An exploration of affine group laws for elliptic curves

Several forms of elliptic curves are suggested for an efficient implementation of Elliptic Curve Cryptography. However, a complete description of the group law has not appeared in the literature for most popular forms. This paper presents group law in affine coordinates for three forms of elliptic curves. With the existence of the proposed affine group laws, stating the projective group law for each form becomes trivial. This work also describes an automated framework for studying elliptic curve group law, which is applied internally when preparing this work.

Preliminary validation of a novel high-resolution melt-based typing method based on the multilocus sequence typing scheme of Streptococcus pyogenes

The major limitation of current typing methods for Streptococcus pyogenes, such as emm sequence typing and T typing, is that these are based on regions subject to considerable selective pressure. Multilocus sequence typing (MLST) is a better indicator of the genetic backbone of a strain but is not widely used due to high costs. The objective of this study was to develop a robust and cost-effective alternative to S. pyogenes MLST. A 10-member single nucleotide polymorphism (SNP) set that provides a Simpson’s Index of Diversity (D) of 0.99 with respect to the S. pyogenes MLST database was derived. A typing format involving high-resolution melting (HRM) analysis of small fragments nucleated by each of the resolution-optimized SNPs was developed. The fragments were 59–119 bp in size and, based on differences in G+C content, were predicted to generate three to six resolvable HRM curves. The combination of curves across each of the 10 fragments can be used to generate a melt type (MelT) for each sequence type (ST). The 525 STs currently in the S. pyogenes MLST database are predicted to resolve into 298 distinct MelTs and the method is calculated to provide a D of 0.996 against the MLST database. The MelTs are concordant with the S. pyogenes population structure. To validate the method we examined clinical isolates of S. pyogenes of 70 STs. Curves were generated as predicted by G+C content discriminating the 70 STs into 65 distinct MelTs.

CT and X-Ray analysis of sagittal curve changes following thoracoscopic anterior scoliosis surgery

Normal thoracic kyphosis Cobb angle for T5-T12 is most commonly reported as a range of 20-40º [1]. Patients with adolescent idiopathic scoliosis (AIS) exhibit a reduced thoracic kyphosis or hypokyphosis [2] accompanying the coronal and rotary distortion components. As a result, surgical restoration of the thoracic kyphosis while maintaining lumbar lordosis and overall sagittal balance is a critical aspect of achieving good clinical outcomes in AIS patients. Previous studies report an increase in thoracic kyphosis after anterior surgical approaches [3] and a flattening of sagittal contours following posterior approaches [4]. Difficulties with measuring sagittal parameters on radiographs are avoided with reformatted sagittal CT reconstructions due to the superior endplate clarity afforded by this imaging modality and are the subject of analysis in this study.

The persistence of phase-separation in LiFePO4 with two-dimensional Li+ transport : the Cahn-Hilliard-reaction equation and the role of defects

We examine the solution of the two-dimensional Cahn-Hilliard-reaction (CHR) equation in the xy plane as a model of Li+ intercalation into LiFePO4 material. We validate our numerical solution against the solution of the depth-averaged equation, which has been used to model intercalation in the limit of highly orthotropic diffusivity and gradient penalty tensors. We then examine the phase-change behaviour in the full CHR system as these parameters become more isotropic, and find that as the Li+ diffusivity is increased in the x direction, phase separation persists at high currents, even in small crystals with averaged coherency strain included. The resulting voltage curves decrease monotonically, which has previously been considered a hallmark of crystals that fill homogeneously.

Pore formation during dehydration of polycrystalline gypsum observed and quantified in a time-series synchrotron radiation based X-ray micro-tomography experiment

We conducted an in-situ X-ray micro-computed tomography heating experiment at the Advanced Photon Source (USA) to dehydrate an unconfined 2.3 mm diameter cylinder of Volterra Gypsum. We used a purpose-built X-ray transparent furnace to heat the sample to 388 K for a total of 310 min to acquire a three-dimensional time-series tomography dataset comprising nine time steps. The voxel size of 2.2 μm3 proved sufficient to pinpoint reaction initiation and the organization of drainage architecture in space and time. We observed that dehydration commences across a narrow front, which propagates from the margins to the centre of the sample in more than four hours. The advance of this front can be fitted with a square-root function, implying that the initiation of the reaction in the sample can be described as a diffusion process. Novel parallelized computer codes allow quantifying the geometry of the porosity and the drainage architecture from the very large tomographic datasets (20483 voxels) in unprecedented detail. We determined position, volume, shape and orientation of each resolvable pore and tracked these properties over the duration of the experiment. We found that the pore-size distribution follows a power law. Pores tend to be anisotropic but rarely crack-shaped and have a preferred orientation, likely controlled by a pre-existing fabric in the sample. With on-going dehydration, pores coalesce into a single interconnected pore cluster that is connected to the surface of the sample cylinder and provides an effective drainage pathway. Our observations can be summarized in a model in which gypsum is stabilized by thermal expansion stresses and locally increased pore fluid pressures until the dehydration front approaches to within about 100 μm. Then, the internal stresses are released and dehydration happens efficiently, resulting in new pore space. Pressure release, the production of pores and the advance of the front are coupled in a feedback loop.

Binder effect on microstructure and properties of YBa2Cu3O7-x extruded wires

YBa2Cu3O7-x wires have been extruded with 2 and 5 wt.% of hydroxy propyl methylcellulose (HPMC) as binder. Both sets of wires sintered below 930°C have equiaxed grains while the wires sintered above this temperature have elongated grains. In the temperature range which gives equiaxed grains, the wires extruded with 5 wt.% HPMC have higher grain size and density. Cracks along the grain boundaries are often observed in the wires having elongated grains. Critical current density, Jc, increases initially, reaches a peak and then decreases with the sintering temperature. The sintering temperature giving a peak in Jc strongly depends on the heat treatment scheme for the wires extruded with 5 wt.% HPMC. TEM studies show that defective layers are formed along grain boundaries for the wires extruded with 5 wt.% HPMC after 5 h oxygenation. After 55 h oxygenation, the defective layers become more localised and grain boundaries adopt an overall cleaner appearance. Densification with equiaxed grains and clean grain boundaries produces the highest Jc's for polycrystalline YBa2Cu3O7 wires.

Progress towards slip-casting YBa2Cu3O7-x monoliths

Sintered bars of YBa2Cu3O7-x obtained by slip-casting are investigated for drying and sintering behaviour. High J(cm) values (approximate to 10(6) A/cm(2) at 77K) are obtained, although J(ct) values are low (approximate to 10(2) A/cm(2) at 77K). Microstructural characterisation is undertaken on selected samples which demonstrate significant differences in physical density and critical current density.

The formation of YBa2Cu3O7-x in melt-texture heat treatments

A study of the bulk formation of YBa2Cu3O7-x from the Y2BaCuO5 plus liquid regime reveals that phase formation occurs at appreciable rates below 950°C in air. This result has been observed for phase-pure YBa2Cu3O7-x starting material given two types of heat treatment: held at 1100°C and slow-cooled from 1030°C at 6°C/h or heat-treated isothermally. Differential thermal analysis, with a cooling rate of 10°C/min indicates that the degree of undercooling for the peritectic formation of YBa2Cu3O7-x is greater than 100°C. © 1994.

The extrusion of continuous lengths of YBa2Cu3O7-x wire using hydroxypropyl methylcellulose

Wires of YBa2Cu3O7-x were fabricated by extrusion using a hydroxypropyl methylcellulose (HPMC) binder. As little as 2 wt.% binder was added to an oxide prepared by a novel co-precipitation process, to produce a plastic mass which readily gave continuous extrusion of long lengths of wire in a reproducible fashion. Critical temperatures of 92K were obtained for wires given optimum high-temperature heat treatments. Critical current densities greater than 1000 A cm-1 were measured at 77.3K using heat treatments at around 910°C for 10h. These transport critical current densities, measured on centimeter-long wires, were obtained with microstructures showing a relatively dense and uniform distribution of randomly oriented, small YBa2Cu3O7-x grains. © 1993.

Transmission X-ray microscopy : a new tool in clay mineral floccules characterization

Effective flocculation and dewatering of mineral processing streams containing clays are microstructure dependent in clay-water systems. Initial clay flocculation is crucial in the design and for the development of a new methodology of gas exploitation. Microstructural engineering of clay aggregates using covalent cations and Keggin macromolecules have been monitored using the new state of the art Transmission X-ray Microscope (TXM) with 60 nm tomography resolution installed in a Taiwanese synchrotron. The 3-D reconstructions from TXM images show complex aggregation structures in montmorillonite aqueous suspensions after treatment with Na+, Ca2+ and Al13 Keggin macromolecules. Na-montmorillonite displays elongated, parallel, well-orientated and closed-void cellular networks, 0.5–3 μm in diameter. After treatment by covalent cations, the coagulated structure displays much smaller, randomly orientated and openly connected cells, 300–600 nm in diameter. The average distances measured between montmorillonite sheets was around 450 nm, which is less than half of the cell dimension measured in Na-montmorillonite. The most dramatic structural changes were observed after treatment by Al13 Keggin; aggregates then became arranged in compacted domains of a 300 nm average diameter composed of thick face-to-face oriented sheets, which forms porous aggregates with larger intra-aggregate open and connected voids.

The correlation between electric field emission phenomenon and Schottky contact reverse bias characteristics in nanostructured systems

Two different morphologies of nanotextured molybdenum oxide were deposited by thermal evaporation. By measuring their field emission (FE) properties, an enhancement factor was extracted. Subsequently, these films were coated with a thin layer of Pt to form Schottky contacts. The current-voltage (I-V) characteristics showed low magnitude reverse breakdown voltages, which we attributed to the localized electric field enhancement. An enhancement factor was obtained from the I-V curves. We will show that the enhancement factor extracted from the I-V curves is in good agreement with the enhancement factor extracted from the FE measurements.

Improved estimates of percolation and anisotropic permeability from 3-D X-ray microtomography using stochastic analyses and visualization

X-ray microtomography (micro-CT) with micron resolution enables new ways of characterizing microstructures and opens pathways for forward calculations of multiscale rock properties. A quantitative characterization of the microstructure is the first step in this challenge. We developed a new approach to extract scale-dependent characteristics of porosity, percolation, and anisotropic permeability from 3-D microstructural models of rocks. The Hoshen-Kopelman algorithm of percolation theory is employed for a standard percolation analysis. The anisotropy of permeability is calculated by means of the star volume distribution approach. The local porosity distribution and local percolation probability are obtained by using the local porosity theory. Additionally, the local anisotropy distribution is defined and analyzed through two empirical probability density functions, the isotropy index and the elongation index. For such a high-resolution data set, the typical data sizes of the CT images are on the order of gigabytes to tens of gigabytes; thus an extremely large number of calculations are required. To resolve this large memory problem parallelization in OpenMP was used to optimally harness the shared memory infrastructure on cache coherent Non-Uniform Memory Access architecture machines such as the iVEC SGI Altix 3700Bx2 Supercomputer. We see adequate visualization of the results as an important element in this first pioneering study.

Reconstructing 3D x-ray CT images of polymer gel dosimeters using the zero-scan method

In this study x-ray CT has been used to produce a 3D image of an irradiated PAGAT gel sample, with noise-reduction achieved using the ‘zero-scan’ method. The gel was repeatedly CT scanned and a linear fit to the varying Hounsfield unit of each pixel in the 3D volume was evaluated across the repeated scans, allowing a zero-scan extrapolation of the image to be obtained. To minimise heating of the CT scanner’s x-ray tube, this study used a large slice thickness (1 cm), to provide image slices across the irradiated region of the gel, and a relatively small number of CT scans (63), to extrapolate the zero-scan image. The resulting set of transverse images shows reduced noise compared to images from the initial CT scan of the gel, without being degraded by the additional radiation dose delivered to the gel during the repeated scanning. The full, 3D image of the gel has a low spatial resolution in the longitudinal direction, due to the selected scan parameters. Nonetheless, important features of the dose distribution are apparent in the 3D x-ray CT scan of the gel. The results of this study demonstrate that the zero-scan extrapolation method can be applied to the reconstruction of multiple x-ray CT slices, to provide useful 2D and 3D images of irradiated dosimetry gels.