Scalar and Spinor Perturbation to the Kerr-NUT Spacetime

We study the scalar and spinor perturbation, namely the Klein-Gordan and Dirac equations, in the Kerr-NUT space-time. The metric is invariant under the duality transformation involving the exchange of mass and NUT parameters on one hand and radial and angle coordinates on the other. We show that this invariance is also shared by the scalar and spinor perturbation equations. Further, by the duality transformation, one can go from the Kerr to the dual Kerr solution, and vice versa, and the same applies to the perturbation equations. In particular, it turns out that the potential barriers felt by the incoming scalar and spinor fields are higher for the dual Kerr than that for the Kerr. We also comment on existence of horizon and singularity.Comment: 31 pages including 20 figures, RevTeX style: Final version to appear in Classical and Quantum Gravit

Fabrication of a repulsive-type magnetic bearing using a novel arrangement of permanent magnets for vertical-rotor suspension

A repulsive-type magnetic bearing system has been fabricated in which the rotor of a vertical-shaft-type motor is levitated due to the repulsive force between two sets of permanent magnets. A novel arrangement of permanent magnets has been reported here, which has made the suspension of the rotor possible. The system is planned to be applied for pumping milks and other related products in the New Zealand dairy industry

Relative contributions of crust and mantle to the origin of the Bijli Rhyolite in a palaeoproterozoic bimodal volcanic sequence (Dongargarh group), central India

New mineralogical, bulk chemical and oxygen isotope data on the Palaeoproterozoic Bijli Rhyolite, the basal unit of a bimodal volcanic sequence (Dongargarh Group) in central India, and one of the most voluminous silicic volcanic expressions in the Indian Shield, are presented. The Bijli Rhyolite can be recognized as a poorly sorted pyroclastic deposit, and comprises of phenocrystic K-feldspar + albite ± anorthoclase set in fine-grained micro-fragmental matrix of quartz-feldspar-sericite-chlorite-iron-oxide ± calcite. The rocks are largely metaluminous with high SiO2, Na2O + K2O, Fe/Mg, Ga/Al, Zr, Ta, Sn, Y, REE and low CaO, Ba, Sr contents; the composition points to an 'A-type granite' melt. The rocks show negative Cs-, Sr-, Eu- and Ti- anomalies with incompatible element concentrations 2-3 times more than the upper continental crust (UCC). LREE is high (La/Yb ~20) and HREE 20-30 times chondritic. δ18Owhole-rock varies between 4.4 and 7.8‰ (mean 5.87±1.26‰). The Bijli melt is neither formed by fractionation of a basaltic magma, nor does it represent a fractionated crustal melt. It is shown that the mantle-derived high temperature basaltic komatiitic melts/high Mg basalts triggered crustal melting, and interacted predominantly with deep crust compositionally similar to the Average Archaean Granulite (AAG), and a shallower crustal component with low CaO and Al2O3 to give rise to the hybrid Bijli melts. Geochemical mass balance suggests that ~30% partial melting of AAG under anhydrous condition, instead of the upper continental crust (UCC) including the Amgaon granitoid gneiss reported from the area, better matches the trace element concentrations in the rocks. The similar Ta/Th of the rhyolites (0.060) and average granulite (0.065) vs. UCC (0.13) also support a deep crustal protolith. Variable contributions of crust and mantle, and action of hydrothermal fluid are attributed for the spread in δ18Owhole-rock values. The fast eruption of high temperature ~900°C) rhyolitic melts suggests a rapid drop in pressure of melting related to decompression in an extensional setting

Mass of highly magnetized white dwarfs exceeding the Chandrasekhar limit: An analytical view

In recent years a number of white dwarfs has been observed with very high surface magnetic fields. We can expect that the magnetic field in the core of these stars would be much higher (~ 10^{14} G). In this paper, we analytically study the effect of high magnetic field on relativistic cold electron, and hence its effect on the stability and the mass-radius relation of a magnetic white dwarf. In strong magnetic fields, the equation of state of the Fermi gas is modified and Landau quantization comes into play. For relatively very high magnetic fields (with respect to the energy density of matter) the number of Landau levels is restricted to one or two. We analyse the equation of states for magnetized electron degenerate gas analytically and attempt to understand the conditions in which transitions from the zero-th Landau level to first Landau level occur. We also find the effect of the strong magnetic field on the star collapsing to a white dwarf, and the mass-radius relation of the resulting star. We obtain an interesting theoretical result that it is possible to have white dwarfs with mass more than the mass set by Chandrasekhar limit.Comment: 18 pages including 3 figures; to appear in Modern Physics Letters

Development and testing of methodology for evaluating the performance of multi-input/multi-output digital control systems

A Controller Performance Evaluation (CPE) methodology for multi-input/multi-output digital control systems was developed and tested on an aeroelastic wind-tunnel model. Modern signal processing methods were used to implement control laws and to acquire time domain data of the whole system (controller and plant) from which appropriate transfer matrices of the control system could be generated. Matrix computational procedures were used to calculate singular values of return-difference matrices at the plant input and output points to evaluate the performance of the control system. The CPE procedures effectively identified potentially destabilizing controllers and confirmed the satisfactory performance of stabilizing ones

Homogeneous Relaxation at Strong Coupling from Gravity

Homogeneous relaxation is a ubiquitous phenomenon in semiclassical kinetic theories where the quasiparticles are distributed uniformly in space, and the equilibration involves only their velocity distribution. For such solutions, the hydrodynamic variables remain constant. We construct asymptotically AdS solutions of Einstein's gravity dual to such processes at strong coupling, perturbatively in the amplitude expansion, where the expansion parameter is the ratio of the amplitude of the non-hydrodynamic shear-stress tensor to the pressure. At each order, we sum over all time derivatives through exact recursion relations. We argue that the metric has a regular future horizon, order by order in the amplitude expansion, provided the shear-stress tensor follows an equation of motion. At the linear order, this equation of motion implies that the metric perturbations are composed of zero wavelength quasinormal modes. Our method allows us to calculate the non-linear corrections to this equation perturbatively in the amplitude expansion. We thus derive a special case of our previous conjecture on the regularity condition on the boundary stress tensor that endows the bulk metric with a regular future horizon, and also refine it further. We also propose a new outlook for heavy-ion phenomenology at RHIC and ALICE.Comment: 60 pages, a section titled "Outlook for RHIC and ALICE" has been added, accepted for publication in Physical Review

Two-dimensional Induced Ferromagnetism

Magnetic properties of materials confined to nanometer length scales are providing important information regarding low dimensional physics. Using gadolinium based Langmuir-Blodgett films, we demonstrate that two-dimensional ferromagnetic order can be induced by applying magnetic field along the in-plane (perpendicular to growth) direction. Field dependent exchange coupling is evident in the in-plane magnetization data that exhibit absence of hysteresis loop and show reduction in field required to obtain saturation in measured moment with decreasing temperature.Comment: 4 pages, 3 postscript figures, corrected paper forma