A similarity solution for a shock reflection problem in isentropic gas dynamics

A one-dimensional shock-reflection test problem in the case of slab, cylindrical, or spherical symmetry is discussed. The differential equations for a similarity solution are derived and solved numerically in conjunction with the Rankie-Hugoniot shock relations.

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.

A refined LEED analysis of water on Ru{0001}: an experimental test of the partial dissociation model

Despite a number of earlier studies which seemed to confirm molecular adsorption of water on close-packed surfaces of late transition metals, new controversy has arisen over a recent theoretical work by Feibelman, according to which partial dissociation occurs on the Ru{0001} surface leading to a mixed (H2O + OH + H) superstructure. Here, we present a refined LEED-IV analysis of the (root3 x root3)R30degrees-D2O-Ru{0001} structure, testing explicitly this new model by Feibelman. Our results favour the model proposed earlier by Held and Menzel assuming intact water molecules with almost coplanar oxygen atoms and out-of-plane hydrogen atoms atop the slightly higher oxygen atoms. The partially dissociated model with an almost identical arrangement of oxygen atoms can, however, not unambiguously be excluded, especially when the single hydrogen atoms are not present in the surface unit cell. In contrast to the earlier LEED-IV analysis, we can, however, clearly exclude a buckled geometry of oxygen atoms.

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.

Comparing tube models for predicting the linear rheology of branched polymer melts

The hierarchical and "bob" (or branch-on-branch) models are tube-based computational models recently developed for predicting the linear rheology of general mixtures of polydisperse branched polymers. These two models are based on a similar tube-theory framework but differ in their numerical implementation and details of relaxation mechanisms. We present a detailed overview of the similarities and differences of these models and examine the effects of these differences on the predictions of the linear viscoelastic properties of a set of representative branched polymer samples in order to give a general picture of the performance of these models. Our analysis confirms that the hierarchical and bob models quantitatively predict the linear rheology of a wide range of branched polymer melts but also indicate that there is still no unique solution to cover all types of branched polymers without case-by-case adjustment of parameters such as the dilution exponent alpha and the factor p(2) which defines the hopping distance of a branch point relative to the tube diameter. An updated version of the hierarchical model, which shows improved computational efficiency and refined relaxation mechanisms, is introduced and used in these analyses.

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.

Detecting the number of signals using antenna array: a single threshold solution

A new approach is presented to identify the number of incoming signals in antenna array processing. The new method exploits the inherent properties existing in the noise eigenvalues of the covariance matrix of the array output. A single threshold has been established concerning information about the signal and noise strength, data length, and array size. When the subspace-based algorithms are adopted the computation cost of the signal number detector can almost be neglected. The performance of the threshold is robust against low SNR and short data length.

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.

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.