1,310 research outputs found
Conformal regularization of Einstein's field equations
To study asymptotic structures, we regularize Einstein's field equations by
means of conformal transformations. The conformal factor is chosen so that it
carries a dimensional scale that captures crucial asymptotic features. By
choosing a conformal orthonormal frame we obtain a coupled system of
differential equations for a set of dimensionless variables, associated with
the conformal dimensionless metric, where the variables describe ratios with
respect to the chosen asymptotic scale structure. As examples, we describe some
explicit choices of conformal factors and coordinates appropriate for the
situation of a timelike congruence approaching a singularity. One choice is
shown to just slightly modify the so-called Hubble-normalized approach, and one
leads to dimensionless first order symmetric hyperbolic equations. We also
discuss differences and similarities with other conformal approaches in the
literature, as regards, e.g., isotropic singularities.Comment: New title plus corrections and text added. To appear in CQ
A measure on the set of compact Friedmann-Lemaitre-Robertson-Walker models
Compact, flat Friedmann-Lemaitre-Robertson-Walker (FLRW) models have recently
regained interest as a good fit to the observed cosmic microwave background
temperature fluctuations. However, it is generally thought that a globally,
exactly-flat FLRW model is theoretically improbable. Here, in order to obtain a
probability space on the set F of compact, comoving, 3-spatial sections of FLRW
models, a physically motivated hypothesis is proposed, using the density
parameter Omega as a derived rather than fundamental parameter. We assume that
the processes that select the 3-manifold also select a global mass-energy and a
Hubble parameter. The inferred range in Omega consists of a single real value
for any 3-manifold. Thus, the obvious measure over F is the discrete measure.
Hence, if the global mass-energy and Hubble parameter are a function of
3-manifold choice among compact FLRW models, then probability spaces
parametrised by Omega do not, in general, give a zero probability of a flat
model. Alternatively, parametrisation by the injectivity radius r_inj ("size")
suggests the Lebesgue measure. In this case, the probability space over the
injectivity radius implies that flat models occur almost surely (a.s.), in the
sense of probability theory, and non-flat models a.s. do not occur.Comment: 19 pages, 4 figures; v2: minor language improvements; v3:
generalisation: m, H functions of
Overview of the Nordic Seas CARINA data and salinity measurements
Water column data of carbon and carbon relevant hydrographic and hydrochemical parameters from 188 previously non-publicly available cruises in the Arctic, Atlantic, and Southern Ocean have been retrieved and merged into a new database: CARINA (CARbon IN the Atlantic). The data have been subject to rigorous quality control (QC) in order to ensure highest possible quality and consistency. The data for most of the parameters included were examined in order to quantify systematic biases in the reported values, i.e. secondary quality control. Significant biases have been corrected for in the data products, i.e. the three merged files with measured, calculated and interpolated values for each of the three CARINA regions; the Arctic Mediterranean Seas (AMS), the Atlantic (ATL) and the Southern Ocean (SO). With the adjustments the CARINA database is consistent both internally as well as with GLODAP (Key et al., 2004) and is suitable for accurate assessments of, for example, oceanic carbon inventories and uptake rates and for model validation. The Arctic Mediterranean Seas include the Arctic Ocean and the Nordic Seas, and the quality control was carried out separately in these two areas. This contribution provides an overview of the CARINA data from the Nordic Seas and summarises the findings of the QC of the salinity data. One cruise had salinity data that were of questionable quality, and these have been removed from the data product. An evaluation of the consistency of the quality controlled salinity data suggests that they are consistent to at least ±0.005
Wormholes and Supersymmetry
Revisions: reference added to: G. Gilbert, {\sl Nucl.Phys.} {\bf B328}, 159
(1989)Comment: 29 pages, jnl, McGill/92-2
Topology Change in Canonical Quantum Cosmology
We develop the canonical quantization of a midisuperspace model which
contains, as a subspace, a minisuperspace constituted of a
Friedman-Lema\^{\i}tre-Robertson-Walker Universe filled with homogeneous scalar
and dust fields, where the sign of the intrinsic curvature of the spacelike
hypersurfaces of homogeneity is not specified, allowing the study of topology
change in these hypersurfaces. We solve the Wheeler-DeWitt equation of the
midisuperspace model restricted to this minisuperspace subspace in the
semi-classical approximation. Adopting the conditional probability
interpretation, we find that some of the solutions present change of topology
of the homogeneous hypersurfaces. However, this result depends crucially on the
interpretation we adopt: using the usual probabilistic interpretation, we find
selection rules which forbid some of these topology changes.Comment: 23 pages, LaTex file. We added in the conclusion some comments about
path integral formalism and corrected litle misprinting
GATE : a simulation toolkit for PET and SPECT
Monte Carlo simulation is an essential tool in emission tomography that can
assist in the design of new medical imaging devices, the optimization of
acquisition protocols, and the development or assessment of image
reconstruction algorithms and correction techniques. GATE, the Geant4
Application for Tomographic Emission, encapsulates the Geant4 libraries to
achieve a modular, versatile, scripted simulation toolkit adapted to the field
of nuclear medicine. In particular, GATE allows the description of
time-dependent phenomena such as source or detector movement, and source decay
kinetics. This feature makes it possible to simulate time curves under
realistic acquisition conditions and to test dynamic reconstruction algorithms.
A public release of GATE licensed under the GNU Lesser General Public License
can be downloaded at the address http://www-lphe.epfl.ch/GATE/
Domain walls and instantons in N=1, d=4 supergravity
We study the supersymmetric sources of (multi-) domain-wall and (multi-)
instanton solutions of generic N=1, d=4 supergravities, that is: the
worldvolume effective actions for said supersymmetric topological defects. The
domain-wall solutions naturally couple to the two 3-forms recently found as
part of the N=1, d=4 tensor hierarchy (i.e. they have two charges in general)
and their tension is the absolute value of the superpotential section L. The
introduction of sources (we study sources with finite and vanishing thickness)
is equivalent to the introduction of local coupling constants and results in
dramatic changes of the solutions. Our results call for a democratic
reformulation of N=1,d=4 supergravity in which coupling constants are,
off-shell, scalar fields. The effective actions for the instantons are always
proportional to the coordinate orthogonal to the twist-free embedding of the
null-geodesic (in the Wick-rotated scalar manifold) describing the instanton.
We show their supersymmetry and find the associated supersymmetric (multi-)
instanton solutions.Comment: 34 pages, 4 figures, references adde
Applications of Field-Theoretic Renormalization Group Methods to Reaction-Diffusion Problems
We review the application of field-theoretic renormalization group (RG)
methods to the study of fluctuations in reaction-diffusion problems. We first
investigate the physical origin of universality in these systems, before
comparing RG methods to other available analytic techniques, including exact
solutions and Smoluchowski-type approximations. Starting from the microscopic
reaction-diffusion master equation, we then pedagogically detail the mapping to
a field theory for the single-species reaction k A -> l A (l < k). We employ
this particularly simple but non-trivial system to introduce the
field-theoretic RG tools, including the diagrammatic perturbation expansion,
renormalization, and Callan-Symanzik RG flow equation. We demonstrate how these
techniques permit the calculation of universal quantities such as density decay
exponents and amplitudes via perturbative eps = d_c - d expansions with respect
to the upper critical dimension d_c. With these basics established, we then
provide an overview of more sophisticated applications to multiple species
reactions, disorder effects, L'evy flights, persistence problems, and the
influence of spatial boundaries. We also analyze field-theoretic approaches to
nonequilibrium phase transitions separating active from absorbing states. We
focus particularly on the generic directed percolation universality class, as
well as on the most prominent exception to this class: even-offspring branching
and annihilating random walks. Finally, we summarize the state of the field and
present our perspective on outstanding problems for the future.Comment: 10 figures include
Novel non-equilibrium critical behavior in unidirectionally coupled stochastic processes
Phase transitions from an active into an absorbing, inactive state are
generically described by the critical exponents of directed percolation (DP),
with upper critical dimension d_c = 4. In the framework of single-species
reaction-diffusion systems, this universality class is realized by the combined
processes A -> A + A, A + A -> A, and A -> \emptyset. We study a hierarchy of
such DP processes for particle species A, B,..., unidirectionally coupled via
the reactions A -> B, ... (with rates \mu_{AB}, ...). When the DP critical
points at all levels coincide, multicritical behavior emerges, with density
exponents \beta_i which are markedly reduced at each hierarchy level i >= 2.
This scenario can be understood on the basis of the mean-field rate equations,
which yield \beta_i = 1/2^{i-1} at the multicritical point. We then include
fluctuations by using field-theoretic renormalization group techniques in d =
4-\epsilon dimensions. In the active phase, we calculate the fluctuation
correction to the density exponent for the second hierarchy level, \beta_2 =
1/2 - \epsilon/8 + O(\epsilon^2). Monte Carlo simulations are then employed to
determine the values for the new scaling exponents in dimensions d<= 3,
including the critical initial slip exponent. Our theory is connected to
certain classes of growth processes and to certain cellular automata, as well
as to unidirectionally coupled pair annihilation processes. We also discuss
some technical and conceptual problems of the loop expansion and their possible
interpretation.Comment: 29 pages, 19 figures, revtex, 2 columns, revised Jan 1995: minor
changes and additions; accepted for publication in Phys. Rev.
Quantum Fluctuations, Decoherence of the Mean Field, and Structure Formation in the Early Universe
We examine from first principles one of the basic assumptions of modern
quantum theories of structure formation in the early universe, i.e., the
conditions upon which fluctuations of a quantum field may transmute into
classical stochastic perturbations, which grew into galaxies. Our earlier works
have discussed the quantum origin of noise in stochastic inflation and quantum
fluctuations as measured by particle creation in semiclassical gravity. Here we
focus on decoherence and the relation of quantum and classical fluctuations.
Instead of using the rather ad hoc splitting of a quantum field into long and
short wavelength parts, the latter providing the noise which decoheres the
former, we treat a nonlinear theory and examine the decoherence of a quantum
mean field by its own quantum fluctuations, or that of other fields it
interacts with. This is an example of `dynamical decoherence' where an
effective open quantum system decoheres through its own dynamics. The model we
use to discuss fluctuation generation has the inflation field coupled to the
graviton field. We show that when the quantum to classical transition is
properly treated, with due consideration of the relation of decoherence, noise,
fluctuation and dissipation, the amplitude of density contrast predicted falls
in the acceptable range without requiring a fine tuning of the coupling
constant of the inflation field (). The conventional treatment which
requires an unnaturally small stems from a basic
flaw in naively identifying classical perturbations with quantum fluctuations.Comment: 35 pages, latex, 0 figure
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