Controllability and asymptotic stabilization of the Camassa-Holm equation

We investigate the problems of exact controllability and asymptotic stabilization of the Camassa-Holm equation on the circle, by means of a distributed control. The results are global, and in particular the control prevents the solution from blowing up.     

Selective direct fluorination of quinoline derivatives

Direct fluorination of various quinoline derivatives in acidic reaction media gives fluorinated quinoline products arising from selective, efficient electrophilic substitution processes.     

Over forty years of continuous research at UTIAS on nonstationary flows and shock waves

Analytical and experimental research on non-stationary shock waves, rarefaction waves and contact surfaces has been conducted continuously at UTIAS since its inception in 1948. Some unique facilities were used to study the properties of planar, cylindrical and spherical shock waves and their interactions. Investigations were also performed on shock-wave structure and boundary layers in ionizing argon, water-vapour condensation in rarefaction waves, magnetogasdynamic flows, and the regions of regular and various types of Mach reflections of oblique shock waves. Explosively-driven implosions have been employed as drivers for projectile launchers and shock tubes, and as a means of producing industrial-type diamonds from graphite, and fusion plasmas in deuterium. The effects of sonic-boom on humans, animals and structures have also formed an important part of the investigations. More recently, interest has focussed on shock waves in dusty gases, the viscous and vibrational structure of weak spherical blast waves in air, and oblique shock-wave reflections. In all of these studies instrumentation and computational methods have played a very important role. A brief survey of this work is given herein and in more detail in the relevant references.This article was processed using Springer-Verlag T_EX Shock Waves macro package 1990.     

Self-assembled E(2)L(3) cryptands (E = P, As, Sb, Bi): transmetalation, homo- and heterometallic assemblies, and conformational isomerism

A series of Group 15-containing homometallic (E(2)L(3), E = P, As, Sb, Bi) and heterometallic (AsSbL(3), AsBiL(3), PSbL(3)) supramolecular cryptands were prepared by the self-assembly of pnictogen halides with dithiolate ligand or by direct transmetalation from a heavier congener. Structural characterization by single crystal X-ray diffraction shows that the E-S bond distances and S-E-S bond angles are significantly affected by the identity of the pnictogen. (1)H NMR spectroscopy reveals that the homometallic cryptands are dynamic in solution: surprisingly one ligand "flips", perturbing the C(3) symmetry of the complex and giving a new asymmetric conformer. Density functional theory calculations were carried out on both the symmetric and the asymmetric conformations of the cryptands, and the energies were compared to those observed by NMR spectroscopy. It was found that the relative stability of the asymmetric cryptand to its symmetric conformer increases with increasing size of the Group 15 element. Finally, it is reported that if two metals are present during the self-assembly process, heterometallic cryptands form. These supramolecular cryptands are reminiscent of their organic analogues, but result from a self-assembly process rather than a stepwise synthesis. Surprisingly, they possess conformational isomerism and exhibit dynamic transmetalation in their reactivity which provides access to otherwise unattainable assemblies.     

An oxidative coupling for the synthesis of arylated quaternary stereocentres and its application in the total synthesis of powelline and buphanidrine

Catechol derivatives directly bonded to all-carbon quaternary stereocentres are prevalent in nature. An oxidative coupling strategy for the synthesis of this motif is described. Pivoting on the base-catalysed Michael addition of carbon-centred pro-nucleophiles to in situ generated ortho-benzoquinones, the method is broad in scope, high yielding and provides remarkably simple access to this challenging motif. The application of this methodology in the total synthesis of the crinane-type amaryllidaceae alkaloids (±)-powelline and (±)-buphanidrine is demonstrated and our efforts towards an enantioselective synthesis described.     

NMR studies into colloidal stability and magnetic order in fatty acid stabilised aqueous magnetic fluids

We report the physico-chemical characterisation of fatty acid stabilised aqueous magnetic fluids, which are ideal systems for studying the influence of nanoparticle aggregation on the emergent magnetic resonance properties of the suspensions. Stable colloids of superparamagnetic magnetite, Fe(3)O(4), nanoparticle clusters in the 80 to 100 nm size range were produced by in situ nanoparticle growth and stabilisation, and by suspending pre-formed nanoparticles. NMR relaxation analysis shows that the magnetic resonance properties of the two types of suspension differ substantially and provides new insights into how the relaxation mechanisms are determined by the organisation of the nanoparticles within the clusters.     

Picosecond pulses from a cryogenically cooled, composite amplifier using Yb:YAG and Yb:GSAG

A cryogenic Yb amplifier using two laser materials, Gd3Sc2Al3O12 and Y3Al5O12 (YAG), has been used to obtain 70 W average power at 5 kHz pulse repetition frequency; the output was compressed to 1.6 ps, compared with an input compressible to 1.4 ps. The gain broadening obtained by combining two media enables shorter pulses than using Yb:YAG alone but retains the power-scaling advantages of cryogenic Yb:YAG.