Robust chiral zirconium alkoxide initiators for the room-temperature stereoselective ring-opening polymerisation of rac-lactide

Chiral Schiff bases (1H to 4H) and a series of their Group 4 metal alkoxide complexes [(R-1)2Ti(O(i)Pr)2, (R-2)2Ti(O(i)Pr)2, (R-1)(2)Zr(O(i)Pr)2, (R-2)2Zr(O(i)Pr)2, (R-3)2Zr(O(i)Pr)2, (R-4)2Zr(O(i)Pr)2, (S-1)2Zr(O(i)Pr)2 and (rac-1)2Zr(O(i)Pr)2] have been prepared and characterised by 1H, and 13C NMR spectroscopy. In solution, both Lambda and Delta isomers were observed, suggesting a low degree of chiral induction from the ligand. One ligand (R-4H) and three complexes [Delta-(R,R-2)2Ti(O(i)Pr)2, Lambda-(R,R-1)2Zr(O(i)Pr)2 and Delta-(R,R-3)2Zr(O(i)Pr)2] have also been characterised by single crystal X-ray diffraction. All complexes were found to have a pseudo-octahedral alpha-cis geometry. The complexes were tested as initiators for the ring-opening polymerisation of rac-lactide in solution and in the melt. The titanium complexes are inactive in solution and afford atactic polylactide in the melt. Zr(iv) complexes afford heterotactically enriched polylactide both in toluene solution (at 20 degrees C and 80 degrees C) and in the melt. Polymerisations were generally found to be well-controlled, giving predictable molecular weights and low molecular weight distributions. Ligand variation (substituents and/or chirality) has little effect on either the activity or selectivity of initiators. Zirconium initiators were found to be unusually robust as they were able to maintain well-controlled polymerisation following addition of water to reactions in solution and when using unpurified monomer for reactions in the melt.     

New connections between finite element formulations of the Navier–Stokes equations

We show the velocity solutions to the convective, skew-symmetric, and rotational Galerkin finite element formulations of the Navier–Stokes equations are identical if Scott–Vogelius elements are used, and thus all three formulations will be the same pointwise divergence free solution velocity. A connection is then established between the formulations for grad-div stabilized Taylor–Hood elements: under mild restrictions, the formulations’ velocity solutions converge to each other (and to the Scott–Vogelius solution) as the stabilization parameter tends to infinity. Thus the benefits of using Scott–Vogelius elements can be obtained with the less expensive Taylor–Hood elements, and moreover the benefits of all the formulations can be retained if the rotational formulation is used. Numerical examples are provided that confirm the theory.     

Real meromorphic functions and linear differential polynomials

We determine all real meromorphic functions f in the plane such that f has finitely many zeros, the poles of f have bounded multiplicities, and f and F have finitely many non-real zeros, where F is a linear differential polynomial given by F = f (k) +Σk-1j=0ajf(j) , in which k≥2 and the coefficients aj are real numbers with a0≠0.     

The development of a thermal neutron activation (TNA) system as a confirmatory non-metallic land mine detector

In order to detect and locate buried landmines for peacekeeping, the Canadian Department of National Defence (DND), under the Improved Landmine Detection Project, is developing a vehicle-mounted, two-phase mine detection system. The first phase constitutes a suite of detectors used to indicate the possibility of a mine at a particular location (to ±30 cm in accuracy). In the second phase a Thermal Neutron Activation (TNA) system is used to confirm the presence of explosives via detection of the 10.83 MeV gamma-ray associated with nitrogen decay. The TNA system developed for this uses a 100 μg²⁵²Cf neutron source surrounded by four 3″×3″ NaI(Tl) detectors. Combining the use of state-of-the art radiation transport codes for design, judicious choice of specialized shielding materials and development of high-rate, fast-pulse processing electronics, has led to a system which can; (i) confirm the presence of all surface- or lightly-buried anti-tank mines in a few seconds to a minute (depending on mass of explosive), (ii) confirm the presence of anti-tank mines down to 20 cm depth in less than 5 minutes, (iii) confirm the presence of large (>100 g nitrogen) anti-personnel mines in less than five minutes, (iv) operate in adverse climatic conditions. These results have been verified in field trials and the system is due to be fielded in 1999.     

Enforcing energy, helicity and strong mass conservation in finite element computations for incompressible Navier-Stokes simulations

We study a finite element scheme for the 3D Navier-Stokes equations (NSE) that globally conserves energy and helicity and, through the use of Scott-Vogelius elements, enforces pointwise the solenoidal constraints for velocity and vorticity. A complete numerical analysis is given, including proofs for conservation laws, unconditional stability and optimal convergence. We also show the method can be efficiently computed by exploiting a connection between this method, its associated penalty method, and the method arising from using grad-div stabilized Taylor-Hood elements. Finally, we give numerical examples which verify the theory and demonstrate the effectiveness of the scheme.     

Boundary conditions for hemodynamics: The structured tree revisited

The structured tree boundary condition is a physiologically-based outflow boundary condition used in hemodynamics. We propose an alternative derivation that is considerably simpler than the original one and yields similar, but not identical, results. We analyze the sensitivity of this boundary condition to its parameters and discuss its domain of validity. Several implementation issues are discussed and tested in the case of arterial flow in the Circle of Willis. Additionally, we compare results obtained from the structured tree boundary condition to the Windkessel boundary condition and measured data.     

The acid dissolution of sulfide mineral samples under pressure in a microwave oven

A system for the rapid dissolution of sulfide samples from mines, mills and smelters is described. The samples and an acid mixture are placed in sealed teflon-PFA vessels, which are then heated in a microwave oven for 3 min. Following the dissolution, metals of interest (copper and nickel) are quantified by atomic absorption spectrometry. The system described produces significant savings in time and materials and increased output and efficiency in comparison with traditional methods; it is also much cleaner. Results are similar to those obtained with a more conventional dissolution method     

The origin of nuclear magnetism in solid He films: determination of multi-spin exchange frequencies

Solid ³He films adsorbed on graphite display remarkable magnetic properties due to quantum exchange, reduced dimensionality and frustration. We discuss the relevance of the multiple spin exchange Hamiltonian to describe these systems. Our high precision NMR data and the results of heat capacity measurements performed in other laboratories allow us to unambiguously determine the most significant multi-spin exchange frequencies. This result gives a quantitative understanding of the thermodynamical properties of solid ³He films, explaining the evolution from a pure Heisenberg behavior at high areal densities to a novel spin liquid state at low coverages.