into the [VO(L)(hq)] complexes containing VO3+ motif on reaction with equimolar amount of 8-hydroxyquinoline (Hhq) in methanol.

Puroindoline-a, a lipid binding protein from common wheat, spontaneously forms prolate protein micelles in solution

The self-assembly in solution of puroindoline-a (Pin-a), an amphiphilic lipid binding protein from common wheat, was investigated by small angle neutron scattering, dynamic light scattering and size exclusion chromatography. Pin-a was found to form monodisperse prolate ellipsoidal micelles with a major axial radius of 112 +/- 4.5 A ˚ and minor axial radius of 40.4 +/- 0.18 A ˚ . These protein micelles were formed by the spontaneous self-assembly of 38 Pin-a molecules in solution and were stable over a wide pH range (3.5–11) and at elevated temperatures (20–65 degC). Pin-a micelles could be disrupted upon addition of the non-ionic surfactant dodecyl-b-maltoside, suggesting that the protein self-assembly is driven by hydrophobic forces, consisting of intermolecular interactions between Trp residues located within a well-defined Trp-rich domain of Pin-a.