A comparison of sequential Delaunay triangulation algorithms

This paper presents an experimental comparison of a number of different algorithms for computing the Delaunay triangulation. The algorithms examined are: Dwyer's divide and conquer algorithm, Fortune's sweepline algorithm, several versions of the incremental algorithm (including one by Ohya, Iri and Murota, a new bucketing-based algorithm described in this paper, and Devillers's version of a Delaunay-tree based algorithm that appears in LEDA), an algorithm that incrementally adds a correct Delaunay triangle adjacent to a current triangle in a manner similar to gift wrapping algorithms for convex hulls, and Barber's convex hull based algorithm.

Most of the algorithms examined are designed for good performance on uniformly distributed sites. However, we also test implementations of these algorithms on a number of non-uniform distributions. The experiments go beyond measuring total running time, which tends to be machine-dependent. We also analyze the major high-level primitives that algorithms use and do an experimental analysis of how often implementations of these algorithms perform each operation.     

Hydrogenation of

The course of the hydrogenation of [5]- and [6]metacyclophane (1b and 1c) and their thermochemistry is described. Both compounds are hydrogenated rapidly (within 10 s) to furnish the bridgehead olefins 13b and 12c. The accompanying hydrogenation enthalpies are -220 and -141 kJmol(-1), respectively. Strain energies (SE) and olefinic strains (OS) of a number of bridgehead olefins have been evaluated by DFT calculations; it was concluded that 13b belongs to the class of hyperstable olefins which correlates nicely with its reluctance to undergo hydrogenation. By combining experimental hydrogenation enthalpies and DFT calculations, SE of 187 and 121 kJmol(-1) were derived for 1b and 1c.     

Behaviour of a confined fire located in an unventilated zone

The behaviour of a fire in an enclosure is studied for a configuration where the fuel source is located in the upper hot unventilated zone trapped by a soffit. The experimental study, undertaken in a laboratory-scale compartment with a fuel source above the level of a soffit, included the determination of the parameters (ventilation factor, rate of fuel supply) controlling the combustion or leading to extinction. Measurements (PIV, thermocouples, gas sampling and analysis) were performed to propose a hypothesis on the structure of the flame (flame stabilisation mechanisms, premixed or diffusion types). Video photography is used to determine the area covered by the flames. This information is used as a criterion to identify the combustion regimes. The results show that the gaseous fuel is diluted in the combustion products (CP) in the upper layer and that a recirculatory motion is formed, driven by buoyancy forces, which enhances the mixing of fuel and CP. These then travel horizontally towards the vent along the interface between the lower fresh air and upper zones, and are premixed with the convected air in the enclosure, before entering the reaction zone and being burnt. The flame stabilises at the interface between the upper hot and lower ventilated layers in the compartment. The observed “ghosting flame” is stabilised by a triple flame if the flame speed of the premixed flame is higher than the natural convection velocity induced in the compartment. The flame stability is quantified by a criterion based on the area of the horizontal flame. It has been observed that the combustion is controlled by the available mass fuel flux at the reaction zone if the ventilation is sufficient. This information is essential for the modelling of the phenomena involved in fires with such an underventilated fuel source.     

The Riemann problem for a generalized Burgers equation with spatially decaying sound speed. I Large-time asymptotics

In this paper, we consider the classical Riemann problem for a generalized Burgers equation, $$u_t+h_{\alpha }(x)u{u}_x=u_{xx},$$ with a spatially dependent, nonlinear sound speed, $h_{\alpha }(x)\equiv {(1+x^2)}^{-\alpha }$ with $\alpha >0$, which decays algebraically with increasing distance from a fixed spatial origin. When $\alpha =0$, this reduces to the classical Burgers equation. In this first part of a pair of papers, we focus attention on the large-time structure of the associated Riemann problem, and obtain its detailed structure, as $t\to \infty$, via the method of matched asymptotic coordinate expansions (this uses the classical method of matched asymptotic expansions, with the asymptotic parameters being the independent coordinates in the evolution problem; this approach is developed in detail in the monograph of Leach and Needham, as referenced in the text), over all parameter ranges. We identify a significant bifurcation in structure at $\alpha =\frac{1}{2}$.