149,424 research outputs found
Variations on Birkhoff's theorem
The relation between the expanding universe and local vacuum solutions, such
as that for the Solar System, is crucially mediated by Birkhoff's theorem. Here
we consider how that relation works, and give generalizations of Birkhoff's
theorem when there are geometric and matter and perturbations. The issue of to
what degree dark matter might influence the solar system emerges as a
significant question.Comment: Conference proceeding for ERE 2012, submitted to GRG for ERE2012
special issue, based on arXiv:1005.1809, arXiv:1101.4520 and arXiv:1202.024
Estimating anisotropy parameters and traveltimes in the tau-p domain
The presence of anisotropy influences many aspects of
seismic wave propagation and has therefore implications
for conventional processing schemes. To estimate the
anisotropy, we need both forward modelling and inversion
tools. Exact forward modelling in anisotropic media
is generally done by raytracing. However, we present a
new and fast method, using the tau-p transform, to calculate
exact P and SV reflection moveout curves in stratified,
laterally homogeneous, anisotropic media which
requires no ray tracing. Results are exact even if the
SV-waves display cusps. In addition, we show how the
same method can be used for parameter estimation.
Since inversion for anisotropic parameters is very
nonunique, we develop expressions requiring only a reduced
number of parameters. Nevertheless, predictions
using these expressions are more accurate than Taylor
series expansions and are also able to handle cusps in
the SV traveltime curves. In addition, layer stripping is
a linear process. Therefore, both effective (average) and
local (interval) estimates can be obtained
Counting Majorana zero modes in superconductors
A counting formula for computing the number of (Majorana) zero modes bound to
topological point defects is evaluated in a gradient expansion for systems with
charge-conjugation symmetry. This semi-classical counting of zero modes is
applied to some examples that include graphene and a chiral p-wave
superconductor in two-dimensional space. In all cases, we explicitly relate the
counting of zero modes to Chern numbers.Comment: 21 pages, 3 figure
Evolution of radial profiles in regular Lemaitre-Tolman-Bondi dust models
We undertake a comprehensive and rigorous analytic study of the evolution of
radial profiles of covariant scalars in regular Lemaitre-Tolman-Bondi dust
models. We consider specifically the phenomenon of "profile inversions" in
which an initial clump profile of density, spatial curvature or the expansion
scalar, might evolve into a void profile (and vice versa). Previous work in the
literature on models with density void profiles and/or allowing for density
profile inversions is given full generalization, with some erroneous results
corrected. We prove rigorously that if an evolution without shell crossings is
assumed, then only the 'clump to void' inversion can occur in density profiles,
and only in hyperbolic models or regions with negative spatial curvature. The
profiles of spatial curvature follow similar patterns as those of the density,
with 'clump to void' inversions only possible for hyperbolic models or regions.
However, profiles of the expansion scalar are less restrictive, with profile
inversions necessarily taking place in elliptic models. We also examine radial
profiles in special LTB configurations: closed elliptic models, models with a
simultaneous big bang singularity, as well as a locally collapsing elliptic
region surrounded by an expanding hyperbolic background. The general analytic
statements that we obtain allow for setting up the right initial conditions to
construct fully regular LTB models with any specific qualitative requirements
for the profiles of all scalars and their time evolution. The results presented
can be very useful in guiding future numerical work on these models and in
revising previous analytic work on all their applications.Comment: Final version to appear in Classical and Quantum Gravity. Readers
eager to know the results and implications without having to go through the
technical detail are recommended to go directly to the summary and discussion
in the final section (section 11). Typos have been corrected and an important
reference has been adde
Local and non-local measures of acceleration in cosmology
Current cosmological observations, when interpreted within the framework of a
homogeneous and isotropic Friedmann-Lemaitre-Robertson-Walker (FLRW) model,
strongly suggest that the Universe is entering a period of accelerating
expansion. This is often taken to mean that the expansion of space itself is
accelerating. In a general spacetime, however, this is not necessarily true. We
attempt to clarify this point by considering a handful of local and non-local
measures of acceleration in a variety of inhomogeneous cosmological models.
Each of the chosen measures corresponds to a theoretical or observational
procedure that has previously been used to study acceleration in cosmology, and
all measures reduce to the same quantity in the limit of exact spatial
homogeneity and isotropy. In statistically homogeneous and isotropic
spacetimes, we find that the acceleration inferred from observations of the
distance-redshift relation is closely related to the acceleration of the
spatially averaged universe, but does not necessarily bear any resemblance to
the average of the local acceleration of spacetime itself. For inhomogeneous
spacetimes that do not display statistical homogeneity and isotropy, however,
we find little correlation between acceleration inferred from observations and
the acceleration of the averaged spacetime. This shows that observations made
in an inhomogeneous universe can imply acceleration without the existence of
dark energy.Comment: 19 pages, 10 figures. Several references added or amended, some minor
clarifications made in the tex
Bootstrapping the 3d Ising twist defect
Recent numerical results point to the existence of a conformally invariant
twist defect in the critical 3d Ising model. In this note we show that this
fact is supported by both epsilon expansion and conformal bootstrap
calculations. We find that our results are in good agreement with the numerical
data. We also make new predictions for operator dimensions and OPE coefficients
from the bootstrap approach. In the process we derive universal bounds on
one-dimensional conformal field theories and conformal line defects.Comment: 24+8 pages, 12 figures, references adde
A fast integral equation method for solid particles in viscous flow using quadrature by expansion
Boundary integral methods are advantageous when simulating viscous flow
around rigid particles, due to the reduction in number of unknowns and
straightforward handling of the geometry. In this work we present a fast and
accurate framework for simulating spheroids in periodic Stokes flow, which is
based on the completed double layer boundary integral formulation. The
framework implements a new method known as quadrature by expansion (QBX), which
uses surrogate local expansions of the layer potential to evaluate it to very
high accuracy both on and off the particle surfaces. This quadrature method is
accelerated through a newly developed precomputation scheme. The long range
interactions are computed using the spectral Ewald (SE) fast summation method,
which after integration with QBX allows the resulting system to be solved in M
log M time, where M is the number of particles. This framework is suitable for
simulations of large particle systems, and can be used for studying e.g. porous
media models
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