GRB Afterglows from Anisotropic Jets

Some progenitor models of gamma-ray bursts (GRBs) (e.g., collapsars) may produce anisotropic jets in which the energy per unit solid angle is a power-law function of the angle ($\propto\theta^{-k}$). We calculate light curves and spectra for GRB afterglows when such jets expand either in the interstellar medium or in the wind medium. In particular, we take into account two kinds of wind: one ($n\propto r^{-3/2}$) possibly from a typical red supergiant star and another ($n\propto r^{-2}$) possibly from a Wolf-Rayet star. We find that in each type of medium, one break appears in the late-time afterglow light curve for small $k$ but becomes weaker and smoother as $k$ increases. When $k\ge 2$, the break seems to disappear but the afterglow decays rapidly. Thus, one expects that the emission from expanding, highly anisotropic jets provides a plausible explanation for some rapidly fading afteglows whose light curves have no break. We also present good fits to the optical afterglow light curve of GRB 991208. Finally, we argue that this burst might arise from a highly anisotropic jet expanding in the wind ($n\propto r^{-3/2}$) from a red supergiant to interpret the observed radio-to-optical-band afterglow data (spectrum and light curve).Comment: 12 pages + 10 figures, accepted by Ap

Post density functional theoretical studies of highly polar semiconductive Pb(Ti1−x_{1-x}Nix_{x})O3−x_{3-x} solid solutions: The effects of cation arrangement on band gap

We use a combination of conventional density functional theory (DFT) and post-DFT methods, including the local density approximation plus Hubbard $U$ (LDA+$U$), PBE0, and self-consistent $GW$ to study the electronic properties of Ni-substituted PbTiO$_{3}$ (Ni-PTO) solid solutions. We find that LDA calculations yield unreasonable band structures, especially for Ni-PTO solid solutions that contain an uninterrupted NiO$_{2}$ layer. Accurate treatment of localized states in transition-metal oxides like Ni-PTO requires post-DFT methods. $B$-site Ni/Ti cation ordering is also investigated. The $B$-site cation arrangement alters the bonding between Ni and O, and therefore strongly affects the band gap ($E_{\rm g}$) of Ni-PTO. We predict that Ni-PTO solid solutions should have a direct band gap in the visible light energy range, with polarization similar to the parent PbTiO$_{3}$. This combination of properties make Ni-PTO solid solutions promising candidate materials for solar energy conversion devices.Comment: 19 pages, 6 figure

Dark pair coherent states of the motion of a trapped ion

We propose a scheme for generating vibrational pair coherent states of the motion of an ion in a two-dimensional trap. In our scheme, the trapped ion is excited bichromatically by three laser beams along different directions in the X-Y plane of the ion trap. We show that if the initial vibrational state is given by a two-mode Fock state, the final steady state, indicated by the extinction of the fluorescence emitted by the ion, is a pure state. The motional state of the ion in the equilibrium realizes that of the highly-correlated pair coherent state.Comment: 14 pages, 3 figure

Bending-wave Instability of a Vortex Ring in a Trapped Bose-Einstein Condensate

Based on a velocity formula derived by matched asymptotic expansion, we investigate the dynamics of a circular vortex ring in an axisymmetric Bose-Einstein condensate in the Thomas-Fermi limit. The trajectory for an axisymmetrically placed and oriented vortex ring is entirely determined, revealing that the vortex ring generally precesses in condensate. The linear instability due to bending waves is investigated both numerically and analytically. General stability boundaries for various perturbed wavenumbers are computed. In particular, the excitation spectrum and the absolutely stable region for the static ring are analytically determined.Comment: 4 pages, 4 figure

Transcritical flow of a stratified fluid over topography: analysis of the forced Gardner equation

Transcritical flow of a stratified fluid past a broad localised topographic obstacle is studied analytically in the framework of the forced extended Korteweg--de Vries (eKdV), or Gardner, equation. We consider both possible signs for the cubic nonlinear term in the Gardner equation corresponding to different fluid density stratification profiles. We identify the range of the input parameters: the oncoming flow speed (the Froude number) and the topographic amplitude, for which the obstacle supports a stationary localised hydraulic transition from the subcritical flow upstream to the supercritical flow downstream. Such a localised transcritical flow is resolved back into the equilibrium flow state away from the obstacle with the aid of unsteady coherent nonlinear wave structures propagating upstream and downstream. Along with the regular, cnoidal undular bores occurring in the analogous problem for the single-layer flow modeled by the forced KdV equation, the transcritical internal wave flows support a diverse family of upstream and downstream wave structures, including solibores, rarefaction waves, reversed and trigonometric undular bores, which we describe using the recent development of the nonlinear modulation theory for the (unforced) Gardner equation. The predictions of the developed analytic construction are confirmed by direct numerical simulations of the forced Gardner equation for a broad range of input parameters.Comment: 34 pages, 24 figure

An adjustable law of motion for relativistic spherical shells

A classical and a relativistic law of motion for an advancing shell are deduced applying the thin layer approximation. A new parameter connected with the quantity of absorbed matter in the expansion is introduced; this allows of matching theory and observation.Comment: 15 pages, 10 figures and article in press; Central European Journal of Physics 201

A Dynamical Study of the Black Hole X-ray Binary Nova Muscae 1991

We present a dynamical study of the Galactic black hole binary system Nova Muscae 1991 (GS/GRS 1124-683). We utilize 72 high resolution Magellan Echellette (MagE) spectra and 72 strictly simultaneous V-band photometric observations; the simultaneity is a unique and crucial feature of this dynamical study. The data were taken on two consecutive nights and cover the full 10.4-hour orbital cycle. The radial velocities of the secondary star are determined by cross-correlating the object spectra with the best-match template spectrum obtained using the same instrument configuration. Based on our independent analysis of five orders of the echellette spectrum, the semi-amplitude of the radial velocity of the secondary is measured to be K_2 = 406.8+/-2.7 km/s, which is consistent with previous work, while the uncertainty is reduced by a factor of 3. The corresponding mass function is f(M) = 3.02+/-0.06 M_\odot. We have also obtained an accurate measurement of the rotational broadening of the stellar absorption lines (v sin i = 85.0+/-2.6 km/s) and hence the mass ratio of the system q = 0.079+/-0.007. Finally, we have measured the spectrum of the non-stellar component of emission that veils the spectrum of the secondary. In a future paper, we will use our veiling-corrected spectrum of the secondary and accurate values of K_2 and q to model multi-color light curves and determine the systemic inclination and the mass of the black hole.Comment: ApJ accepted version; minor revision; added a subsection about systematic uncertaintie

Quantum-state synthesis of multi-mode bosonic fields: Preparation of arbitrary states of 2-D vibrational motion of trapped ions

We present a universal algorithm for an efficient deterministic preparation of an arbitrary two--mode bosonic state. In particular, we discuss in detail preparation of entangled states of a two-dimensional vibrational motion of a trapped ion via a sequence of laser stimulated Raman transitions. Our formalism can be generalized for multi-mode bosonic fields. We examine stability of our algorithm with respect to a technical noise.Comment: 8 pages, revtex, including 2 ps-figures, section about physical implementation added, references updated, submitted to Phys. Rev. A, computer program available at http://www.savba.sk/sav/inst/fyzi/qo