Muon Pair Production by Electron-Photon Scatterings

The cross section for muon pair productions by electrons scattering over photons, $\sigma_{MPP}$, is calculated analytically in the leading order. It is pointed out that for the center-of-mass energy range, $s \geq 5 m^{2}_{\mu}$, the cross section for $\sigma_{MPP}$ is less than $1 \mu$b. The differential energy spectrum for either of the resulting muons is given for the purpose of high-energy neutrino astronomy. An implication of our result for a recent suggestion concerning the high-energy cosmic neutrino generation through this muon pair is discussed.Comment: a comment added, to appear in Phys. Rev. D, Rapid Communicatio

A Noisy Monte Carlo Algorithm

We propose a Monte Carlo algorithm to promote Kennedy and Kuti's linear accept/reject algorithm which accommodates unbiased stochastic estimates of the probability to an exact one. This is achieved by adopting the Metropolis accept/reject steps for both the dynamical and noise configurations. We test it on the five state model and obtain desirable results even for the case with large noise. We also discuss its application to lattice QCD with stochastically estimated fermion determinants.Comment: 10 pages, 1 tabl

Effect of soil type on seismic demand

This paper investigates the validity of the soil considerations used in the determination of seismic demand as part of NZS1170.5, which currently specifies seismic design spectra corresponding to 5 different soil types. According to the current provisions stipulated in NZS1170.5, for all natural periods, the building demand for soft soil is either equal to or greater than that for hard soil. It is noted that this is opposite to the basic structural dynamics theory which suggests that an increase in stiffness of a system results in an increase in the acceleration response. In this pretext, a numerical parametric study is undertaken using a 1-D nonlinear site response analysis in order to capture the effect of soil characteristics on structural seismic demand and to scrutinize the validity of the current site specific seismic design spectra. It is identified that the level of input ground motion intensity and shear stiffness of the column (represented by its shear wave velocity, Vs) are the main parameters affecting the surface response. The study found some shortfalls in the way the current code defines seismic design demand, in particular the hierarchy of soil stiffness at low structural periods. It was found that stiff soils generally tend to have a higher spectral acceleration response in comparison to soft soils although this trend is less prominent for high intensity bed rock motions. It was also found that for medium to hard soil types the spectral acceleration response at short period is grossly underestimated by the current NZS1170.5 provisions. Based on the outcomes of the parametric numerical analyses, a revised strategy to determine seismic structural demand is proposed and demonstrated

Blow up criterion for compressible nematic liquid crystal flows in dimension three

In this paper, we consider the short time strong solution to a simplified hydrodynamic flow modeling the compressible, nematic liquid crystal materials in dimension three. We establish a criterion for possible breakdown of such solutions at finite time in terms of the temporal integral of both the maximum norm of the deformation tensor of velocity gradient and the square of maximum norm of gradient of liquid crystal director field.Comment: 22 page

Gauged (2,2) Sigma Models and Generalized Kahler Geometry

We gauge the (2,2) supersymmetric non-linear sigma model whose target space has bihermitian structure (g, B, J_{\pm}) with noncommuting complex structures. The bihermitian geometry is realized by a sigma model which is written in terms of (2,2) semi-chiral superfields. We discuss the moment map, from the perspective of the gauged sigma model action and from the integrability condition for a Hamiltonian vector field. We show that for a concrete example, the SU(2) x U(1) WZNW model, as well as for the sigma models with almost product structure, the moment map can be used together with the corresponding Killing vector to form an element of T+T* which lies in the eigenbundle of the generalized almost complex structure. Lastly, we discuss T-duality at the level of a (2,2) sigma model involving semi-chiral superfields and present an explicit example.Comment: 33 page

Calibrated X-ray micro-tomography for mineral ore quantification

Scanning Electron Microscopy (SEM) based assessments are the most widely used and trusted imaging technique for mineral ore quantification. X-ray micro tomography (XMT) is a more recent addition to the mineralogy toolbox, but with the potential to extend the measurement capabilities into the three dimensional (3D) assessment of properties such as mineral liberation, grain size and textural characteristics. In addition, unlike SEM based assessments which require the samples to be sectioned, XMT is non-invasive and non-destructive. The disadvantage of XMT, is that the mineralogy must be inferred from the X-ray attenuation measurements, which can make it hard to distinguish from one another, whereas SEM when coupled with Energy-Dispersive X-ray Spectroscopy (EDX) provides elemental compositions and thus a more direct method for distinguishing different minerals. A new methodology that combines both methods at the mineral grain level is presented. The rock particles used to test the method were initially imaged in 3D using XMT followed by sectioning and the 2D imaging of the slices using SEM-EDX. An algorithm was developed that allowed the mineral grains in the 2D slice to be matched with their 3D equivalents in the XMT based images. As the mineralogy of the grains from the SEM images can be matched to a range of X-ray attenuations, this allows minerals which have similar attenuations to one another to be distinguished, with the level of uncertainty in the classification quantified. In addition, the methodology allowed for the estimation of the level of uncertainty in the quantification of grain size by XMT, the assessment of stereological effects in SEM 2D images and ultimately obtaining a simplified 3D mineral map from low energy XMT images. Copper sulphide ore fragments, with chalcopyrite and pyrite as the main sulphide minerals, were used to demonstrate the effectiveness of this procedure