Waveforms for Gravitational Radiation from Cosmic String Loops

We obtain general formulae for the plus- and cross- polarized waveforms of gravitational radiation emitted by a cosmic string loop in transverse, traceless (synchronous, harmonic) gauge. These equations are then specialized to the case of piecewise linear loops, and it is shown that the general waveform for such a loop is a piecewise linear function. We give several simple examples of the waveforms from such loops. We also discuss the relation between the gravitational radiation by a smooth loop and by a piecewise linear approximation to it.Comment: 16 pages, 6 figures, Revte

Using gravitational lenses to detect gravitational waves

Gravitational lenses could be used to detect gravitational waves, because a gravitational wave affects the travel-time of a light ray. In a gravitational lens, this effect produces time-delays between the different images. Thus the bending of light, which was the first experimental confirmation of Einstein's theory, can be used to search for gravitational waves, which are the most poorly confirmed aspect of that same theory. Applying this method to the gravitational lens 0957+561 gives new upper bounds on the amplitude of low-frequency gravitational waves in the universe, and new limits on the energy-density during an early ldquoinflationaryrdquo phase

The graviton propagator in homogeneous and isotropic spacetimes

We find the propagator for gravitons in spacetimes with homogeneous and isotropic flat (k=0) spatial sections. The method also applies to the k = + 1 and K = −1 cases. The vacuum state is assumed to be homogeneous and isotropic in the same way as the spacetime. In the four most interesting physical cases, which are de Sitter space, the radiation and dust dominated models, and flat space, we obtain the graviton propagator in closed form for the adiabatic vacuum state

Estimating the age of renal tumors

We present a Bayesian method for estimating the age of a renal tumor given its size. We use a model of tumor growth based on published data from observations of untreated tumors. We find, for example, that the median age of a 5 cm tumor is 20 years, with interquartile range 16-23 and 90% confidence interval 11-30 years.Comment: 3 pages, 3 figure

Electron Self-Energy and Generalized Drude Formula for Infrared Conductivity of Metals

Goetze and Woelfle (GW) wrote the conductivity in terms of a memory function M as (ine2/m)/(omega+M(omega)), where M=i/tau in the Drude limit. The analytic properties of -M are the same as those of the self-energy of a retarded Green's function. In the approximate treatment of GW, -M closely resembles a self-energy, with differences, e.g., the imaginary part is twice too large. The correct relation between -M and the self-energy is known for the electron-phonon case and is conjectured to be similar for other perturbations. When vertex corrections are ignored there is a known relation. A derivation using Matsubara temperature Green's functions is given.Comment: The original version (arXiv:cond-mat/0407777v1) of July 2004 has been slightly improved. It is now (July 2015) belatedly "in production" at Phys. Rev. B. This new version is the one which will appear in print. The referees made useful suggestions, and some more recent papers are now cited. There are 4 pages, 0 figure

Modularity of nearly ordinary 2-adic residually dihedral Galois representations

We prove modularity of some two dimensional, 2-adic Galois representations over totally real fields that are nearly ordinary and that are residually dihedral. We do this by employing the strategy of Skinner and Wiles, using Hida families, together with the 2-adic patching method of Khare and Wintenberger. As an application we deduce modularity of some elliptic curves over totally real fields that have good ordinary or multiplicative reduction at places above 2.Comment: 87 pages. Typos correcte