Approximate Minimum Diameter

We study the minimum diameter problem for a set of inexact points. By inexact, we mean that the precise location of the points is not known. Instead, the location of each point is restricted to a contineus region (\impre model) or a finite set of points (\indec model). Given a set of inexact points in one of \impre or \indec models, we wish to provide a lower-bound on the diameter of the real points. In the first part of the paper, we focus on \indec model. We present an $O(2^{\frac{1}{\epsilon^d}} \cdot \epsilon^{-2d} \cdot n^3 )$ time approximation algorithm of factor $(1+\epsilon)$ for finding minimum diameter of a set of points in $d$ dimensions. This improves the previously proposed algorithms for this problem substantially. Next, we consider the problem in \impre model. In $d$-dimensional space, we propose a polynomial time $\sqrt{d}$-approximation algorithm. In addition, for $d=2$, we define the notion of $\alpha$-separability and use our algorithm for \indec model to obtain $(1+\epsilon)$-approximation algorithm for a set of $\alpha$-separable regions in time $O(2^{\frac{1}{\epsilon^2}}\allowbreak . \frac{n^3}{\epsilon^{10} .\sin(\alpha/2)^3} )$

Ceramics from the Whelan Site : a temporal and functional analysis of a Late Caddoan mound site assemblage

The vessel ceramics from the Whelan site, a Late Caddoan mound center in northeast Texas, are analyzed to determine the site's temporal placement and the functional implications of an assemblage from a ceremonial site. The first goal is handled through a typological study; the second is accomplished by a functional analysis of vessel batches, from which specific vessel shapes, size classes and inferred activities are determined. Intrasite activity differences are suggested by the distribution of these vessel batches. Intersite comparisons with other Late Caddoan mound sites reveal ceramics functionally similar to Whelan and suggest that cooking and storage were important activities at these sites.Anthropolog

Laser surface modification of steel

The presented work is an investigation of the laser surface modification of H13 tool steel using pulse laser processing mode. Initial screening experimental designs conducted lead to more optimised detailed designs. A carbon dioxide (CO2) laser system with 10.6 μm wavelength was used. In the experimental designs investigated three different sizes of laser spot used were 0.4, 0.2 and 0.09 mm diameter. The other controlled parameters were laser peak power, pulse repetition frequency and pulse overlap. The laser processing was constantly assisted by in line argon gas at 0.1 MPa pressure. H13 samples were roughened and chemically etched prior processing to improve the surface absorbance at the CO2 laser wavelength. Laser processed samples were prepared for metallographic study and were characterised for physical and mechanical properties. The metallographic study and chemical composition analysis were conducted using scanning electron microscope integrated with energy dispersive x-ray spectroscopy. The crystallinity and phase detection of the modified surface were conducted using an XRD system with Cu Kα radiation and wavelength of 1.54 Å. The surface profile was measured using stylus profilometry measuring systems. The hardness properties of the modified surface were measured by micro- Vickers diamond indentation. A customized thermal fatigue system was used to investigate the effect of surface roughness on the modified surface fatigue properties. A modified surface grain with an ultrafine size of less than 500 nm was observed to be achievable. A modified surface depth which ranged between 35 and 150 μm was developed on the laser processed H13 samples. A reduction of crystallinity was noticeable for the modified H13 surface which was related to the more random distribution of crystallites after laser processing. A minimum modified H13 average surface roughness, Ra, of 1.9 μm was achieved. Another important finding was that at different settings of laser parameters, the modified H13 surface exhibited a range of hardness between 728 and 905 HV0.1. A relationship between thermal simulations findings (heating and cooling rates) and hardness results was established for further understanding of the effects of the laser parameters. These findings are significant to the establishment of surface hardening techniques for wear resistance and thermal barrier coating applications

The design of a deep water catenary riser

The overall aim of this study is to propose and develop a cost effective production design concept suitable for oil reservoirs situated in deep (1500 m) water which can be quickly and safely installed in areas with limited weather windows. The proposed design is based upon a steel catenary riser which will connect an FPSO directly into either a wellhead or seabed pipeline system thereby eliminating both the connection complexes and high cost associated with a central manifold. The catenary geometry will ensure that the structure is inherently compliant whilst a carrier pipe arrangement will provide structural protection and buoyancy to a flowline bundle contained within. The interface between the riser and the surface production vessel is a critical part of any riser system and so for the purposes of this study two design arrangements are considered. The first is based upon a direct connection between an FPSO turret and riser whereas the second is a hybrid design in which the riser is supported by a sub-surface buoy which is hydraulically connected to an FPSO using flexible flowlines. This hybrid connection has the advantage of decoupling FPSO and riser motions. Design development is carried out by examining a range of critical areas