1,403 research outputs found
Numerical Analysis of the Big Bounce in Loop Quantum Cosmology
Loop quantum cosmology homogeneous models with a massless scalar field show
that the big-bang singularity can be replaced by a big quantum bounce. To gain
further insight on the nature of this bounce, we study the semi-discrete loop
quantum gravity Hamiltonian constraint equation from the point of view of
numerical analysis. For illustration purposes, we establish a numerical analogy
between the quantum bounces and reflections in finite difference
discretizations of wave equations triggered by the use of nonuniform grids or,
equivalently, reflections found when solving numerically wave equations with
varying coefficients. We show that the bounce is closely related to the method
for the temporal update of the system and demonstrate that explicit
time-updates in general yield bounces. Finally, we present an example of an
implicit time-update devoid of bounces and show back-in-time, deterministic
evolutions that reach and partially jump over the big-bang singularity.Comment: 5 pages, 3 figures, new title, replaced with version accepted for
publicatio
Physical consequences of PNP and the DMRG-annealing conjecture
Computational complexity theory contains a corpus of theorems and conjectures
regarding the time a Turing machine will need to solve certain types of
problems as a function of the input size. Nature {\em need not} be a Turing
machine and, thus, these theorems do not apply directly to it. But {\em
classical simulations} of physical processes are programs running on Turing
machines and, as such, are subject to them. In this work, computational
complexity theory is applied to classical simulations of systems performing an
adiabatic quantum computation (AQC), based on an annealed extension of the
density matrix renormalization group (DMRG). We conjecture that the
computational time required for those classical simulations is controlled
solely by the {\em maximal entanglement} found during the process. Thus, lower
bounds on the growth of entanglement with the system size can be provided. In
some cases, quantum phase transitions can be predicted to take place in certain
inhomogeneous systems. Concretely, physical conclusions are drawn from the
assumption that the complexity classes {\bf P} and {\bf NP} differ. As a
by-product, an alternative measure of entanglement is proposed which, via
Chebyshev's inequality, allows to establish strict bounds on the required
computational time.Comment: Accepted for publication in JSTA
Super-Extremal Spinning Black Holes via Accretion
A Kerr black hole with mass and angular momentum satisfies the
extremality inequality . In the presence of matter and/or
gravitational radiation, this bound needs to be reformulated in terms of local
measurements of the mass and the angular momentum directly associated with the
black hole. The isolated and dynamical horizon framework provides such
quasi-local characterization of black hole mass and angular momentum. With this
framework, it is possible in axisymmetry to reformulate the extremality limit
as , with the irreducible mass of the black hole
computed from its apparent horizon area and obtained using approximate
rotational Killing vectors on the apparent horizon. The
condition is also equivalent to requiring a non-negative black hole surface
gravity. We present numerical experiments of an accreting black hole that
temporarily violates this extremality inequality. The initial configuration
consists of a single, rotating black hole surrounded by a thick, shell cloud of
negative energy density. For these numerical experiments, we introduce a new
matter-without-matter evolution method.Comment: 11 pages, 10 figure
Why, when, and how fast innovations are adopted
When the full stock of a new product is quickly sold in a few days or weeks,
one has the impression that new technologies develop and conquer the market in
a very easy way. This may be true for some new technologies, for example the
cell phone, but not for others, like the blue-ray. Novelty, usefulness,
advertising, price, and fashion are the driving forces behind the adoption of a
new product. But, what are the key factors that lead to adopt a new technology?
In this paper we propose and investigate a simple model for the adoption of an
innovation which depends mainly on three elements: the appeal of the novelty,
the inertia or resistance to adopt it, and the interaction with other agents.
Social interactions are taken into account in two ways: by imitation and by
differentiation, i.e., some agents will be inclined to adopt an innovation if
many people do the same, but other will act in the opposite direction, trying
to differentiate from the "herd". We determine the conditions for a successful
implantation of the new technology, by considering the strength of advertising
and the effect of social interactions. We find a balance between the
advertising and the number of anti-herding agents that may block the adoption
of a new product. We also compare the effect of social interactions, when
agents take into account the behavior of the whole society or just a part of
it. In a nutshell, the present model reproduces qualitatively the available
data on adoption of innovation.Comment: 11 pages, 13 figures (with subfigures), full paper (EPJB 2012) on
innovation adoption mode
Gravitational recoil from spinning binary black hole mergers
The inspiral and merger of binary black holes will likely involve black holes
with both unequal masses and arbitrary spins. The gravitational radiation
emitted by these binaries will carry angular as well as linear momentum. A net
flux of emitted linear momentum implies that the black hole produced by the
merger will experience a recoil or kick. Previous studies have focused on the
recoil velocity from unequal mass, non-spinning binaries. We present results
from simulations of equal mass but spinning black hole binaries and show how a
significant gravitational recoil can also be obtained in these situations. We
consider the case of black holes with opposite spins of magnitude
aligned/anti-aligned with the orbital angular momentum, with the
dimensionless spin parameters of the individual holes. For the initial setups
under consideration, we find a recoil velocity of V = 475 \KMS a.
Supermassive black hole mergers producing kicks of this magnitude could result
in the ejection from the cores of dwarf galaxies of the final hole produced by
the collision.Comment: 8 pages, 8 figures, replaced with version accepted for publication in
Ap
Defect formation and local gauge invariance
We propose a new mechanism for formation of topological defects in a U(1)
model with a local gauge symmetry. This mechanism leads to definite
predictions, which are qualitatively different from those of the Kibble-Zurek
mechanism of global theories. We confirm these predictions in numerical
simulations, and they can also be tested in superconductor experiments. We
believe that the mechanism generalizes to more complicated theories.Comment: REVTeX, 4 pages, 2 figures. The explicit form of the Hamiltonian and
the equations of motion added. To appear in PRL (http://prl.aps.org/
Moving black holes via singularity excision
We present a singularity excision algorithm appropriate for numerical
simulations of black holes moving throughout the computational domain. The
method is an extension of the excision procedure previously used to obtain
stable simulations of single, non-moving black holes. The excision procedure
also shares elements used in recent work to study the dynamics of a scalarfield
in the background of a single, boosted black hole. The robustness of our
excision method is tested with single black-hole evolutions using a coordinate
system in which the coordinate location of the black hole, and thus the
excision boundary, moves throughout the computational domain.Comment: 9 pages and 11 figure
A multivariate time-frequency method to characterize the influence of respiration over heart period and arterial pressure
Respiratory activity introduces oscillations both in arterial pressure and heart period, through mechanical and autonomic mechanisms. Respiration, arterial pressure, and heart period are, generally, non-stationary processes and the interactions between them are dynamic. In this study we present a methodology to robustly estimate the time course of cross spectral indices to characterize dynamic interactions between respiratory oscillations of heart period and blood pressure, as well as their interactions with respiratory activity. Time-frequency distributions belonging to Cohen's class are used to estimate time-frequency (TF) representations of coherence, partial coherence and phase difference. The characterization is based on the estimation of the time course of cross spectral indices estimated in specific TF regions around the respiratory frequency. We used this methodology to describe the interactions between respiration, heart period variability (HPV) and systolic arterial pressure variability (SAPV) during tilt table test with both spontaneous and controlled respiratory patterns. The effect of selective autonomic blockade was also studied. Results suggest the presence of common underling mechanisms of regulation between cardiovascular signals, whose interactions are time-varying. SAPV changes followed respiratory flow both in supine and standing positions and even after selective autonomic blockade. During head-up tilt, phase differences between respiration and SAPV increased. Phase differences between respiration and HPV were comparable to those between respiration and SAPV during supine position, and significantly increased during standing. As a result, respiratory oscillations in SAPV preceded respiratory oscillations in HPV during standing. Partial coherence was the most sensitive index to orthostatic stress. Phase difference estimates were consistent among spontaneous and controlled breathing patterns, whereas coherence was higher in spontaneous breathing. Parasympathetic blockade did not affect interactions between respiration and SAPV, reduced the coherence between SAPV and HPV and between respiration and HPV. Our results support the hypothesis that non-autonomic, possibly mechanically mediated, mechanisms also contributes to the respiratory oscillations in HPV. A small contribution of sympathetic activity on HPV-SAPV interactions around the respiratory frequency was also observed
Observational Signature of Tidal Disruption of a Star by a Massive Black Hole
We have modeled the time-variable profiles of the Halpha emission line from
the non-axisymmetric disk and debris tail created in the tidal disruption of a
solar-type star by a million solar mass black hole. We find that the line
profiles at these very early stages of the evolution of the post-disruption
debris do not resemble the double peaked profiles expected from a rotating disk
since the debris has not yet settled into such a stable structure. The
predicted line profiles vary on fairly short time scales (of order hours to
days). As a result of the uneven distribution of the debris and the existence
of a ``tidal tail'' (the stream of returning debris), the line profiles depend
sensitively on the orientation of the tail relative to the line of sight. Given
the illuminating UV/X-ray light curve, we also model the Halpha light curve
from the debris.Comment: 2 pages, 1 figure, to appear in the proceedings of "The Interplay
among Black Holes, Stars and ISM in Galactic Nuclei", IAU 222, eds. Th.
Storchi Bergmann, L.C. Ho, and H.R. Schmit
Electroweak String Configurations with Baryon Number
In the context of electroweak strings, the baryon number anomaly equation may
be reinterpreted as a conservation law for baryon number minus helicity. Since
the helicity is a sum of the link and twist numbers, linked or twisted loops of
electroweak string carry baryon number. We evaluate the change in the baryon
number obtained by delinking loops of electroweak string and show that
twisted electroweak string segments may be regarded as extended sphalerons. We
also suggest an alternative scenario for electroweak baryogenesis.Comment: 11 pages, figure available on request. Added discussion of
string-sphaleron connection for non-vanishing Weinberg angle and shortened
discussion on formation of linked configuration
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