The instability of a viscous sheet floating on an air cushion

The dynamics of a thin sheet of viscous liquid levitating on an air cushion is studied. Experimentally, it is observed that, after an initial settling stage, a local disturbance grows, eventually leading to the sheet blowing up like a viscous balloon. We derive a dynamical model for the levitating sheet and propose a mechanism for the onset of the instability. This instability is driven by the local drainage of the sheet due to a growing disturbance on its lower surface and is moderated by surface tension, the bending stiffness of the sheet and advection in the air layer. The balance between these effects determines the most unstable wavelength and this is illustrated by some numerical simulations

Fringe Science: Defringing CCD Images with Neon Lamp Flat Fields

Fringing in CCD images is troublesome from the aspect of photometric quality and image flatness in the final reduced product. Additionally, defringing during calibration requires the inefficient use of time during the night to collect and produce a "supersky" fringe frame. The fringe pattern observed in a CCD image for a given near-IR filter is dominated by small thickness variations across the detector with a second order effect caused by the wavelength extent of the emission lines within the bandpass which produce the interference pattern. We show that essentially any set of emission lines which generally match the wavelength coverage of the night sky emission lines within a bandpass will produce an identical fringe pattern. We present an easy, inexpensive, and efficient method which uses a neon lamp as a flat field source and produces high S/N fringe frames to use for defringing an image during the calibration process.Comment: accepted to PAS

Test particle propagation in magnetostatic turbulence. 3: The approach to equilibrium

The asymptotic behavior, for large time, of the quasi-linear diabatic solutions and their local approximations is considered. A time averaging procedure is introduced which yields the averages of these solutions over time intervals which contain only large time values. A discussion of the quasi-linear diabatic solutions which is limited to those solutions that are bounded from below as functions of time is given. It is shown that as the upper limit of the time averaging interval is allowed to approach infinity the time averaged quasi-linear diabatic solutions must approach isotropy (mu-independence). The first derivative with respect to mu of these solutions is also considered. This discussion is limited to first derivatives which are bounded functions of time. It is shown that as the upper limit of the time averaging interval is allowed to approach infinity, the time averaged first derivative must approach zero everywhere in mu except at mu = 0 where it must approach a large value which is calculated. The impact of this large derivative on the quasi-linear expansion scheme is discussed. An H-theorem for the first local approximation to the quasi-linear diabatic solutions is constructed. Without time averaging, the H-theorem is used to determine sufficient conditions for the first local approximate solutions to asymptote, with increasing time, to exactly the same final state which the time averaged quasi-linear diabatic solutions must approach as discussed above

Test particle propagation in magnetostatic turbulence. 2: The local approximation method

An approximation method for statistical mechanics is presented and applied to a class of problems which contains a test particle propagation problem. All of the available basic equations used in statistical mechanics are cast in the form of a single equation which is integrodifferential in time and which is then used as the starting point for the construction of the local approximation method. Simplification of the integrodifferential equation is achieved through approximation to the Laplace transform of its kernel. The approximation is valid near the origin in the Laplace space and is based on the assumption of small Laplace variable. No other small parameter is necessary for the construction of this approximation method. The n'th level of approximation is constructed formally, and the first five levels of approximation are calculated explicitly. It is shown that each level of approximation is governed by an inhomogeneous partial differential equation in time with time independent operator coefficients. The order in time of these partial differential equations is found to increase as n does. At n = 0 the most local first order partial differential equation which governs the Markovian limit is regained

Test particle propagation in magnetostatic turbulence. 1. Failure of the diffusion approximation

The equation which governs the quasi-linear approximation to the ensemble and gyro-phase averaged one-body probability distribution function is constructed from first principles. This derived equation is subjected to a thorough investigation in order to calculate the possible limitations of the quasi-linear approximation. It is shown that the reduction of this equation to a standard diffusion equation in the Markovian limit can be accomplished through the application of the adiabatic approximation. A numerical solution of the standard diffusion equation in the Markovian limit is obtained for the narrow parallel beam injection. Comparison of the diabatic and adiabatic results explicitly demonstrates the failure of the Markovian description of the probability distribution function. Through the use of a linear time-scale extension the failure of the adiabatic approximation, which leads to the Markovian limit, is shown to be due to mixing of the relaxation and interaction time scales in the presence of the strong mean field

On the gravitational wave background from compact binary coalescences in the band of ground-based interferometers

This paper reports a comprehensive study on the gravitational wave (GW) background from compact binary coalescences. We consider in our calculations newly available observation-based neutron star and black hole mass distributions and complete analytical waveforms that include post-Newtonian amplitude corrections. Our results show that: (i) post-Newtonian effects cause a small reduction in the GW background signal; (ii) below 100 Hz the background depends primarily on the local coalescence rate $r_0$ and the average chirp mass and is independent of the chirp mass distribution; (iii) the effects of cosmic star formation rates and delay times between the formation and merger of binaries are linear below 100 Hz and can be represented by a single parameter within a factor of ~ 2; (iv) a simple power law model of the energy density parameter $\Omega_{GW}(f) ~ f^{2/3}$ up to 50-100 Hz is sufficient to be used as a search template for ground-based interferometers. In terms of the detection prospects of the background signal, we show that: (i) detection (a signal-to-noise ratio of 3) within one year of observation by the Advanced LIGO detectors (H1-L1) requires a coalescence rate of $r_0 = 3 (0.2) Mpc^{-3} Myr^{-1}$ for binary neutron stars (binary black holes); (ii) this limit on $r_0$ could be reduced 3-fold for two co-located detectors, whereas the currently proposed worldwide network of advanced instruments gives only ~ 30% improvement in detectability; (iii) the improved sensitivity of the planned Einstein Telescope allows not only confident detection of the background but also the high frequency components of the spectrum to be measured. Finally we show that sub-threshold binary neutron star merger events produce a strong foreground, which could be an issue for future terrestrial stochastic searches of primordial GWs.Comment: A few typos corrected to match the published version in MNRA

Is there Evidence for a Hubble bubble? The Nature of Type Ia Supernova Colors and Dust in External Galaxies

We examine recent evidence from the luminosity-redshift relation of Type Ia Supernovae (SNe Ia) for the $\sim 3 \sigma$ detection of a ``Hubble bubble'' -- a departure of the local value of the Hubble constant from its globally averaged value \citep{Jha:07}. By comparing the MLCS2k2 fits used in that study to the results from other light-curve fitters applied to the same data, we demonstrate that this is related to the interpretation of SN color excesses (after correction for a light-curve shape-color relation) and the presence of a color gradient across the local sample. If the slope of the linear relation ($\beta$) between SN color excess and luminosity is fit empirically, then the bubble disappears. If, on the other hand, the color excess arises purely from Milky Way-like dust, then SN data clearly favors a Hubble bubble. We demonstrate that SN data give $\beta \simeq 2$, instead of the $\beta \simeq 4$ one would expect from purely Milky-Way-like dust. This suggests that either SN intrinsic colors are more complicated than can be described with a single light-curve shape parameter, or that dust around SN is unusual. Disentangling these possibilities is both a challenge and an opportunity for large-survey SN Ia cosmology.Comment: Further information and data at http://qold.astro.utoronto.ca/conley/bubble/ Accepted for publication in ApJ

A model for the screen printing of Newtonian fluids

A preliminary investigation into aspects of the off-contact screen-printing process is presented. A mathematical model for the printing of a thin film of Newtonian fluid is proposed, in which the screen is modelled as a permeable membrane, and the entire region above and below the screen is flooded. By drawing upon widely used industrial circuit printing practices, the distinguished limit of greatest interest to this industry is identified. Numerical and asymptotic solutions of this distinguished limit are presented that reproduce many of the features observed in industrial screen-printing