51,121 research outputs found
A Modified Version of the Waxman Algorithm
The iterative algorithm recently proposed by Waxman for solving eigenvalue
problems, which relies on the method of moments, has been modified to improve
its convergence considerably without sacrificing its benefits or elegance. The
suggested modification is based on methods to calculate low-lying eigenpairs of
large bounded hermitian operators or matrices
The Singularity in Generic Gravitational Collapse Is Spacelike, Local, and Oscillatory
A longstanding conjecture by Belinskii, Khalatnikov, and Lifshitz that the
singularity in generic gravitational collapse is spacelike, local, and
oscillatory is explored analytically and numerically in spatially inhomogeneous
cosmological spacetimes. With a convenient choice of variables, it can be seen
analytically how nonlinear terms in Einstein's equations control the approach
to the singularity and cause oscillatory behavior. The analytic picture
requires the drastic assumption that each spatial point evolves toward the
singularity as an independent spatially homogeneous universe. In every case,
detailed numerical simulations of the full Einstein evolution equations support
this assumption.Comment: 7 pages includes 4 figures. Uses Revtex and psfig. Received
"honorable mention" in 1998 Gravity Research Foundation essay contest.
Submitted to Mod. Phys. Lett.
The Mellin Transform Technique for the Extraction of the Gluon Density
A new method is presented to determine the gluon density in the proton from
jet production in deeply inelastic scattering. By using the technique of Mellin
transforms not only for the solution of the scale evolution equation of the
parton densities but also for the evaluation of scattering cross sections, the
gluon density can be extracted in next-to-leading order QCD. The method
described in this paper is, however, more general, and can be used in
situations where a repeated fast numerical evaluation of scattering cross
sections for varying parton distribution functions is required.Comment: 13 pages (LaTeX); 2 figures are included via epsfig; the
corresponding postscript files are uuencode
Improved inorganic ion exchange membranes
New method makes solid ion exchange membrane electrolytes for use in hydrocarbon-oxygen and hydrogen-oxygen fuel cells. The membrane is a sintered composite of zirconia, phosphoric acid, and zeolite
A Radio Flare from GRB 020405: Evidence for a Uniform Medium Around a Massive Stellar Progenitor
We present radio observations of GRB 020405 starting 1.2 days after the
burst, which reveal a rapidly-fading ``radio flare''. Based on its temporal and
spectral properties, we interpret the radio flare as emission from the reverse
shock. This scenario rules out a circumburst medium with a radial density
profile \rho ~ r^{-2} expected around a mass-losing massive star, since in that
case the reverse shock emission decays on the timescale of the burst duration
t~100 s. Using published optical and X-ray data, along with the radio data
presented here, we further show that a self-consistent model requires
collimated ejecta with an opening angle of 6 degrees (t_j~0.95 days). As a
consequence of the early jet break, the late-time (t>10 days) emission measured
with the Hubble Space Telescope significantly deviates from an extrapolation of
the early, ground-based data. This, along with an unusually red spectrum, F_\nu
\~ \nu^{-3.9}, strengthens the case for a supernova that exploded at about the
same time as GRB 020405, thus pointing to a massive stellar progenitor for this
burst. This is the first clear association of a massive progenitor with a
uniform medium, indicating that a \rho ~ r^{-2} profile is not a required
signature, and in fact may not be present on the lengthscales probed by the
afterglow in the majority of bursts.Comment: Submitted to ApJ; 14 pages, 2 tables, 3 figure
Improving the Convergence of an Iterative Algorithm Proposed By Waxman
In the iterative algorithm recently proposed by Waxman for solving eigenvalue
problems, we point out that the convergence rate may be improved. For many
non-singular symmetric potentials which vanish asymptotically, a simple
analytical relationship between the coupling constant of the potential and the
ground state eigenvalue is obtained which can be used to make the algorithm
more efficient
Manufacture of Gowdy spacetimes with spikes
In numerical studies of Gowdy spacetimes evidence has been found for the
development of localized features (spikes) involving large gradients near the
singularity. The rigorous mathematical results available up to now did not
cover this kind of situation. In this work we show the existence of large
classes of Gowdy spacetimes exhibiting features of the kind discovered
numerically. These spacetimes are constructed by applying certain
transformations to previously known spacetimes without spikes. It is possible
to control the behaviour of the Kretschmann scalar near the singularity in
detail. This curvature invariant is found to blow up in a way which is
non-uniform near the spike in some cases. When this happens it demonstrates
that the spike is a geometrically invariant feature and not an artefact of the
choice of variables used to parametrize the metric. We also identify another
class of spikes which are artefacts. The spikes produced by our method are
compared with the results of numerical and heuristic analyses of the same
situation.Comment: 25 page
Competing charge density waves and temperature-dependent nesting in 2H-TaSe2
Multiple charge density wave (CDW) phases in 2H-TaSe2 are investigated by
high-resolution synchrotron x-ray diffraction. In a narrow temperature range
immediately above the commensurate CDW transition, we observe a multi-q
superstructure with coexisting commensurate and incommensurate order
parameters, clearly distinct from the fully incommensurate state at higher
temperatures. This multi-q ordered phase, characterized by a temperature
hysteresis, is found both during warming and cooling, in contrast to previous
reports. In the normal state, the incommensurate superstructure reflection
gives way to a broad diffuse peak that persists nearly up to room temperature.
Its position provides a direct and accurate estimate of the Fermi surface
nesting vector, which evolves non-monotonically and approaches the commensurate
position as the temperature is increased. This behavior agrees with our recent
observations of the temperature-dependent Fermi surface in the same compound
[Phys. Rev. B 79, 125112 (2009)]
Optical properties of periodic systems within the current-current response framework: pitfalls and remedies
We compare the optical absorption of extended systems using the
density-density and current-current linear response functions calculated within
many-body perturbation theory. The two approaches are formally equivalent for a
finite momentum of the external perturbation. At
, however, the equivalence is maintained only if a small
expansion of the density-density response function is used. Moreover, in
practical calculations this equivalence can be lost if one naively extends the
strategies usually employed in the density-based approach to the current-based
approach. Specifically we discuss the use of a smearing parameter or of the
quasiparticle lifetimes to describe the finite width of the spectral peaks and
the inclusion of electron-hole interaction. In those instances we show that the
incorrect definition of the velocity operator and the violation of the
conductivity sum rule introduce unphysical features in the optical absorption
spectra of three paradigmatic systems: silicon (semiconductor), copper (metal)
and lithium fluoride (insulator). We then demonstrate how to correctly
introduce lifetime effects and electron-hole interactions within the
current-based approach.Comment: 17 pages, 6 figure
- …