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

Fuzzy modeling and control for conical magnetic bearings using linear matrix inequality

A general nonlinear model with six degree-of-freedom rotor dynamics and electromagnetic force equations for conical magnetic bearings is developed. For simplicity, a T-S (Takagi Sugeno) fuzzy model for the nonlinear magnetic bearings assumed no rotor eccentricity is first derived, and a fuzzy control design based on the T-S fuzzy model is then proposed for the high speed and high accuracy control of the complex magnetic bearing systems. The suggested fuzzy control design approach for nonlinear magnetic bearings can be cast into a linear matrix inequality (LMI) problem via robust performance analysis, and the LMI problem can be solved efficiently using the convex optimization techniques. Computer simulations are presented for illustrating the performance of the control strategy considering simultaneous rotor rotation tracking and gap deviations regulation