On the Einstein-Vlasov system with hyperbolic symmetry

It is shown that a spacetime with collisionless matter evolving from data on a compact Cauchy surface with hyperbolic symmetry can be globally covered by compact hypersurfaces on which the mean curvature is constant and by compact hypersurfaces on which the area radius is constant. Results for the related cases of spherical and plane symmetry are reviewed and extended. The prospects of using the global time coordinates obtained in this way to investigate the global geometry of the spacetimes concerned are discussed.Comment: 23 pages LaTeX2

Antisymmetric PT-photonic structures with balanced positive and negative index materials

We propose a new class of synthetic optical materials in which the refractive index satisfies n(-\bx)=-n^*(\bx). We term such systems antisymmetric parity-time (APT) structures. Unlike PT-symmetric systems which require balanced gain and loss, i.e. n(-\bx)=n^*(\bx), APT systems consist of balanced positive and negative index materials. Despite the seemingly PT-symmetric optical potential V(\bx)\equiv n(\bx)^2\omega^2/c^2, APT systems are not invariant under combined PT operations due to the discontinuity of the spatial derivative of the wavefunction. We show that APT systems can display intriguing properties such as spontaneous phase transition of the scattering matrix, bidirectional invisibility, and a continuous lasing spectrum.Comment: 5 pages, 4 figure

Solutions for certain classes of Riccati differential equation

We derive some analytic closed-form solutions for a class of Riccati equation y'(x)-\lambda_0(x)y(x)\pm y^2(x)=\pm s_0(x), where \lambda_0(x), s_0(x) are C^{\infty}-functions. We show that if \delta_n=\lambda_n s_{n-1}-\lambda_{n-1}s_n=0, where \lambda_{n}= \lambda_{n-1}^\prime+s_{n-1}+\lambda_0\lambda_{n-1} and s_{n}=s_{n-1}^\prime+s_0\lambda_{k-1}, n=1,2,..., then The Riccati equation has a solution given by y(x)=\mp s_{n-1}(x)/\lambda_{n-1}(x). Extension to the generalized Riccati equation y'(x)+P(x)y(x)+Q(x)y^2(x)=R(x) is also investigated.Comment: 10 page

Spectral Theory for Non-linear Superconducting Microwave Systems: Extracting Relaxation Rates and Mode Hybridization

The accurate modeling of mode hybridization and calculation of radiative relaxation rates have been crucial to the design and optimization of superconducting quantum devices. In this work, we introduce a spectral theory for the electrohydrodynamics of superconductors that enables the extraction of the relaxation rates of excitations in a general three-dimensional distribution of superconducting bodies. Our approach addresses the long-standing problem of formulating a modal description of open systems that is both efficient and allows for second quantization of the radiative hybridized fields. This is achieved through the implementation of finite but transparent boundaries through which radiation can propagate into and out of the computational domain. The resulting spectral problem is defined within a coarse-grained formulation of the electrohydrodynamical equations that is suitable for the analysis of the non-equilibrium dynamics of multiscale superconducting quantum systems.Comment: 21 pages, 12 figures, journal pape

Energies and wave functions for a soft-core Coulomb potential

For the family of model soft Coulomb potentials represented by V(r) = -\frac{Z}{(r^q+\beta^q)^{\frac{1}{q}}}, with the parameters Z>0, \beta>0, q \ge 1, it is shown analytically that the potentials and eigenvalues, E_{\nu\ell}, are monotonic in each parameter. The potential envelope method is applied to obtain approximate analytic estimates in terms of the known exact spectra for pure power potentials. For the case q =1, the Asymptotic Iteration Method is used to find exact analytic results for the eigenvalues E_{\nu\ell} and corresponding wave functions, expressed in terms of Z and \beta. A proof is presented establishing the general concavity of the scaled electron density near the nucleus resulting from the truncated potentials for all q. Based on an analysis of extensive numerical calculations, it is conjectured that the crossing between the pair of states [(\nu,\ell),(\nu',\ell')], is given by the condition \nu'\geq (\nu+1) and \ell' \geq (\ell+3). The significance of these results for the interaction of an intense laser field with an atom is pointed out. Differences in the observed level-crossing effects between the soft potentials and the hydrogen atom confined inside an impenetrable sphere are discussed.Comment: 13 pages, 5 figures, title change, minor revision

Modes of Random Lasers

In conventional lasers, the optical cavity that confines the photons also determines essential characteristics of the lasing modes such as wavelength, emission pattern, ... In random lasers, which do not have mirrors or a well-defined cavity, light is confined within the gain medium by means of multiple scattering. The sharp peaks in the emission spectra of semiconductor powders, first observed in 1999, has therefore lead to an intense debate about the nature of the lasing modes in these so-called lasers with resonant feedback. In this paper, we review numerical and theoretical studies aimed at clarifying the nature of the lasing modes in disordered scattering systems with gain. We will discuss in particular the link between random laser modes near threshold (TLM) and the resonances or quasi-bound (QB) states of the passive system without gain. For random lasers in the localized regime, QB states and threshold lasing modes were found to be nearly identical within the scattering medium. These studies were later extended to the case of more lossy systems such as random systems in the diffusive regime where differences between quasi-bound states and lasing modes were measured. Very recently, a theory able to treat lasers with arbitrarily complex and open cavities such as random lasers established that the TLM are better described in terms of the so-called constant-flux states.Comment: Review paper submitted to Advances in Optics and Photonic

On the rotational dynamics of magnetically threaded disks around neutron stars

We investigate the rotational dynamics of disk accretion around a strongly magnetized neutron star with an aligned dipole field. The magnetospheric field is assumed to thread the disk plasma both inside and outside the corotation radius. As a result of disk-star interaction, the magnetic torque on the disk affects the structure of accretion flow to yield the observed spin- up or spin- down rates for a source of given fastness, magnetic field strength, and mass accretion rate. Within the model we obtain a prescription for the dynamical viscosity of such magnetically modified solutions for a Keplerian disk. We then use this prescription to find a model solution for the rotation rate profile throughout the entire disk, including the non-Keplerian inner disk. We find that the non-Keplerian angular velocity transition region is not necessarily narrow for a source of given spin state. The boundary layer approximation, as in the standard magnetically threaded disk model, holds only in the case of dynamical viscosity decreasing all the way to the innermost edge of the disk. These results are applied to several observed disk-fed X-ray pulsars that have exhibited quasi-periodic oscillations (QPOs). The QPO frequencies provide a constraint on the fastness parameter and enable one to determine uniquely the width of the angular velocity transition zone for each source within model assumptions. We discuss the implications of these results on the value of the critical fastness parameter for a magnetized star in spin equilibrium. Applications of our model are also made with relevant parameters from recent numerical simulations of quasi-stationary disk - magnetized star interactions

Accounting for construction contracts : a case study on Gama Corporation

Ankara : Faculty of Management and Graduate School of Business Administration, Bilkent Univ., 1995.Thesis (Master's) -- Bilkent University, 1995.Includes bibliographical refences.This study focuses on the Accounting for Construction Contracts in Turkey, by giving examples from GAMA Corporation. The major characters involved in contracts and types of contracts are discussed in the study. Main methods for the accounting of construction contracts are examined. The most favorable contract method for Turkey is selected.Egel, D HakanM.S