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.

Interaction of 6,6′′-bis(5,5,8,8-tetramethyl-5,6,7,8-tetrahydro-1,2,4-benzotriazin-3-yl)-2,2′:6′,2′′-terpyridine (CyMe4-BTTP) with some trivalent ions such as lanthanide(iii) ions and americium(iii)

The new ligand 6,6 ''-bis(5,5,8,8-tetramethyl-5,6,7,8-tetrahydro-1,2,4-benzotriazin-3-yl)2,2':6 ',2 ''-terpyridine (CyMe4-BTTP) has been synthesized in 4 steps from 2,2':6',2 ''-terpyridine. Detailed NMR and mass spectrometry studies indicate that the ligand forms 1 : 2 complexes with lanthanide(III) perchlorates where the aliphatic rings are conformationally constrained whereas 1 : 1 complexes are formed with lanthanide(III) nitrates where the rings are conformationally mobile. An optimized structure of the 1 : 2 solution complex with Yb(III) was obtained from the relative magnitude of the induced paramagnetic shifts. X-Ray crystallographic structures of the ligand and of its 1 : 1 complex with Y(III) were also obtained. The NMR and mass spectra of [Pd(CyMe4-BTTP)](n)(2n+) are consistent with a dinuclear double helical structure (n = 2). In the absence of a phase-modifier, CyMe4-BTTP in n-octanol showed a maximum distribution coefficient of Am(III) of 0.039 (+/-20%) and a maximum separation factor of Am(III) over Eu(III) of 12.0 from nitric acid. The metal(III) cations are extracted as the 1 : 1 complex from nitric acid. The generally low distribution coefficients observed compared with the BTBPs arise because the 1 : 1 complex of CyMe4-BTTP is considerably less hydrophobic than the 1 : 2 complexes formed by the BTBPs. In M(BTTP)(3+) complexes, there is a competition between the nitrate ions and the ligand for the complexation of the metal.

Hydrogen bonded supramolecular elastomers : correlating hydrogen bonding strength with morphology and rheology

A series of six low molecular weight elastomers with hydrogen bonding end-groups have been designed, synthesised and studied. The poly(urethane) based elastomers all contained essentially the same hard block content (ca. 11%) and differ only in the nature of their end-groups. Solution state 1H NMR spectroscopic analysis of model compounds featuring the end-groups demonstrate that they all exhibit very low binding constants, in the range 1.4 to 45.0 M-1 in CDCl3, yet the corresponding elastomers each possess a markedly different nanoscale morphology and rheology in the bulk. We are able to correlate small variations of the binding constant of the end-groups with dramatic changes in the bulk properties of the elastomers. These results provide an important insight into the way in which weak non-covalent interactions can be utilized to afford a range of self-assembled polyurethane based materials that feature different morphologies.

Self-assembly of a designed amyloid peptide containing the functional thienylalanine unit

The self-assembly of a peptide based on a sequence from the amyloid beta peptide but incorporating the non-natural amino acid beta-2-thienylalanine (2-Thi) has been investigated in aqueous and methanol solutions. The peptide AAKLVFF was used as a design motif, replacing the phenylalanine residues (F) with 2-Thi units to yield (2-Thi)(2-Thi)VLKAA. The 2-Thi residues are expected to confer interesting electronic properties due to charge delocalization and pi-stacking. The peptide is shown to form beta-sheet-rich amyloid fibrils with a twisted morphology, in both water and methanol solutions at sufficiently high concentration. The formation of a self-assembling hydrogel is observed at high concentration. Detailed molecular modeling using molecular dynamics methods was performed using NOE constraints provided by 2D-NMR experiments. The conformational and charge properties of 2-Thi were modeled using quantum mechanical methods, and found to be similar to those previously reported for the beta-3-thienylalanine analogue. The molecular dynamics simulations reveal well-defined folded structures (turn-like) in dilute aqueous solution, driven by self-assembly of the hydrophobic aromatic units, with charged lysine groups exposed to water.

Induced-fit binding of π-electron donor substrates to macrocyclic aromatic ether-imide-sulfones: a versatile approach to molecular assembly

Novel macrocyclic receptors which bind electron-donor aromatic substrates via π-stacking donor- acceptor interactions are obtained by cyclo-imidization of an amine-functionalized arylether-sulfone with pyromellitic- and 1,4,5,8-naphthalene-tetracarboxylic dianhydrides. These macrocycles complex with a wide variety of π-donor substrates including tetrathiafulvalene, naphthalene, anthracene, pyrene, perylene, and functional derivatives of these polycyclic hydrocarbons. The resulting supramolecular assemblies range from simple 1:1 complexes, to [2]- and [3]-pseudorotaxanes, and even (as a result of crystallographic disorder) an apparent polyrotaxane. Direct, five-component self-assembly of a metal-centred [3]pseudorotaxane is also observed, on complexation of a macrocyclic ether-imide with 8-hydroxyquinoline in the presence of palladium(II) ions. Binding studies in solution were carried out by 1H NMR and UV-visible spectroscopy, and the stoichiometries of binding were confirmed by Job plots based on charge-transfer absorption bands. The highest association constants are found for strong π-donor guests with large surface-areas, notably perylene and 1-hydroxypyrene, for which Ka values of 1.4 x 103 and 2.3 x 103 M-1 respectively are found. Single crystal X-ray analyses of the receptors and their derived complexes reveal large, induced-fit distortions of the macrocyclic frameworks as a result of complexation. These structures provide compelling evidence for the existence of strong, attractive forces between the electronically-complementary aromatic π-systems of host and guest.

Synthesis, x-ray structure and anion binding properties of a cryptand-like hybrid calixpyrrole

The novel cryptand in/out-3, containing two tripyrrolemethane units briged by three 1,3- diisopropylidenbenzene arms was readily synthesized by a convergent three-step synthesis. It binds fluoride by inclusion with excellent selectivity with respect to a number of other tested anions. The structure of the free receptor and that of its fluoride complex were investigated in solution by NMR spectroscopy. The solid state X-ray structure of the free cryptand 3 was also determined.

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.

NMR studies of the conformational effect of single and double 3'-S-phosphorothiolate substitutions within deoxythymidine trinucleotides

NMR spectroscopy has been used to investigate the conformational effects of single and two consecutive 3′-S-phosphorothiolate modifications within a deoxythymidine trinucleotide. The presence of a single 3′-phosphorothioate modification shifts the conformation of the sugar ring it is attached to, from a mainly south to north pucker; this effect is also transmitted to the 3′-neighbour deoxyribose. This transmission is thought to be caused by favourable stacking of the heterocyclic bases. Similar observations have been made previously by this group. When two adjacent modifications are present, the conformations of the attached deoxyribose rings are again shifted almost completely to the north, however, there is no transmission to the 3′ deoxyribose ring. Base proton chemical shift analysis and molecular modelling have been used to aid elucidation of the origin of this feature. The observation for the dimodified sequence is consistent with our previously reported results for a related system in which spaced modifications are more thermodynamically stable than consecutive ones.

Synthesis, X-ray crystal structures and properties of complex salts and sterically crowded heteroleptic complexes of group 10 metal ions with aromatic sulfonyl dithiocarbimates and triphenylphosphine ligand

Two new complex salts of the form (Bu4N)(2)[Ni(L)(2)] (1) and (Ph4P)(2)[Ni(L)(2)] (2) and four heteroleptic complexes cis-M(PPh3)(2)(L) [M = Ni(II) (3), Pd(II) (4), L = 4-CH3OC6H4SO2N=CS2] and cis-M(PPh3)(2)(L') [M = Pd(II) (5), Pt(II) (6), L' = C6H5SO2N=CS2] were prepared and characterized by elemental analyses, IR, H-1, C-13 and P-31 NMR and UV-Vis spectra, solution and solid phase conductivity measurements and X-ray crystallography. A minor product trans-Pd(PPh3)(2)(SH)(2), 4a was also obtained with the synthesis of 4. The NiS4 and MP2S2 core in the complex salts and heteroleptic complexes are in the distorted square-plane whereas in the trans complex, 4a the centrosymmetric PdS2P2 core is perforce square planar. X-ray crystallography revealed the proximity of the ortho phenyl proton of the PPh3 ligand to Pd(II) showing rare intramolecular C-H center dot center dot center dot Pd anagostic binding interactions in the palladium cis-5 and trans-4a complexes. The complex salts with sigma(rt) values similar to 10 (5) S cm (1) show semi-conductor behaviors. The palladium and platinum complexes show photoluminescence properties in solution at room temperature.