8,506 research outputs found
Local phase space and edge modes for diffeomorphism-invariant theories
We discuss an approach to characterizing local degrees of freedom of a
subregion in diffeomorphism-invariant theories using the extended phase space
of Donnelly and Freidel, [JHEP 2016 (2016) 102]. Such a characterization is
important for defining local observables and entanglement entropy in
gravitational theories. Traditional phase space constructions for subregions
are not invariant with respect to diffeomorphisms that act at the boundary. The
extended phase space remedies this problem by introducing edge mode fields at
the boundary whose transformations under diffeomorphisms render the extended
symplectic structure fully gauge invariant. In this work, we present a general
construction for the edge mode symplectic structure. We show that the new
fields satisfy a surface symmetry algebra generated by the Noether charges
associated with the edge mode fields. For surface-preserving symmetries, the
algebra is universal for all diffeomorphism-invariant theories, comprised of
diffeomorphisms of the boundary, transformations of the
normal plane, and, in some cases, normal shearing transformations. We also show
that if boundary conditions are chosen such that surface translations are
symmetries, the algebra acquires a central extension.Comment: 29+12 pages, references added and minor typos fixe
Non-linear Redshift-Space Power Spectra
Distances in cosmology are usually inferred from observed redshifts - an
estimate that is dependent on the local peculiar motion - giving a distorted
view of the three dimensional structure and affecting basic observables such as
the correlation function and power spectrum. We calculate the full non-linear
redshift-space power spectrum for Gaussian fields, giving results for both the
standard flat sky approximation and the directly-observable angular correlation
function and angular power spectrum. Coupling between large and small scale
modes boosts the power on small scales when the perturbations are small. On
larger scales power is slightly suppressed by the velocities perturbations on
smaller scales. The analysis is general, but we comment specifically on the
implications for future high-redshift observations, and show that the
non-linear spectrum has significantly more complicated angular structure than
in linear theory. We comment on the implications for using the angular
structure to separate cosmological and astrophysical components of 21 cm
observations.Comment: 22 pages, 6 figures, changed to version accepted in Physics Review
Improving CMB non-Gaussianity estimators using tracers of local structure
Local non-Gaussianity causes correlations between large scale perturbation
modes and the small scale power. The large-scale CMB signal has contributions
from the integrated Sachs Wolfe (ISW) effect, which does not correlate with the
small scale power. If this ISW contribution can be removed, the sensitivity to
local non-Gaussianity is improved. Gravitational lensing and galaxy counts can
be used to trace the ISW contribution; in particular we show that the CMB
lensing potential is highly correlated with the ISW signal. We construct a
nearly-optimal estimator for the local non-Gaussianity parameter \fnl and
investigate to what extent we can use this to decrease the variance on
{\fnl}. We show that the variance can be decreased by up to at Planck
sensitivity using galaxy counts. CMB lensing is a good bias-independent ISW
tracer for future more sensitive observations, though the fractional decrease
in variance is small if good polarization data is also available.Comment: 8 pages, 3 figures. Comments welcom
Multigrid solution of the Navier-Stokes equations on triangular meshes
A Navier-Stokes algorithm for use on unstructured triangular meshes is presented. Spatial discretization of the governing equations is achieved using a finite element Galerkin approximation, which can be shown to be equivalent to a finite volume approximation for regular equilateral triangular meshes. Integration steady-state is performed using a multistage time-stepping scheme, and convergence is accelerated by means of implicit residual smoothing and an unstructured multigrid algorithm. Directional scaling of the artificial dissipation and the implicit residual smoothing operator is achieved for unstructured meshes by considering local mesh stretching vectors at each point. The accuracy of the scheme for highly stretched triangular meshes is validated by comparing computed flat-plate laminar boundary layer results with the well known similarity solution, and by comparing laminar airfoil results with those obtained from various well-established structured quadrilateral-mesh codes. The convergence efficiency of the present method is also shown to be competitive with those demonstrated by structured quadrilateral-mesh algorithms
Reconstructing ice-sheet accumulation rates at ridge B, East Antarctica
Understanding how ice sheets responded to past climate change is fundamental to forecasting how they will respond in the future. Numerical models calculating the evolution of ice sheets depend upon accumulation data, which are principally available from ice cores. Here, we calculate past rates of ice accumulation using internal layering. The englacial structure of the East Antarctic ice divide at ridge B is extracted from airborne ice-penetrating radar. The isochronous surfaces are dated at their intersection with the Vostok ice-core site, where the depth–age relationship is known. The dated isochrons are used as input to a one-dimensional ice-flow model to investigate the spatial accumulation distribution. The calculations show that ice-accumulation rates generally increase from Vostok lake towards ridge B. The western flank of the ice divide experiences markedly more accumulation than in the east. Further, ice accumulation increases northwards along the ice divide. The results also show the variability of accumulation in time and space around the ridge B ice divide over the last 124 000 years
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