Persistence of black holes through a cosmological bounce

We discuss whether black holes could persist in a universe which recollapses and then bounces into a new expansion phase. Whether the bounce is of classical or quantum gravitational origin, such cosmological models are of great current interest. In particular, we investigate the mass range in which black holes might survive a bounce and ways of differentiating observationally between black holes formed just after and just before the last bounce. We also discuss the consequences of the universe going through a sequence of dimensional changes as it passes through a bounce.Comment: 8 pages, 1 figur

An investigation into grid patching techniques

In the past decade significant advances were made using flow field methods in the calculation of external transonic flows over aerodynamic configurations. It is now possible to calculate inviscid transonic flow over three dimensional configurations by solving the potential equation. However, with the exception of the transonic small disturbance methods which have the advantage of a simple cartesian grid, the configurations over which it is possible to calculate such flows are relatively simple. The major reason for this is the difficulty of producing compatibility between grid generation and flow equation solutions. The main programs in use, use essentially analytic transformations for prescribed configurations and, as such, are not easy to extend. While there is work in progress to extend this type of system to a limited extent, the long term effort is directed towards a more general approach. This approach should not be restricted to producing grid systems in isolation but rather a consideration of the overall problem of flow field solution

Spontaneous soliton formation and modulational instability in Bose-Einstein condensates

The dynamics of an elongated attractive Bose-Einstein condensate in an axisymmetric harmonic trap is studied. It is shown that density fringes caused by self-interference of the condensate order parameter seed modulational instability. The latter has novel features in contradistinction to the usual homogeneous case known from nonlinear fiber optics. Several open questions in the interpretation of the recent creation of the first matter-wave bright soliton train [Strecker {\it et al.} Nature {\bf 417} 150 (2002)] are addressed. It is shown that primary transverse collapse, followed by secondary collapse induced by soliton--soliton interactions, produce bursts of hot atoms at different time scales.Comment: 4 pages, 3 figures. Phys. Rev. Lett. in pres

A pulsed atomic soliton laser

It is shown that simultaneously changing the scattering length of an elongated, harmonically trapped Bose-Einstein condensate from positive to negative and inverting the axial portion of the trap, so that it becomes expulsive, results in a train of self-coherent solitonic pulses. Each pulse is itself a non-dispersive attractive Bose-Einstein condensate that rapidly self-cools. The axial trap functions as a waveguide. The solitons can be made robustly stable with the right choice of trap geometry, number of atoms, and interaction strength. Theoretical and numerical evidence suggests that such a pulsed atomic soliton laser can be made in present experiments.Comment: 11 pages, 4 figure

Dynamic behavior of an unsteady trubulent boundary layer

Experiments on an unsteady turbulent boundary layer are reported in which the upstream portion of the flow is steady (in the mean) and in the downstream region, the boundary layer sees a linearly decreasing free stream velocity. This velocity gradient oscillates in time, at frequencies ranging from zero to approximately the bursting frequency. For the small amplitude, the mean velocity and mean turbulence intensity profiles are unaffected by the oscillations. The amplitude of the periodic velocity component, although as much as 70% greater than that in the free stream for very low frequencies, becomes equal to that in the free stream at higher frequencies. At high frequencies, both the boundary layer thickness and the Reynolds stress distribution across the boundary layer become frozen. The behavior at higher amplitude is quite similar. At sufficiently high frequencies, the boundary layer thickness remains frozen at the mean value over the oscillation cycle, even though flow reverses near the wall during a part of the cycle

Effect of Piezo Electric Oscillations on X-Ray Patterns of Quartz

Experiments have been made to determine the amplitude of vibration of the atoms in a quartz lattice due to piezo electric oscillations. A series of Laue X-ray patterns have been made of quartz plates cut at various angles to the electric axes. Very marked intensity differences are apparent between the patterns made with the plates oscillating and not oscillating

Signatures of superconducting gap inhomogeneities in optical properties

Scanning tunneling spectroscopy applied to the high-$T_{c}$ cuprates has revealed significant spatial inhomogeneity on the nanoscale. Regions on the order of a coherence length in size show variations of the magnitude of the superconducting gap of order $\pm20$ or more. An important unresolved question is whether or not these variations are also present in the bulk, and how they influence superconducting properties. As many theories and data analyses for high-$T_{c}$ superconductivity assume spatial homogeneity of the gap magnitude, this is a pressing question. We consider the far-infrared optical conductivity and evaluate, within an effective medium approximation, what signatures of spatial variations in gap magnitude are present in various optical quantities. In addition to the case of d-wave superconductivity, relevant to the high-$T_c$ cuprates, we have also considered s-wave gap symmetry in order to provide expected signatures of inhomogeneities for superconductors in general. While signatures of gap inhomogeneities can be strongly manifested in s-wave superconductors, we find that the far-infrared optical conductivity in d-wave is robust against such inhomogeneity.Comment: 8 pages, 7 figure

Functional co-monotony of processes with applications to peacocks and barrier options

We show that several general classes of stochastic processes satisfy a functional co-monotony principle, including processes with independent increments, Brownian diffusions, Liouville processes. As a first application, we recover some recent results about peacock processes obtained by Hirsch et al. which were themselves motivated by a former work of Carr et al. about the sensitivity of Asian Call options with respect to their volatility and residual maturity (seniority). We also derive semi-universal bounds for various barrier options.Comment: 27 page

Grey solitons in a strongly interacting superfluid Fermi Gas

The Bardeen-Cooper-Schrieffer to Bose-Einstein condensate (BCS to BEC) crossover problem is solved for stationary grey solitons via the Boguliubov-de Gennes equations at zero temperature. These \emph{crossover solitons} exhibit a localized notch in the gap and a characteristic phase difference across the notch for all interaction strengths, from BEC to BCS regimes. However, they do not follow the well-known Josephson-like sinusoidal relationship between velocity and phase difference except in the far BEC limit: at unitary the velocity has a nearly linear dependence on phase difference over an extended range. For fixed phase difference the soliton is of nearly constant depth from the BEC limit to unitarity and then grows progressively shallower into the BCS limit, and on the BCS side Friedel oscillations are apparent in both gap amplitude and phase. The crossover soliton appears fundamentally in the gap; we show, however, that the density closely follows the gap, and the soliton is therefore observable. We develop an approximate power law relationship to express this fact: the density of grey crossover solitons varies as the square of the gap amplitude in the BEC limit and a power of about 1.5 at unitarity.Comment: 10 pages, 6 figures, part of New Journal of Physics focus issue "Strongly Correlated Quantum Fluids: From Ultracold Quantum Gases to QCD Plasmas," in pres