Two dimensional general covariance from three dimensions

A 3d generally covariant field theory having some unusual properties is described. The theory has a degenerate 3-metric which effectively makes it a 2d field theory in disguise. For 2-manifolds without boundary, it has an infinite number of conserved charges that are associated with graphs in two dimensions and the Poisson algebra of the charges is closed. For 2-manifolds with boundary there are additional observables that have a Kac-Moody Poisson algebra. It is further shown that the theory is classically integrable and the general solution of the equations of motion is given. The quantum theory is described using Dirac quantization, and it is shown that there are quantum states associated with graphs in two dimensions.Comment: 10 pages (Latex), Alberta-Thy-19-9

Magnetotransport properties of lithographically defined lateral Co/Ni80Fe20 wires

In this article we have investigated the magnetization reversal process of laterally defined coupled magnetic structures consisting of micron-sized sputtered Co and Ni80Fe20 wires lying side by side at temperatures ranging from 3 to 300 K. We have used a microfabrication technique to create an array of planar, laterally coupled magnetic wires made of two ferromagnetic materials. We observed two distinct peaks in the magnetoresistance (MR) curves corresponding to the magnetization reversals of Co and Ni80Fe20 wires. Below a critical temperature of 20 K we observed an asymmetric shift in the Ni80Fe20 peak position for both forward and reverse field sweeps due to the exchange coupling between the ferromagnetic (Ni80Fe20) and antiferromagnetic (Co–oxide at the interface of Co and Ni80Fe20 formed during fabrication) parts. The Co peaks gradually disappeared as the temperature was reduced. At low temperature we also observed that the Ni80Fe20 peaks in the MR loops are considerably shifted to larger fields corresponding to the increase in coercivity

Canonical Quantization of the Gowdy Model

The family of Gowdy universes with the spatial topology of a three-torus is studied both classically and quantum mechanically. Starting with the Ashtekar formulation of Lorentzian general relativity, we introduce a gauge fixing procedure to remove almost all of the non-physical degrees of freedom. In this way, we arrive at a reduced model that is subject only to one homogeneous constraint. The phase space of this model is described by means of a canonical set of elementary variables. These are two real, homogeneous variables and the Fourier coefficients for four real fields that are periodic in the angular coordinate which does not correspond to a Killing field of the Gowdy spacetimes. We also obtain the explicit expressions for the line element and reduced Hamiltonian. We then proceed to quantize the system by representing the elementary variables as linear operators acting on a vector space of analytic functionals. The inner product on that space is selected by imposing Lorentzian reality conditions. We find the quantum states annihilated by the operator that represents the homogeneous constraint of the model and construct with them the Hilbert space of physical states. Finally, we derive the general form of the quantum observables of the model.Comment: 13 pages, Revte

Einstein's equations and the chiral model

The vacuum Einstein equations for spacetimes with two commuting spacelike Killing field symmetries are studied using the Ashtekar variables. The case of compact spacelike hypersurfaces which are three-tori is considered, and the determinant of the Killing two-torus metric is chosen as the time gauge. The Hamiltonian evolution equations in this gauge may be rewritten as those of a modified SL(2) principal chiral model with a time dependent `coupling constant', or equivalently, with time dependent SL(2) structure constants. The evolution equations have a generalized zero-curvature formulation. Using this form, the explicit time dependence of an infinite number of spatial-diffeomorphism invariant phase space functionals is extracted, and it is shown that these are observables in the sense that they Poisson commute with the reduced Hamiltonian. An infinite set of observables that have SL(2) indices are also found. This determination of the explicit time dependence of an infinite set of spatial-diffeomorphism invariant observables amounts to the solutions of the Hamiltonian Einstein equations for these observables.Comment: 22 pages, RevTeX, to appear in Phys. Rev.

A Novel Hybrid Notch (HN) Substrate Integrated Waveguide (SIW) Bandstop Filter

The advent of substrate integrated waveguide has seen an influx of researches on the study and design of microwave filters employing such a technique[1]-[4]. This technique provides an excellent avenue to design millimeter wave circuits such as filters, resonators and antennae [5]. A great advantage is that these devices can be easily connected to other planar microwave transmission lines and devices by using very simple transitions [6]. While many researches on SIW primarily focused on bandpass filters, researches on SIW bandstop filters for the GHz frequency ranges are gaining momentum working on the big list of advantages of SIW over microstrips. This paper presents the analysis and design of a novel Hybrid Notch Bandstop Filter working in the X-Band of the Frequency Spectrum

Background independent quantization and the uncertainty principle

It is shown that polymer quantization leads to a modified uncertainty principle similar to that obtained from string theory and non-commutative geometry. When applied to quantum field theory on general background spacetimes, corrections to the uncertainty principle acquire a metric dependence. For Friedmann-Robertson-Walker cosmology this translates to a scale factor dependence which gives a large effect in the early universe.Comment: 6 page

Design and development of Modified-Proportional Fair scheduler for LTE/LTE-advanced

Long Term Evolution (LTE) is well known as a cellular network that can support very high data rates in diverse traffic conditions. One way of achieving it is through packet scheduling which is the key scheme of Radio Resource Management (RRM) for LTE traffic processing that is functioning to allocate resources for both frequency and time dimensions. The main contribution of this paper is the design of a new scheduling scheme and its performance is compared with the Proportional Fair (PF) and Round Robin (RR) downlink schedulers for LTE by utilizing LTE Downlink System Level Simulator. The proposed new scheduling algorithm, namely the Modified-PF scheduler divides a single subframe into multiple time slots and allocates the resource block (RB) to the targeted User Equipment (UE) in all time slots for each subframe based on the instantaneous Channel Quality Indicator (CQI) feedback received from UEs. Simulation results show that the Modified-PF scheduler provides the best performance in terms of throughput and spectral efficiency with comparale fairness as compared to RR and PF schedulers. Although PF scheduler has the best fairness index, the Modified-PF scheduler provides a better compromise between the throughput/spectral efficiency and fairness. This shows that the newly proposed scheme improves the LTE output performances while at the same time maintains minimal required fairness among the UEs

Modified general relativity as a model for quantum gravitational collapse

We study a class of Hamiltonian deformations of the massless Einstein-Klein-Gordon system in spherical symmetry for which the Dirac constraint algebra closes. The system may be regarded as providing effective equations for quantum gravitational collapse. Guided by the observation that scalar field fluxes do not follow metric null directions due to the deformation, we find that the equations take a simple form in characteristic coordinates. We analyse these equations by a unique combination of numerical methods and find that Choptuik's mass scaling law is modified by a mass gap as well as jagged oscillations. Furthermore, the results are universal with respect to different initial data profiles and robust under changes of the deformation.Comment: 22 pages, 4 figure

On a class of second-order PDEs admitting partner symmetries

Recently we have demonstrated how to use partner symmetries for obtaining noninvariant solutions of heavenly equations of Plebanski that govern heavenly gravitational metrics. In this paper, we present a class of scalar second-order PDEs with four variables, that possess partner symmetries and contain only second derivatives of the unknown. We present a general form of such a PDE together with recursion relations between partner symmetries. This general PDE is transformed to several simplest canonical forms containing the two heavenly equations of Plebanski among them and two other nonlinear equations which we call mixed heavenly equation and asymmetric heavenly equation. On an example of the mixed heavenly equation, we show how to use partner symmetries for obtaining noninvariant solutions of PDEs by a lift from invariant solutions. Finally, we present Ricci-flat self-dual metrics governed by solutions of the mixed heavenly equation and its Legendre transform.Comment: LaTeX2e, 26 pages. The contents change: Exact noninvariant solutions of the Legendre transformed mixed heavenly equation and Ricci-flat metrics governed by solutions of this equation are added. Eq. (6.10) on p. 14 is correcte