A critical evaluation of seven discretization schemes for convection–diffusion equations

A comparative study of seven discretization schemes for the equations describing convection-diffusion transport phenomena is presented. The (differencing) schemes considered are the conventional central- and upwind-difference schemes, together with the Leonard,¹ Leonard upwind¹ and Leonard super upwind difference¹ schemes. Also tested are the so called locally exact difference scheme² and the quadratic-upstream difference scheme.^3,4 In multidimensional problems errors arise from ‘false-diffusion’ and function approximations. It is asserted that false diffusion is essentially a multidimensional source of error. No mesh constraints are associated with errors in function approximation and discretization. Hence errors associated with discretization only may be investigated via one-dimensional problems. Thus, although the above schemes have been tested for one- and two-dimensional flows with sources, only the former are presented here. For 1D flows, the Leonard super upwind difference scheme and the locally exact scheme are shown to be far superior in accuracy to the others at all Peclet numbers and for most source distributions, for the test cases considered. Furthermore, the latter is shown to be considerably cheaper in computational terms than the former. The stability of the schemes and their CPU time requirements are also discussed.     

Precision branching ratio measurement for the superallowed beta+ emitter 62Ga and isospin-symmetry-breaking corrections in A>or=62 nuclei

A high-precision branching ratio measurement for the superallowed beta+ decay of 62Ga was performed at the Isotope Separator and Accelerator radioactive ion beam facility. Nineteen gamma rays emitted following beta+ decay of 62Ga were identified, establishing the dominant superallowed branching ratio to be (99.861+/-0.011)%. Combined with recent half-life and Q-value measurements, this branching ratio yields a superallowed ft value of 3075.6+/-1.4 s for 62Ga decay. These results demonstrate the feasibility of high-precision superallowed branching ratio measurements in the A>or=62 mass region and provide the first stringent tests of the large isospin-symmetry-breaking effects predicted for these decays.     

High-field NMR using resistive and hybrid magnets

Resistive and resistive-superconducting hybrid magnets can generate dc magnetic fields much higher than conventional superconducting NMR magnets but the field spatial homogeneity and temporal stability are usually not sufficient for high-resolution NMR experiments. Hardware and technique development addressing these issues are presented for high-resolution NMR at magnetic fields up to 40T. Passive ferromagnetic shimming and magic-angle spinning are used effectively to reduce the broadening from inhomogeneous magnetic field. A phase correction technique based on simultaneous heteronuclear detection is developed to compensate magnetic field fluctuations to achieve high spectral resolution.     

Interpreting technical evidence from spectral imaging of paintings by Édouard Manet in the Courtauld Gallery

The paintings by Édouard Manet in The Courtauld Gallery Déjeuner sur l'herbe (1863–68), Marguerite de Conflans en Toilette de Bal (1870–1880), Banks of the Seine at Argenteuil (1874), and A Bar at the Folies–Bergère (1882) were investigated for the first time using a range of non-invasive in situ analyses. The aims of the study were to investigate the painting techniques and materials used for this group of works and to critically evaluate the technical evidence derived from the integrated use of imaging techniques and portable spectroscopic methods in this context. The paintings were investigated by means of macro X-ray fluorescence (MA-XRF), reflection spectral imaging, portable UV–Vis–NIR spectroscopy, portable Raman spectroscopy, and reflection FTIR. MA-XRF and reflection spectral imaging allowed visualising elements in the compositions that were not visible using traditional methods of technical study. For example, MA-XRF analysis of Déjeuner sur l'herbe revealed elements of the development of the composition that provided new evidence to consider its relationship to other versions of the composition. The study also highlighted questions about the interpretation of elemental distribution maps and spectral images that did not correspond to the reworking visible in X-radiographs. For example, in A Bar at the Folies–Bergère Manet made numerous changes during painting, which were not clearly visualised with any of the techniques used. The research has wider implications for the study of Impressionist paintings, as the results will support technical studies of works by other artists of the period who used similar materials and painting methods.     

Nonbelief and the Desire-As-Belief Thesis

I show the incompatibility of two theses: (a) to desire the truth of p amounts to believing a certain proposition about the value of p’s truth; (b) one cannot be said to desire the truth of p if one believes that p is true. Thesis (a), the Desire-As-Belief Thesis, has received much attention since the late 1980s. Thesis (b) is an epistemic variant of Socrates’ remark in the Symposium that one cannot desire what one already has. It turns out that (a) and (b) cannot both be true if it is possible for there to exist an agent who has a desire initially, say the desire for the truth of p, and then expands the corpus of propositions she believes to include p. This result provides a new route to the denial of (a).

Concise construction of novel bridged bicyclic lactams by sequenced Ugi/RCM/Heck reactions

Herein we report a concise protocol for the diastereoselective synthesis of novel bridged bicyclic lactams from commercially available components by the sequence of Ugi, ring-closing metathesis (RCM), and Heck reactions. X-ray diffraction studies revealed that the bicyclic products contain varying degrees of pyramidalization of the bridgehead nitrogen atom.     

Azobenzene-linked porphyrin-fullerene dyads

A new group of porphyrin-fullerene dyads with an azobenzene linker was synthesized, and the photochemical and photophysical properties of these materials were investigated using steady-state and time-resolved spectroscopic methods. The electrochemical properties of these compounds were also studied in detail. The synthesis involved oxidative heterocoupling of free base tris-aryl-p-aminophenyl porphyrins with a p-aminophenylacetal, followed by deprotection to give the aldehyde, and finally Prato 1,3-dipolar azomethineylide cycloaddition to C60. The corresponding Zn(II)-porphyrin (ZnP) dyads were made by treating the free base dyads with zinc acetate. The final dyads were characterized by their 1H NMR, mass, and UV-vis spectra. 3He NMR was used to determine if the products are a mixture of cis and trans stereoisomers, or a single isomer. The data are most consistent with the isolation of only a single configurational isomer, assigned to the trans (E) configuration. The ground-state UV-vis spectra are virtually a superimposition of the spectral features of the individual components, indicating there is no interaction of the fullerene (F) and porphyrin (H2P/ZnP) moieties in the ground state. This conclusion is supported by the electrochemical data. The steady-state and time-resolved fluorescence spectra indicate that the porphyrin fluorescence in the dyads is very strongly quenched at room temperature in the three solvents studied: toluene, tetrahydrofuran (THF), and benzonitrile (BzCN). The fluorescence lifetimes of the dyads in all solvents are sharply reduced compared to those of H2P and ZnP standards. In toluene, the lifetimes of the free base dyads are 600-790 ps compared to 10.1 ns for the standard, while in THF and BzCN the dyad lifetimes are less than 100 ps. For the ZnP dyads, the fluorescence lifetimes were 10-170 ps vs 2.1-2.2 ns for the ZnP references. The mechanism of the fluorescence quenching was established using time-resolved transient absorption spectroscopy. In toluene, the quenching process is singlet-singlet energy transfer (k approximately 10(11) s-1) to give C60 singlet excited states which decay with a lifetime of 1.2 ns to give very long-lived C60 triplet states. In THF and BzCN, quenching of porphyrin singlet states occurs at a similar rate, but now by electron transfer, to give charge-separated radical pair (CSRP) states, which show transient absorption spectra very similar to those reported for other H2P-C60 and ZnP-C60 dyad systems. The lifetimes of the CSRP states are in the range 145-435 ns in THF, much shorter than for related systems with amide, alkyne, silyl, and hydrogen-bonded linkers. Thus, both forward and back electron transfer is facilitated by the azobenzene linker. Nonetheless, the charge recombination is 3-4 orders of magnitude slower than charge separation, demonstrating that for these types of donor-acceptor systems back electron transfer is occurring in the Marcus inverted region.     

Novel surface treatments for glass fillers

Glass fillers were suface modified by direct formation of a silicon-carbon non-hydrolyzable linkage between glass and coupling agent. The grafted silane monolayer was evaluated by infrared spectroscopy. Samples were subjected to hydrolytic conditions to compare their surface treatment stability with traditional surface treatment hydrolytic stability. Composite specimens were fabricated and their mechanical properties were compared with traditional aminopropylsilane coupling agent treatment.     

14N Polarization Inversion Spin Exchange at Magic Angle (PISEMA)

Polarization Inversion Spin Exchange at Magic Angle (PISEMA) is a powerful experiment for determining peptide orientation in uniformly aligned samples such as planar membranes. In this paper, we present (14)N-PISEMA experiment which correlates (14)N quadrupolar coupling and (14)N-(1)H dipolar coupling. (14)N-PISEMA enables the use of (14)N quadrupolar coupling tensor as an ultra sensitive probe for peptide orientation and can be carried out without the need of isotope enrichment. The experiment is based on selective spin-exchange between a proton and a single-quantum transition of (14)N spins. The spin-exchange dynamics is described and the experiment is demonstrated with a natural abundant N-acetyl valine crystal sample.