Models for thin viscous sheets

Leading-order equations governing the dynamics of a two-dimensional thin viscous sheet are derived. The inclusion of inertia effects is found to result in an ill-posed model when the sheet is compressed, and the resulting paradox is resolved by rescaling the equations over new length- and timescales which depend on the Reynolds number of the flow and the aspect ratio of the sheet. Physically this implies a dominant lengthscale for transverse displacements during viscous buckling. The theory is generalised to give new models for fully three-dimensional sheets

An improved method for estimating source densities using the temporal distribution of Cosmological Transients

It has been shown that the observed temporal distribution of transient events in the cosmos can be used to constrain their rate density. Here we show that the peak flux--observation time relation takes the form of a power law that is invariant to the luminosity distribution of the sources, and that the method can be greatly improved by invoking time reversal invariance and the temporal cosmological principle. We demonstrate how the method can be used to constrain distributions of transient events, by applying it to Swift gamma-ray burst data and show that the peak flux--observation time relation is in good agreement with recent estimates of source parameters. We additionally show that the intrinsic time dependence allows the method to be used as a predictive tool. Within the next year of Swift observation, we find a 50% chance of obtaining a peak flux greater than that of GRB 060017 -- the highest Swift peak flux to date -- and the same probability of detecting a burst with peak flux > 100 photons s^{-1} cm^{-2} within 6 years.Comment: Submitted to ApJ Letter

Using temporal distributions of transient events to characterize cosmological source populations

The brightest events in a time series of cosmological transients obey an observation time dependence which is often overlooked. This dependence can be exploited to probe the global properties of electromagnetic and gravitational wave transients (Howell et al. 2007a, Coward & Burman 2005). We describe a new relation based on a peak flux--observation time distribution and show that it is invariant to the luminosity distribution of the sources (Howell et al. 2007b). Applying this relation, in combination with a new data analysis filter, to \emph{Swift} gamma-ray burst data, we demonstrate that it can constrain their rate density.Comment: published in proceedings of FRONTIERS OF FUNDAMENTAL AND COMPUTATIONAL PHYSICS: 10th International Symposium, AIP,1246,203, (2010

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