4,754 research outputs found
The heat kernel coefficient for oblique boundary conditions
We present a method for the calculation of the heat kernel
coefficient of the heat operator trace for a partial differential operator of
Laplace type on a compact Riemannian manifold with oblique boundary conditions.
Using special case evaluations, restrictions are put on the general form of the
coefficients, which, supplemented by conformal transformation techniques,
allows the entire smeared coefficient to be determined.Comment: 30 pages, LaTe
Index-free Heat Kernel Coefficients
Using index-free notation, we present the diagonal values of the first five
heat kernel coefficients associated with a general Laplace-type operator on a
compact Riemannian space without boundary. The fifth coefficient appears here
for the first time. For a flat space with a gauge connection, the sixth
coefficient is given too. Also provided are the leading terms for any
coefficient, both in ascending and descending powers of the Yang-Mills and
Riemann curvatures, to the same order as required for the fourth coefficient.
These results are obtained by directly solving the relevant recursion
relations, working in Fock-Schwinger gauge and Riemann normal coordinates. Our
procedure is thus noncovariant, but we show that for any coefficient the
`gauged' respectively `curved' version is found from the corresponding
`non-gauged' respectively `flat' coefficient by making some simple covariant
substitutions. These substitutions being understood, the coefficients retain
their `flat' form and size. In this sense the fifth and sixth coefficient have
only 26 and 75 terms respectively, allowing us to write them down. Using
index-free notation also clarifies the general structure of the heat kernel
coefficients. In particular, in flat space we find that from the fifth
coefficient onward, certain scalars are absent. This may be relevant for the
anomalies of quantum field theories in ten or more dimensions.Comment: 38 pages, LaTe
A Study of 3CR Radio Galaxies from z = 0.15 to 0.65. II. Evidence for an Evolving Radio Structure
Radio structure parameters were measured from the highest quality radio maps
available for a sample of 3CR radio galaxies in the redshift range 0.15 < z <
0.65. Combined with similar data for quasars in the same redshift range, these
morphology data are used in conjunction with a quantification of the richness
of the cluster environment around these objects (the amplitude of the
galaxy-galaxy spatial covariance function, Bgg) to search for indirect evidence
of a dense intracluster medium (ICM). This is done by searching for confinement
and distortions of the radio structure that are correlated with Bgg.
Correlations between physical size and hot spot placement with Bgg show
evidence for an ICM only at z 0.4,
suggesting an epoch of z ~ 0.4 for the formation of an ICM in these Abell
richness class 0-1, FR2-selected clusters. X-ray selected clusters at
comparable redshifts, which contain FR1 type sources exclusively, are
demonstrably richer than the FR2-selected clusters found in this study. The
majority of the radio sources with high Bgg values at z < 0.4 can be described
as ``fat doubles'' or intermediate FR2/FR1s. The lack of correlation between
Bgg and bending angle or Bgg and lobe length asymmetry suggests that these
types of radio source distortion are caused by something other than interaction
with a dense ICM. Thus, a large bending angle cannot be used as an unambiguous
indicator of a rich cluster around powerful radio sources. These results
support the hypothesis made in Paper 1 that cluster quasars fade to become
FR2s, then FR1s, on a timescale of 0.9 Gyrs (for H0 = 50 km s^-1 Mpc^-1).Comment: 44 pages, 8 figures, 2 tables; to be published in the September 2002
issue of The Astronomical Journa
Bose-Einstein condensation in arbitrarily shaped cavities
We discuss the phenomenon of Bose-Einstein condensation of an ideal
non-relativistic Bose gas in an arbitrarily shaped cavity. The influence of the
finite extension of the cavity on all thermodynamical quantities, especially on
the critical temperature of the system, is considered. We use two main methods
which are shown to be equivalent. The first deals with the partition function
as a sum over energy levels and uses a Mellin-Barnes integral representation to
extract an asymptotic formula. The second method converts the sum over the
energy levels to an integral with a suitable density of states factor obtained
from spectral analysis. The application to some simple cavities is discussed.Comment: 10 pages, LaTeX, to appear in Physical Review
The hybrid spectral problem and Robin boundary conditions
The hybrid spectral problem where the field satisfies Dirichlet conditions
(D) on part of the boundary of the relevant domain and Neumann (N) on the
remainder is discussed in simple terms. A conjecture for the C_1 coefficient is
presented and the conformal determinant on a 2-disc, where the D and N regions
are semi-circles, is derived. Comments on higher coefficients are made.
A hemisphere hybrid problem is introduced that involves Robin boundary
conditions and leads to logarithmic terms in the heat--kernel expansion which
are evaluated explicitly.Comment: 24 pages. Typos and a few factors corrected. Minor comments added.
Substantial Robin additions. Substantial revisio
Hydrodynamics in full general relativity with conservative AMR
There is great interest in numerical relativity simulations involving matter
due to the likelihood that binary compact objects involving neutron stars will
be detected by gravitational wave observatories in the coming years, as well as
to the possibility that binary compact object mergers could explain
short-duration gamma-ray bursts. We present a code designed for simulations of
hydrodynamics coupled to the Einstein field equations targeted toward such
applications. This code has recently been used to study eccentric mergers of
black hole-neutron star binaries. We evolve the fluid conservatively using
high-resolution shock-capturing methods, while the field equations are solved
in the generalized-harmonic formulation with finite differences. In order to
resolve the various scales that may arise, we use adaptive mesh refinement
(AMR) with grid hierarchies based on truncation error estimates. A noteworthy
feature of this code is the implementation of the flux correction algorithm of
Berger and Colella to ensure that the conservative nature of fluid advection is
respected across AMR boundaries. We present various tests to compare the
performance of different limiters and flux calculation methods, as well as to
demonstrate the utility of AMR flux corrections.Comment: 22 pages, 14 figures; revised according referee comments, PRD in
pres
The spin dependence of high energy proton scattering
Motivated by the need for an absolute polarimeter to determine the beam
polarization for the forthcoming RHIC spin program, we study the spin
dependence of the proton-proton elastic scattering amplitudes at high energy
and small momentum transfer.We examine experimental evidence for the existence
of an asymptotic part of the helicity-flip amplitude phi_5 which is not
negligible relative to the largely imaginary average non-flip amplitude phi_+.
We discuss theoretical estimates of r_5, essentially the ratio of phi_5 to
phi_+, based upon extrapolation of low and medium energy Regge phenomenological
results to high energies, models based on a hybrid of perturbative QCD and
non-relativistic quark models, and models based on eikonalization techniques.
We also apply the model-independent methods of analyticity and unitarity.The
preponderence of evidence at available energy indicates that r_5 is small,
probably less than 10%. The best available experimental limit comes from
Fermilab E704:those data indicate that |r_5|<15%. These bounds are important
because rigorous methods allow much larger values. In contradiction to a
widely-held prejudice that r_5 decreases with energy, general principles allow
it to grow as fast as ln(s) asymptotically, and some models show an even faster
growth in the RHIC range. One needs a more precise measurement of r_5 or to
bound it to be smaller than 5% in order to use the classical Coulomb-nuclear
interference technique for RHIC polarimetry. As part of this study, we
demonstrate the surprising result that proton-proton elastic scattering is
self-analysing, in the sense that all the helicity amplitudes can, in
principle, be determined experimentally at small momentum transfer without a
knowledge of the magnitude of the beam and target polarization
X-ray Spectral Survey of WGACAT Quasars, II: Optical and Radio Properties of Quasars with Low Energy X-ray Cut-offs
We have selected quasars with X-ray colors suggestive of a low energy
cut-off, from the ROSAT PSPC pointed archive. We examine the radio and optical
properties of these 13 quasars. Five out of the seven quasars with good optical
spectra show associated optical absorption lines, with two having high delta-v
candidate systems. Two other cut-off quasars show reddening associated with the
quasar. We conclude that absorption is highly likely to be the cause of the
X-ray cut-offs, and that the absorbing material associated with the quasars,
not intervening along the line-of-sight. The suggestion that Gigahertz Peaked
Sources are associated with X-ray cut-offs remains unclear with this expanded
sample.Comment: 17 pages, LaTeX, including 2 Tables and 1 figure. Ap.J. in pres
Notes on Stein-Sahi representations and some problems of non harmonic analysis
We discuss one natural class of kernels on pseudo-Riemannian symmetric
spaces.Comment: 40p
Analysis of charmonium production at fixed-target experiments in the NRQCD approach
We present an analysis of the existing data on charmonium hadro-production
based on non-relativistic QCD (NRQCD) calculations at the next-to-leading order
(NLO). All the data on J/psi and psi' production in fixed-target experiments
and on pp collisions at low energy are included. We find that the amount of
color octet contribution needed to describe the data is about 1/10 of that
found at the Tevatron
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