Statnote 7: chi-square contingency tables

When the data are counts or the frequencies of particular events and can be expressed as a contingency table, then they can be analysed using the chi-square distribution. When applied to a 2 x 2 table, the test is approximate and care needs to be taken in analysing tables when the expected frequencies are small either by applying Yate’s correction or by using Fisher’s exact test. Larger contingency tables can also be analysed using this method. Note that it is a serious statistical error to use any of these tests on measurement data!

Collective behaviour in a square lattice of driven Duffing resonators coupled to van der Pol oscillators

The global and local synchronisation of a square lattice composed of alternating Duffing resonators and van der Pol oscillators coupled through displacement is studied. The lattice acts as a sensing device in which the input signal is characterised by an external driving force that is injected into the system through a subset of the Duffing resonators. The parameters of the system are taken from MEMS devices. The effects of the system parameters, the lattice architecture and size are discussed.

Monte Carlo and molecular dynamics simulations of methane in potassium montmorillonite clay hydrates at elevated pressures and temperatures

The structure and dynamics of methane in hydrated potassium montmorillonite clay have been studied under conditions encountered in sedimentary basin and compared to those of hydrated sodium montmorillonite clay using computer simulation techniques. The simulated systems contain two molecular layers of water and followed gradients of 150 barkm-1 and 30 Kkm-1 up to a maximum burial depth of 6 km. Methane particle is coordinated to about 19 oxygen atoms, with 6 of these coming from the clay surface oxygen. Potassium ions tend to move away from the center towards the clay surface, in contrast to the behavior observed with the hydrated sodium form. The clay surface affinity for methane was found to be higher in the hydrated K-form. Methane diffusion in the two-layer hydrated K-montmorillonite increases from 0.39×10-9 m2s-1 at 280 K to 3.27×10-9 m2s-1 at 460 K compared to 0.36×10-9 m2s-1 at 280 K to 4.26×10-9 m2s-1 at 460 K in Na-montmorillonite hydrate. The distributions of the potassium ions were found to vary in the hydrates when compared to those of sodium form. Water molecules were also found to be very mobile in the potassium clay hydrates compared to sodium clay hydrates. © 2004 Elsevier Inc. All All rights reserved.

Vortex shedding from a row of square bars

Interactions of wakes in a flow past a row of square bars, which is placed across a uniform flow, are investigated by numerical simulations and experiments on the tassumption that the flow is two-dimensional and incompressible. At small Reynolds numbers the flow is steady and symmetric with respect not only to streamwise lines through the center of each square bar but also to streamwise centerlines between adjacent square bars. However, the steady symmetric flow becomes unstable at larger Reynolds numbers and make a transition to a steady asymmetric flow with respect to the centerlines between adjacent square bars in some cases or to an oscillatory flow in other cases. It is found that vortices are shed synchronously from adjacent square bars in the same phase or in anti-phase depending upon the distance between the bars when the flow is oscillatory. The origin of the transition to the steady asymmetric flow is identified as a pitchfork bifurcation, while the oscillatory flows with synchronous shedding of vortices are clarified to originate from a Hopf bifurcation. The critical Reynolds numbers of the transitions are evaluated numerically and the bifurcation diagram of the flow is obtained.

Molecular dynamics simulation of methane in sodium montmorillonite clay hydrates at elevated pressures and temperatures

Computer simulation has been used to study the structure and dynamics of methane in hydrated sodium montmorillonite clays under conditions encountered in sedimentary basins. Systems containing approximately one, two, three and four molecular layers of water have followed gradients of 150 bar km-1 and 30Kkm-1, to a maximum burial depth of 6 km (900 bar and 460 K). Methane is coordinated to approximately 19 oxygen atoms, of which typically 6 are provided by the clay surface. Only in the three- and four-layer hydrates is methane able to leave the clay surface. Diffusion depends strongly on the porosity (water content) and burial depth: self-diffusion coefficients are in the range 0.12 × 10-9m2s-1 for water and 0.04 × 10−9m2s−1 < D < 8.64 × 10−9m2s−1 for methane. Bearing in mind that porosity decreases with burial depth, it is estimated that maximum diffusion occurs at around 3 km. This is in good agreement with the known location of methane reservoirs in sedimentary basins.

Minimum Mean Square Error Approach in Images Processing for Full-field Displacements and Deformation Measurements

A vision system is applied to full-field displacements and deformation measurements in solid mechanics. A speckle like pattern is preliminary formed on the surface under investigation. To determine displacements field of one speckle image with respect to a reference speckle image, sub-images, referred to Zones Of Interest (ZOI) are considered. The field is obtained by matching a ZOI in the reference image with the respective ZOI in the moved image. Two image processing techniques are used for implementing the matching procedure: – cross correlation function and minimum mean square error (MMSE) of the ZOI intensity distribution. The two algorithms are compared and the influence of the ZOI size on the accuracy of measurements is studied.

Computing with the Square Root of NOT

To the two classical reversible 1-bit logic gates, i.e. the identity gate (a.k.a. the follower) and the NOT gate (a.k.a. the inverter), we add an extra gate, the square root of NOT. Similarly, we add to the 24 classical reversible 2-bit circuits, both the square root of NOT and the controlled square root of NOT. This leads to a new kind of calculus, situated between classical reversible computing and quantum computing.

A geometrical model for surface roughness prediction when face milling Al 7075-T7351 with square insert tools

Surface quality is important in engineering and a vital aspect of it is surface roughness, since it plays an important role in wear resistance, ductility, tensile, and fatigue strength for machined parts. This paper reports on a research study on the development of a geometrical model for surface roughness prediction when face milling with square inserts. The model is based on a geometrical analysis of the recreation of the tool trail left on the machined surface. The model has been validated with experimental data obtained for high speed milling of aluminum alloy (Al 7075-T7351) when using a wide range of cutting speed, feed per tooth, axial depth of cut and different values of tool nose radius (0.8. mm and 2.5. mm), using the Taguchi method as the design of experiments. The experimental roughness was obtained by measuring the surface roughness of the milled surfaces with a non-contact profilometer. The developed model can be used for any combination of material workpiece and tool, when tool flank wear is not considered and is suitable for using any tool diameter with any number of teeth and tool nose radius. The results show that the developed model achieved an excellent performance with almost 98% accuracy in terms of predicting the surface roughness when compared to the experimental data. © 2014 The Society of Manufacturing Engineers.

Commutants of the Square of Differentiation on the Half-Line

MSC 2010: Primary: 447B37; Secondary: 47B38, 47A15

Square and compass: Freemasonry's tools for constructing a global civil society

The concept of a global civil society is gaining greater acceptance among International Relations (IR) scholars, yet few studies exist that look at the role of fraternal organizations and their influence in constructing this realm. Freemasonry, one of the oldest fraternal orders, exerts a powerful influence on its membership through its symbolism, architecture and ritual, based on the tenets of mutual respect and tolerance towards all human beings. Such principles helped in creating a body of practices and institutions as early as the eighteenth century which two hundred years later were identified and conceptualized as global civil society. ^ The allegations of anti-Masons and conspiracy theorists offer a continuous account of Masonry's influence on the political scene since its modern founding in 1717 Great Britain. Conspiracy theorists portray the coming of a New World Order, orchestrated and directed by a secret hierarchy of Masons/Illuminati. Even though the lens of conspiracy theories paints a distorted view of reality, it does focus attention to Freemasonry's activities as a major player in politics over the span of three centuries. Not only do such theories challenge the novelty of practices that make up a global civil society, but also the notion that it is an inclusive and growing sector that unites people across the globe. They also provide a valuable critique by pointing out the inconsistencies and discriminatory practices of Masonry as contrasted with the lofty ideals and aims for humanity. ^ The Masonic influence in the social world is perceived as one that reflects the liberal worldview where the nation-state and power structures are in pursuit of human progress, or profit. The symbolism of Masonry, however, carries a message that can be characterized as representing republican ideals. Masonic symbolism and ritual create spaces of meaning where the contradictions between the ideals and the structures of inequality and elitism can be resolved. Freemasonry as a symbolic system proclaiming their inherent republican values does have a global reach. However, the effectiveness of these values is bounded by the constraints that are inherent in a liberal world dominated by nation-states. ^

Angular distribution of Z(0 power) bosons in Z+jet events at the square root of S = 7 TeV

For the first time, the Z0 boson angular distribution in the center-of-momentum frame is measured in proton-proton collisions at [special characters omitted] = 7 TeV at the CERN LHC. The data sample, recorded with the CMS detector, corresponds to an integrated luminosity of approximately 36 pb–1 . Events in which there is a Z0 and at least one jet, with a jet transverse momentum threshold of 20 GeV and absolute jet rapidity less than 2.4, are selected for the analysis. Only the Z0's muon decay channel is studied. Within experimental and theoretical uncertainties, the measured angular distribution is in agreement with next-to-leading order perturbative QCD predictions.

Angular distribution of prompt photons using the compact muon solenoid detector at a square root of S = 7 TeV

The study of the angular distribution of photon plus jet events in pp collisions at [special characters omitted] = 7 TeV with the Compact Muon Solenoid (CMS) detector is presented. The photon is restricted to the central region of the detector (:η: <1.4442) while the jet is allowed to be present in both central and forward regions of CMS (:η: < 2.4). Dominant backgrounds due to jets fragmenting into neutral mesons are accounted for through the use of a template method that discriminates between signal and background. The angular distribution, :η*:, is defined as the absolute value of the difference in η between the leading photon and leading jet in an event divided by two. The angular distribution ranging from 0–1.4 was examined and compared with next-to-leading order QCD predictions and was found to be in good agreement.

Gas hydrates of nonpressurized (GC) and pressurized (DAPC) sediment cores from the Hakon Mosby Mud Volcano, SW Barents Sea

The occurrence of gas hydrates at submarine mud volcanoes (MVs) located within the gas hydrate stability zone (GHSZ) is controlled by upward fluid and heat flux associated with MV activity. Determining the spatial distribution of gas hydrates at MVs is crucial to evaluate their sensitivity to known episodic changes in volcanic activity. We determined the hydrocarbon inventory and spatial distribution of hydrates at an individual MV structure. The Håkon Mosby Mud Volcano (HMMV), located at 1,250 m water depth on the Barents Sea slope, was investigated by combined pressure core sampling, heat flow measurements, and pore water chemical analysis. Quantitative pressure core degassing revealed gas-sediment ratios between 3.1 and 25.7, corresponding to hydrate concentrations of up to 21.3% of the pore volume. Hydrocarbon compositions and physicochemical conditions imply that gas hydrates incipiently crystallize as structure I hydrate, with a dissociation temperature of around 13.8°C at this water depth. Based on numerous in situ measurements of the geothermal gradient in the seabed, pore water sulfate profiles and microbathymetric data, we show that the thickness of the GHSZ increases from less than 1 m at the warm center to around 47 m in the outer parts of the HMMV. We estimate the total mass of hydrate-bound methane stored at the HMMV to be about 102.5 kt, of which 2.8 kt are located within the morphological Unit I around the center and thus are likely to be dissociated in the course of a large eruption.

Optimized square Fresnel zone plates for microoptics applications

Polygonal Fresnel zone plates with a low number of sides have deserved attention in micro and nanoptics, because they can be straightforwardly integrated in photonic devices, and, at the same time, they represent a balance between the high-focusing performance of a circular zone plate and the easiness of fabrication at micro and nano-scales of polygons. Among them, the most representative family are Square Fresnel Zone Plates (SFZP). In this work, we propose two different customized designs of SFZP for optical wavelengths. Both designs are based on the optimization of a SFZP to perform as close as possible as a usual Fresnel Zone Plate. In the first case, the criterion followed to compute it is the minimization of the difference between the area covered by the angular sector of the zone of the corresponding circular plate and the one covered by the polygon traced on the former. Such a requirement leads to a customized polygon-like Fresnel zone. The simplest one is a square zone with a pattern of phases repeating each five zones. On the other hand, an alternative SFZP can be designed guided by the same criterion but with a new restriction. In this case, the distance between the borders of different zones remains unaltered. A comparison between the two lenses is carried out. The irradiance at focus is computed for both and suitable merit figures are defined to account for the difference between them.