Incremental and Decremental Maintenance of Planar Width

We present an algorithm for maintaining the width of a planar point set dynamically, as points are inserted or deleted. Our algorithm takes time O(kn^epsilon) per update, where k is the amount of change the update causes in the convex hull, n is the number of points in the set, and epsilon is any arbitrarily small constant. For incremental or decremental update sequences, the amortized time per update is O(n^epsilon).Comment: 7 pages; 2 figures. A preliminary version of this paper was presented at the 10th ACM/SIAM Symp. Discrete Algorithms (SODA '99); this is the journal version, and will appear in J. Algorithm

Fully dynamic maintenance of euclidean minimum spanning trees

We maintain the minimum spanning tree of a point set in the plane, subject to point insertions and deletions, in time O(n^5/6 log1^2/2 n) per update operation. No nontrivial dynamic geometric minimum spanning tree algorithm was previously known. We reduce the problem to maintaining bichromatic closest pairs, which we also solve in the same time bounds. Our algorithm uses a novel construction, the ordered nearest neighbors of a sequence of points. Any point set or bichromatic point set can be ordered so that this graph is a simple path

Particle-scale structure in frozen colloidal suspensions from small angle X-ray scattering

During directional solidification of the solvent in a colloidal suspension, the colloidal particles segregate from the growing solid, forming high-particle-density regions with structure on a hierarchy of length scales ranging from that of the particle-scale packing to the large-scale spacing between these regions. Previous work has mostly concentrated on the medium- to large-length scale structure, as it is the most accessible and thought to be more technologically relevant. However, the packing of the colloids at the particle-scale is an important component not only in theoretical descriptions of the segregation process, but also to the utility of freeze-cast materials for new applications. Here we present the results of experiments in which we investigated this structure across a wide range of length scales using a combination of small angle X-ray scattering and direct optical imaging. As expected, during freezing the particles were concentrated into regions between ice dendrites forming a microscopic pattern of high- and low-particle-density regions. X-ray scattering indicates that the particles in the high density regions were so closely packed as to be touching. However, the arrangement of the particles does not conform to that predicted by any standard inter-particle pair potentials, suggesting that the particle packing induced by freezing differs from that formed during equilibrium or steady-state densification processes

Research Towards High Speed Freeforming

Additive manufacturing (AM) methods are currently utilised for the manufacture of prototypes and low volume, high cost parts. This is because in most cases the high material costs and low volumetric deposition rates of AM parts result in higher per part cost than traditional manufacturing methods. This paper brings together recent research aimed at improving the economics of AM, in particular Extrusion Freeforming (EF). A new class of machine is described called High Speed Additive Manufacturing (HSAM) in which software, hardware and materials advances are aggregated. HSAM could be cost competitive with injection moulding for medium sized medium quantity parts. A general outline for a HSAM machine and supply chain is provided along with future required research

High-pressure micro-discharges in etching and deposition applications

High-pressure micro-discharges are promising sources of light, ions, and radicals and offer some advantages in materials processing applications as compared to other more conventional discharges. We review here results from etching experiments using stencil masks where the discharge is formed only in the pattern cutout. The mask consists of a thin metal-dielectric structure and is pressed against a Si wafer, which becomes part of the electric circuit. Pattern transfer takes place, albeit the profile shape appears to be limited by the expansion of the plasma into the etched hole at long etch times. We also review experiments on using micro-discharges as sources of radicals for materials deposition applications. In the latter case, the micro-discharges form in metal capillary tubes permitting incorporation of gas flow and a short reaction zone that can be controlled to favour production of specific radicals. We demonstrate these concepts by using CH4/H2 chemistry for diamond deposition on a heated Mo substrate. Good quality micro- and nano-diamond crystals could be produced

A 275–425-GHz Tunerless Waveguide Receiver Based on AlN-Barrier SIS Technology

We report on a 275–425-GHz tunerless waveguide receiver with a 3.5–8-GHz IF. As the mixing element, we employ a high-current-density Nb–AlN–Nb superconducting–insulating– superconducting (SIS) tunnel junction. Thanks to the combined use of AlN-barrier SIS technology and a broad bandwidth waveguide to thin-film microstrip transition, we are able to achieve an unprecedented 43% instantaneous bandwidth, limited by the receiver's corrugated feedhorn. The measured double-sideband (DSB) receiver noise temperature, uncorrected for optics loss, ranges from 55 K at 275 GHz, 48 K at 345 GHz, to 72 K at 425 GHz. In this frequency range, the mixer has a DSB conversion loss of 2.3 1 dB. The intrinsic mixer noise is found to vary between 17–19 K, of which 9 K is attributed to shot noise associated with leakage current below the gap. To improve reliability, the IF circuit and bias injection are entirely planar by design. The instrument was successfully installed at the Caltech Submillimeter Observatory (CSO), Mauna Kea, HI, in October 2006