Higher categories,strings, cubes and simplex equations

This survey of categorical structures, occurring naturally in mathematics, physics and computer science, deals with monoidal categories; various structures in monoidal categories; free monoidal structures; Penrose string notation; 2-dimensional categorical structures; the simplex equations of field theory and statistical mechanics; higher-order categories and computads; the (v,d)-cube equations; the simplex equations as cubical cocycle equations; and, cubes, braids and higher braids.     

A coupled multigrid-domain-splitting technique for simulating incompressible flows in geometrically complex domains

This paper describes a domain decomposition numerical procedure for solving the Navier-Stokes equations in regions with complex geometries. The numerical method includes a modified version of QUICK (quadratic upstream interpolation convective kinematics) for the formulation of convective terms and a central difference scheme for the diffusion terms. A second-order-accurate predictor-corrector scheme is employed for the explicit time stepping. Although the momentum equations are solved independently on each subdomain, the pressure field is computed simultaneously on the entire flow field. A multigrid technique coupled with a Schwarz-like iteration method is devised to solve the pressure equation over the composite domains. The success of this strategy depends crucially on appropriate methods for specifying intergrid pressure boundary conditions on subdomains. A proper method for exchanging information among subdomains during the Schwarz sweep is equally important to the success of the multigrid solution for the overall pressure field. These methods are described and subsequently applied to two forced convection flow problems involving complex geometries to demonstrate the power and versatility of the technique. The resulting pressure and velocity fields exhibit excellent global consistency. The ability to simulate complex flow fields with this method provides a powerful tool for analysis and prediction of mixing and transport phenomenon.     

Synthesis of conformationally constrained benzoylureas as BH3-mimetics

The design of small molecules that mimic the BH3 domain and bind to Bcl-2 proteins has emerged as a promising approach to discovering novel anti-cancer therapeutics. We reveal the design and synthesis of conformationally constrained benzoylurea scaffolds as conformational probes. Central to helix mimicry, the intramolecular hydrogen bond in the benzoylurea plays a key role in the pre-organisation of the acyclic substrates for cyclisation via ring closing metathesis, providing efficient access to the constrained mimetics.     

Doubling and Tripling Constructions for Defining Sets in Steiner Triple Systems

 A minimal defining set of a Steiner triple system on v points (STS(v)) is a partial Steiner triple system contained in only this STS(v), and such that any of its proper subsets is contained in at least two distinct STS(v)s. We consider the standard doubling and tripling constructions for STS(2v+1) and STS(3v) from STS(v) and show how minimal defining sets of an STS(v) gives rise to minimal defining sets in the larger systems. We use this to construct some new families of defining sets. For example, for Steiner triple systems on 3 ⁿ points, we construct minimal defining sets of volumes varying by as much as 7 ⁿ⁻² . Received: September 16, 2000 Final version received: September 13, 2001 RID="*" ID="*" Research supported by the Australian Research Council A49937047, A49802044     

Spectroscopic analysis of the tribological behavior of a model boundary layer lubricant

Highly ordered alkanethiol self-assembled monolayers (SAMs) on gold substrates are suitable models of boundary layer lubricants and may be used in actual nanoscale device applications. Here, such monolayers were studied by spectroscopic methods as a function of tribological wear (rubbing) using a pin-on-disk microtribometer. The coefficient of friction (COF) (ratio of the frictional force to the load) was measured with the tribometer, and reflectance infrared spectra and X-ray photoelectron spectra were obtained as the monolayer film failed and the COF changed. The results show that it is possible to correlate disorder in the monolayer film with tribological failure of the film, and that continued rubbing produces a chemical change in the monolayer film. Disorder in the monolayer is distinct from the influence of wear in the underlying gold substrate. Aged SAMs, having sulfonate rather than thiol headgroups and initially less well ordered, behave differently to the well-ordered freshly prepared SAMs. Interestingly, they show a lower COF over many more cycles of exposure to the rubbing pin. The impact of the mechanism of film failure in boundary layer lubrication is discussed.     

Phototransport effects in polyacetylene, (CH)x

We have made the first comprehensive measurements of the photovoltaic and photoconductivity effects in polyacetylene in that we have extended the spectral range originally covered by Matsui and Nakamura [17] to include the visible region as well. The photovoltaic experiments were done on Schottky barrier junctions formed between AsF₅ lightly-doped p-type trans-(CH)_x and a low work function metal, the first junctions of this type to be produced in semiconducting polyacetylene. The observation of a photovoltaic response threshold at 1.48 eV provides the first definitive measurement of the single-particle band gap in trans-(CH)_x. In addition, we have found the existence of a peak at 1.35 eV in the photoconductivity spectrum of undoped trans-(CH)_x which may be due either to extrinsic sources or to thermal dissociation of a weakly bound Wannier exciton.     

A composite multigrid method for calculating unsteady incompressible flows in geometrically complex domains

A time-accurate, finite volume method for solving the three-dimensional, incompressible Navier-Stokes equations on a composite grid with arbitrary subgrid overlapping is presented. The governing equations are written in a non-orthogonal curvilinear co-ordinate system and are discretized on a non-staggered grid. A semi-implicit, fractional step method with approximate factorization is employed for time advancement. Multigrid combined with intergrid iteration is used to solve the pressure Poisson equation. Inter-grid communication is facilitated by an iterative boundary velocity scheme which ensures that the governing equations are well-posed on each subdomain. Mass conservation on each subdomain is preserved by using a mass imbalance correction scheme which is secondorder-accurate. Three test cases are used to demonstrate the method's consistency, accuracy and efficiency.     

Flow visualization of a recirculating flow by rheoscopic liquid and liquid crystal techniques

Experiments were conducted in a three-dimensional lid-driven cavity flow to study the behavior of longitudinal Taylor-Görtler-like vortices. Flow visualization was accomplished by use of a rheoscopic liquid and of liquid crystals, together with laser-light and white-light sheets, respectively. Photographs of the lighted planes in the flow confirmed the existence of the vortices for a wide range of Reynolds numbers and for stable, neutrally-buoyant and buoyant global flow conditions. As usual the flow visualization revealed flow patterns not deducible by in situ measurements; the liquid crystal photographs give both flow pathlines and temperature distribution on any lighted plane.