Improved Montgomery modular inverse algorithm

A new, single and unified Montgomery modular inverse algorithm, which performs both classical and Montgomery modular inversion, is proposed. This reduces the number of Montgomery multiplication operations required by 33% when compared with previous algorithms reported in the literature. The use of this in practice has been investigated by implementation of the improved unified algorithm and the previous algorithms on FPGA devices. The unified algorithm implementation shows a significant speed-up and a reduction in silicon area usage.

Delineation of a quick clay zone at Smørgrav, Norway, with electromagnetic methods under geotechnical constraints

In many coastal areas of North America and Scandinavia, post-glacial clay sediments have emerged above sea level due to iso-static uplift. These clays are often destabilised by fresh water leaching and transformed to so-called quick clays as at the investigated area at Smørgrav, Norway. Slight mechanical disturbances of these materials may trigger landslides. Since the leaching increases the electrical resistivity of quick clay as compared to normal marine clay, the application of electromagnetic (EM) methods is of particular interest in the study of quick clay structures.

For the first time, single and joint inversions of direct-current resistivity (DCR), radiomagnetotelluric (RMT) and controlled-source audiomagnetotelluric (CSAMT) data were applied to delineate a zone of quick clay. The resulting 2-D models of electrical resistivity correlate excellently with previously published data from a ground conductivity metre and resistivity logs from two resistivity cone penetration tests (RCPT) into marine clay and quick clay. The RCPT log into the central part of the quick clay identifies the electrical resistivity of the quick clay structure to lie between 10 and 80 O m. In combination with the 2-D inversion models, it becomes possible to delineate the vertical and horizontal extent of the quick clay zone. As compared to the inversions of single data sets, the joint inversion model exhibits sharper resistivity contrasts and its resistivity values are more characteristic of the expected geology. In our preferred joint inversion model, there is a clear demarcation between dry soil, marine clay, quick clay and bedrock, which consists of alum shale and limestone.

Probing Ferroelectrics Using Optical Second Harmonic Generation

Nonlinear optics is an essential component of modern laser systems and optoelectronic devices. It has also emerged as an important tool in probing the electronic, vibrational, magnetic, and crystallographic structure of materials ranging from oxides and metals, to polymers and biological samples. This review focuses on the specific technique of optical second harmonic generation (SHG), and its application in probing ferroelectric complex oxide crystals and thin films. As the dominant SHG interaction mechanism exists only in materials that lack inversion symmetry, SHG is a sensitive probe of broken inversion symmetry, and thus also of bulk polar phenomena in materials. By performing in-situ SHG polarimetry experiments in different experimental conditions such as sample orientation, applied electric field, and temperature, one can probe ferroelectric hysteresis loops and phase transitions. Careful modeling of the polarimetry data allows for the determination of the point group symmetry of the crystal. In epitaxial thin films with a two-dimensional arrangement of well-defined domain orientations, one can extract information about intrinsic material properties such as nonlinear coefficients, as well as microstructural information such as the local statistics of the different domain variants being probed. This review presents several detailed examples of ferroelectric systems where such measurements and modeling are performed. The use of SHG microscopic imaging is discussed, and its ability to reveal domain structures and phases not normally visible with linear optics is illustrated.

Comparing Optical Thomson Scattering With Emission Spectroscopy In He Plasmas Induced By Laser Breakdown At 1 Atmosphere

We have carried out optical Thomson scattering measurements from a laser induced breakdown in He at 1 atmosphere. The breakdown was created with a Nd:YAG laser with 9ns pulse duration and 400mJ pulse energy focused into a chamber filled with He. A second harmonic Nd: YAG laser with 9ns pulses and up to 80mJ energy was used to obtain temporally and spatially resolved data on the electron density and temperature. In parallel experiments, we measured the emission of the 447.1nm line from He I. Initial results suggest good agreement between densities inferred but full Abel inversion is needed for conclusive results.

Predicting Functional Recovery after Acute Ankle Sprain

INTRODUCTION:Ankle sprains are among the most common acute musculoskeletal conditions presenting to primary care. Their clinical course is variable but there are limited recommendations on prognostic factors. Our primary aim was to identify clinical predictors of short and medium term functional recovery after ankle sprain.
METHODS:A secondary analysis of data from adult participants (N = 85) with an acute ankle sprain, enrolled in a randomized controlled trial was undertaken. The predictive value of variables (age, BMI, gender, injury mechanism, previous injury, weight-bearing status, medial joint line pain, pain during weight-bearing dorsiflexion and lateral hop test) recorded at baseline and at 4 weeks post injury were investigated for their prognostic ability. Recovery was determined from measures of subjective ankle function at short (4 weeks) and medium term (4 months) follow ups. Multivariate stepwise linear regression analyses were undertaken to evaluate the association between the aforementioned variables and functional recovery.
RESULTS:Greater age, greater injury grade and weight-bearing status at baseline were associated with lower function at 4 weeks post injury (p<0.01; adjusted R square=0.34). Greater age, weight-bearing status at baseline and non-inversion injury mechanisms were associated with lower function at 4 months (p<0.01; adjusted R square=0.20). Pain on medial palpation and pain on dorsiflexion at 4 weeks were the most valuable prognostic indicators of function at 4 months (p< 0.01; adjusted R square=0.49).
CONCLUSION:The results of the present study provide further evidence that ankle sprains have a variable clinical course. Age, injury grade, mechanism and weight-bearing status at baseline provide some prognostic information for short and medium term recovery. Clinical assessment variables at 4 weeks were the strongest predictors of recovery, explaining 50% of the variance in ankle function at 4 months. Further prospective research is required to highlight the factors that best inform the expected convalescent period, and risk of recurrence.

The influence of the magnetic field on running penumbral waves in the solar chromosphere

We use images of high spatial and temporal resolution, obtained using both ground- and space-based instrumentation, to investigate the role magnetic field inclination angles play in the propagation characteristics of running penumbral waves in the solar chromosphere. Analysis of a near-circular sunspot, close to the center of the solar disk, reveals a smooth rise in oscillatory period as a function of distance from the umbral barycenter. However, in one directional quadrant, corresponding to the north direction, a pronounced kink in the period-distance diagram is found. Utilizing a combination of the inversion of magnetic Stokes vectors and force-free field extrapolations, we attribute this behavior to the cut-off frequency imposed by the magnetic field geometry in this location. A rapid, localized inclination of the magnetic field lines in the north direction results in a faster increase in the dominant periodicity due to an accelerated reduction in the cut-off frequency. For the first time, we reveal how the spatial distribution of dominant wave periods, obtained with one of the highest resolution solar instruments currently available, directly reflects the magnetic geometry of the underlying sunspot, thus opening up a wealth of possibilities in future magnetohydrodynamic seismology studies. In addition, the intrinsic relationships we find between the underlying magnetic field geometries connecting the photosphere to the chromosphere, and the characteristics of running penumbral waves observed in the upper chromosphere, directly supports the interpretation that running penumbral wave phenomena are the chromospheric signature of upwardly propagating magneto-acoustic waves generated in the photosphere.

catena-poly[mercury(II)-di-mu-bromo-mu-pyridazine-kappa N-2 : N ']

The crystal structure of [HgBr2(Pyo)](n) (Pyo = pyridazine, C4H4N2) consists of strands of octahedrally coordinated mercuric centers asymmetrically bridged by bromide and connected by the two neighboring N atoms of pyridazine molecules to complete the octahedral coordination of mercury. The Hg atoms lie on inversion centers.

Bis(tetraethylammonium) decachloro-tetramercurate(II), (Et4N)(2)[Hg4Cl10]

The structure of (Et4N)(2)[Hg4Cl10] contains dinuclear [Hg2Cl6](2-) anions and HgCl2 molecules, with definite interactions so that the anion can also be formulated as [Hg4Cl10](2-). Alternatively the compound can be written as (Et4N)(2)[Hg2Cl6][HgCl2](2). Charge balance is achieved by ordered [Et4N](+) cations. An inversion centre is situated at the centre of the [Hg2Cl6](2-) anions.

Bis(tetraethylammonium) di-mu-bromo-bis[dibromomercurate(II)], (Et4N)(2)[Hg2Br6]

The structure of (Et4N)(2)[Hg2Br6] contains dinuclear [Hg2Br6](2-) species as isolated anions. Charge balance is achieved by ordered [Et4N](+) cations. An inversion centre is located at the centre of the [Hg2Br6](2-) unit.

The nucleus of Comet 67P/Churyumov-Gerasimenko. A new shape model and thermophysical analysis

Context. Comet 67P/Churyumov-Gerasimenko is the target of the European Space Agency Rosetta spacecraft rendez-vous mission. Detailed physical characteristation of the comet before arrival is important for mission planning as well as providing a test bed for ground-based observing and data-analysis methods. Aims: To conduct a long-term observational programme to characterize the physical properties of the nucleus of the comet, via ground-based optical photometry, and to combine our new data with all available nucleus data from the literature. Methods: We applied aperture photometry techniques on our imaging data and combined the extracted rotational lightcurves with data from the literature. Optical lightcurve inversion techniques were applied to constrain the spin state of the nucleus and its broad shape. We performed a detailed surface thermal analysis with the shape model and optical photometry by incorporating both into the new Advanced Thermophysical Model (ATPM), along with all available Spitzer 8-24 μm thermal-IR flux measurements from the literature. Results: A convex triangular-facet shape model was determined with axial ratios b/a = 1.239 and c/a = 0.819. These values can vary by as much as 7% in each axis and still result in a statistically significant fit to the observational data. Our best spin state solution has Psid = 12.76137 ± 0.00006 h, and a rotational pole orientated at Ecliptic coordinates λ = 78°(±10°), β = + 58°(±10°). The nucleus phase darkening behaviour was measured and best characterized using the IAU HG system. Best fit parameters are: G = 0.11 ± 0.12 and HR(1,1,0) = 15.31 ± 0.07. Our shape model combined with the ATPM can satisfactorily reconcile all optical and thermal-IR data, with the fit to the Spitzer 24 μm data taken in February 2004 being exceptionally good. We derive a range of mutually-consistent physical parameters for each thermal-IR data set, including effective radius, geometric albedo, surface thermal inertia and roughness fraction. Conclusions: The overall nucleus dimensions are well constrained and strongly imply a broad nucleus shape more akin to comet 9P/Tempel 1, rather than the highly elongated or "bi-lobed" nuclei seen for comets 103P/Hartley 2 or 8P/Tuttle. The derived low thermal inertia of

Kinetostatic-model-based Stiffness Analysis of Exechon PKM

As a comparative newly-invented PKM with over-constraints in kinematic chains, the Exechon has attracted extensive attention from the research society. Different from the well-recognized kinematics analysis, the research on the stiffness characteristics of the Exechon still remains as a challenge due to the structural complexity. In order to achieve a thorough understanding of the stiffness characteristics of the Exechon PKM, this paper proposed an analytical kinetostatic model by using the substructure synthesis technique. The whole PKM system is decomposed into a moving platform subsystem, three limb subsystems and a fixed base subsystem, which are connected to each other sequentially through corresponding joints. Each limb body is modeled as a spatial beam with a uniform cross-section constrained by two sets of lumped springs. The equilibrium equation of each individual limb assemblage is derived through finite element formulation and combined with that of the moving platform derived with Newtonian method to construct the governing kinetostatic equations of the system after introducing the deformation compatibility conditions between the moving platform and the limbs. By extracting the 6 x 6 block matrix from the inversion of the governing compliance matrix, the stiffness of the moving platform is formulated. The computation for the stiffness of the Exechon PKM at a typical configuration as well as throughout the workspace is carried out in a quick manner with a piece-by-piece partition algorithm. The numerical simulations reveal a strong position-dependency of the PKM's stiffness in that it is symmetric relative to a work plane due to structural features. At the last stage, the effects of some design variables such as structural, dimensional and stiffness parameters on system rigidity are investigated with the purpose of providing useful information for the structural optimization and performance enhancement of the Exechon PKM. It is worthy mentioning that the proposed methodology of stiffness modeling in this paper can also be applied to other overconstrained PKMs and can evaluate the global rigidity over workplace efficiently with minor revisions.

Advanced Ceramic Substrate with Ordered and Designed Micro-Structure for Applications in Automotive Catalysts

This study describes an innovative monolith structure designed for applications in automotive catalysis using an advanced manufacturing approach developed at Imperial College London. The production process combines extrusion with phase inversion of a ceramic-polymer-solvent mixture in order to design highly ordered substrate micro-structures that offer improvements in performance, including reduced PGM loading, reduced catalyst ageing and reduced backpressure.

This study compares the performance of the novel substrate for CO oxidation against commercially available 400 cpsi and 900 cpsi catalysts using gas concentrations and a flow rate equivalent to those experienced by a full catalyst brick when attached to a vehicle. Due to the novel micro-structure, no washcoat was required for the initial testing and 13 g/ft3 of Pd was deposited directly throughout the substrate structure in the absence of a washcoat.

Initial results for CO oxidation indicate that the advanced micro-structure leads to enhanced conversion efficiency. Despite an 79% reduction in metal loading and the absence of a washcoat, the novel substrate sample performs well, with a light-off temperature (LOT) only 15 °C higher than the commercial 400 cpsi sample.

To test the effects of catalyst ageing on light-off temperature, each sample was aged statically at a temperature of 1000 °C, based on the Bench Ageing Time (BAT) equation. The novel substrate performed impressively when compared to the commercial samples, with a variation in light-off temperature of only 3% after 80 equivalent hours of ageing, compared to 12% and 25% for the 400 cpsi and 900 cpsi monoliths, respectively.

Reactions of enantiopure cyclic diols with sulfuryl chloride

Monocyclic allylic cis-1,2-diols reacted with sulfuryl chloride at 0 °C in a regio- and stereo-selective manner to give 2-chloro-1-sulfochloridates, which were hydrolysed to yield the corresponding trans-1,2-chlorohydrins. At −78 °C, with very slow addition of sulfuryl chloride, cyclic sulfates were formed in good yields, proved to be very reactive with nucleophiles and rapidly decomposed on attempted storage. Reaction of a cyclic sulfate with sodium azide yielded a trans-azidohydrin without evidence of allylic rearrangement occurring. An enantiopure bicyclic cis-1,2-diol reacted with sulfuryl chloride to give, exclusively, a trans-1,2-dichloride enantiomer with retention of configuration at the benzylic centre and inversion at the non-benzylic centre; a mechanism is presented to rationalise the observation.

Reactions of nitrogen nucleophiles with enantiopure cyclohexenyl electrophiles:a stereo- and regio- selective study

The reactions of enantiopure cyclohexene epoxides and trans-1,2-bromoacetates, derived from the corresponding substituted benzene cis-dihydrodiol metabolites, with nitrogen nucleophiles, were examined and possible mechanisms proposed. An initial objective was the synthesis of new 1,2-aminoalcohol enantiomers as potential chiral ligands and synthetic scaffolds for library generation. These apparently simple substitution reactions proved to be more complex than initially anticipated and were found to involve a combination of different reaction mechanisms. Allylic trans-1,2-azidohydrins were prepared by Lewis acid-catalysed ring-opening of cyclic vinyl epoxides with sodium azide via an S(N)2 mechanism. On heating, these trans-1,2-azidohydrins isomerized to the corresponding trans-1,4-azidohydrins via a suprafacial allyl azide [3,3]-sigmatropic rearrangement mechanism. Conversion of a 1,2-azidohydrin to a 1,2-azidoacetate moved the equilibrium position in favour of the 1,4-substitution product. Allylic trans-1,2-bromoacetates reacted with sodium azide at room temperature to give C-2 and C-4 substituted products. A clean inversion of configuration at C-2 was found, as expected, from a concerted S(N)2-pathway. However, substitution at C-4 was not stereoselective and resulted in mixtures of 1,4-cis and 1,4-trans products. This observation can be rationalized in terms of competitive S(N)2 and S(N)2 reactions allied to a [3,3]-sigmatropic rearrangement. cis-1,2-Azidohydrins and cis-1,2-azidoacetates were much more prone to rearrange than the corresponding trans-isomers. Reaction of the softer tosamide nucleophile with trans-1,2-bromoacetates resulted, predominantly, in C-4 substitution via a syn-S(N)2 mechanism. One application of the reaction of secondary amines with allylic cyclohexene epoxides, to give trans-1,2-aminoalcohols, is in the synthesis of the anticholinergic drug vesamicol, via an S(N)2 mechanism. Copyright (c) 2013 John Wiley & Sons, Ltd.

Bis(1,4,7-trithiacyclononane-S,S ',S '')nickel(II) dibromide tetrahydrate

The Ni-II centre in the cation of the title compound, [Ni(C6H12S3)(2)]Br-2. 4H(2)O, occupies a crystallographic inversion centre and is octahedrally coordinated by six S-donors from two [9]aneS(3) ligands. Ni-S distances range from 2.3749 (16) to 2.4077 (15) Angstrom and S-Ni-S angles where both thia donors belong to the same ligand lie in a narrow range between 88.09 (5) and 88.67 (6)degrees. The water molecules participate in extensive hydrogen bonding with each other and with the Br- anions to form double chains with eight- and 12-membered hydrogen-bonded rings running along the crystallographic a direction.