5,290 research outputs found
Performance of internal Covariance Estimators for Cosmic Shear Correlation Functions
Data re-sampling methods such as the delete-one jackknife are a common tool
for estimating the covariance of large scale structure probes. In this paper we
investigate the concepts of internal covariance estimation in the context of
cosmic shear two-point statistics. We demonstrate how to use log-normal
simulations of the convergence field and the corresponding shear field to carry
out realistic tests of internal covariance estimators and find that most
estimators such as jackknife or sub-sample covariance can reach a satisfactory
compromise between bias and variance of the estimated covariance.
In a forecast for the complete, 5-year DES survey we show that internally
estimated covariance matrices can provide a large fraction of the true
uncertainties on cosmological parameters in a 2D cosmic shear analysis. The
volume inside contours of constant likelihood in the -
plane as measured with internally estimated covariance matrices is on average
of the volume derived from the true covariance matrix. The
uncertainty on the parameter combination derived from internally estimated covariances is of
the true uncertainty.Comment: submitted to mnra
An exact relation between Eulerian and Lagrangian velocity increment statistics
We present a formal connection between Lagrangian and Eulerian velocity
increment distributions which is applicable to a wide range of turbulent
systems ranging from turbulence in incompressible fluids to magnetohydrodynamic
turbulence. For the case of the inverse cascade regime of two-dimensional
turbulence we numerically estimate the transition probabilities involved in
this connection. In this context we are able to directly identify the processes
leading to strongly non-Gaussian statistics for the Lagrangian velocity
increments.Comment: 5 pages, 3 figure
Cosmic variance of the galaxy cluster weak lensing signal
Intrinsic variations of the projected density profiles of clusters of
galaxies at fixed mass are a source of uncertainty for cluster weak lensing. We
present a semi-analytical model to account for this effect, based on a
combination of variations in halo concentration, ellipticity and orientation,
and the presence of correlated haloes. We calibrate the parameters of our model
at the 10 per cent level to match the empirical cosmic variance of cluster
profiles at M_200m=10^14...10^15 h^-1 M_sol, z=0.25...0.5 in a cosmological
simulation. We show that weak lensing measurements of clusters significantly
underestimate mass uncertainties if intrinsic profile variations are ignored,
and that our model can be used to provide correct mass likelihoods. Effects on
the achievable accuracy of weak lensing cluster mass measurements are
particularly strong for the most massive clusters and deep observations (with
~20 per cent uncertainty from cosmic variance alone at M_200m=10^15 h^-1 M_sol
and z=0.25), but significant also under typical ground-based conditions. We
show that neglecting intrinsic profile variations leads to biases in the
mass-observable relation constrained with weak lensing, both for intrinsic
scatter and overall scale (the latter at the 15 per cent level). These biases
are in excess of the statistical errors of upcoming surveys and can be avoided
if the cosmic variance of cluster profiles is accounted for.Comment: 14 pages, 6 figures; submitted to MNRA
Wannier Function Approach to Realistic Coulomb Interactions in Layered Materials and Heterostructures
We introduce an approach to derive realistic Coulomb interaction terms in
free standing layered materials and vertical heterostructures from ab-initio
modelling of the corresponding bulk materials. To this end, we establish a
combination of calculations within the framework of the constrained random
phase approximation, Wannier function representation of Coulomb matrix elements
within some low energy Hilbert space and continuum medium electrostatics, which
we call Wannier function continuum electrostatics (WFCE). For monolayer and
bilayer graphene we reproduce full ab-initio calculations of the Coulomb matrix
elements within an accuracy of eV or better. We show that realistic
Coulomb interactions in bilayer graphene can be manipulated on the eV scale by
different dielectric and metallic environments. A comparison to electronic
phase diagrams derived in [M. M. Scherer et al., Phys. Rev. B 85, 235408
(2012)] suggests that the electronic ground state of bilayer graphene is a
layered antiferromagnet and remains surprisingly unaffected by these strong
changes in the Coulomb interaction.Comment: 12 pages, 8 figure
On the Effect of Constraint Enforcement on the Quality of Numerical Solutions in General Relativity
In Brodbeck et al 1999 it has been shown that the linearised time evolution
equations of general relativity can be extended to a system whose solutions
asymptotically approach solutions of the constraints. In this paper we extend
the non-linear equations in similar ways and investigate the effect of various
possibilities by numerical means. Although we were not able to make the
constraint submanifold an attractor for all solutions of the extended system,
we were able to significantly reduce the growth of the numerical violation of
the constraints. Contrary to our expectations this improvement did not imply a
numerical solution closer to the exact solution, and therefore did not improve
the quality of the numerical solution.Comment: 14 pages, 9 figures, accepted for publication in Phys. Rev.
Initial boundary value problems for Einstein's field equations and geometric uniqueness
While there exist now formulations of initial boundary value problems for
Einstein's field equations which are well posed and preserve constraints and
gauge conditions, the question of geometric uniqueness remains unresolved. For
two different approaches we discuss how this difficulty arises under general
assumptions. So far it is not known whether it can be overcome without imposing
conditions on the geometry of the boundary. We point out a natural and
important class of initial boundary value problems which may offer
possibilities to arrive at a fully covariant formulation.Comment: 19 page
Correlation effects and orbital magnetism of Co clusters
Recent experiments on isolated Co clusters have shown huge orbital magnetic
moments in comparison with their bulk and surface counterparts. These clusters
hence provide the unique possibility to study the evolution of the orbital
magnetic moment with respect to the cluster size and how competing interactions
contribute to the quenching of orbital magnetism. We investigate here different
theoretical methods to calculate the spin and orbital moments of Co clusters,
and assess the performances of the methods in comparison with experiments. It
is shown that density functional theory in conventional local density or
generalized gradient approximations, or even with a hybrid functional, severely
underestimates the orbital moment. As natural extensions/corrections we
considered the orbital polarization correction, the LDA+U approximation as well
as the LDA+DMFT method. Our theory shows that of the considered methods, only
the LDA+DMFT method provides orbital moments in agreement with experiment, thus
emphasizing the importance of dynamic correlations effects for determining
fundamental magnetic properties of magnets in the nano-size regime
Conformal loop ensembles and the stress-energy tensor
We give a construction of the stress-energy tensor of conformal field theory
(CFT) as a local "object" in conformal loop ensembles CLE_\kappa, for all
values of \kappa in the dilute regime 8/3 < \kappa <= 4 (corresponding to the
central charges 0 < c <= 1, and including all CFT minimal models). We provide a
quick introduction to CLE, a mathematical theory for random loops in simply
connected domains with properties of conformal invariance, developed by
Sheffield and Werner (2006). We consider its extension to more general regions
of definition, and make various hypotheses that are needed for our construction
and expected to hold for CLE in the dilute regime. Using this, we identify the
stress-energy tensor in the context of CLE. This is done by deriving its
associated conformal Ward identities for single insertions in CLE probability
functions, along with the appropriate boundary conditions on simply connected
domains; its properties under conformal maps, involving the Schwarzian
derivative; and its one-point average in terms of the "relative partition
function." Part of the construction is in the same spirit as, but widely
generalizes, that found in the context of SLE_{8/3} by the author, Riva and
Cardy (2006), which only dealt with the case of zero central charge in simply
connected hyperbolic regions. We do not use the explicit construction of the
CLE probability measure, but only its defining and expected general properties.Comment: 49 pages, 3 figures. This is a concatenated, reduced and simplified
version of arXiv:0903.0372 and (especially) arXiv:0908.151
Optimal eigenvalues estimate for the Dirac operator on domains with boundary
We give a lower bound for the eigenvalues of the Dirac operator on a compact
domain of a Riemannian spin manifold under the \MIT bag boundary condition.
The limiting case is characterized by the existence of an imaginary Killing
spinor.Comment: 10 page
Influence of molecular temperature on the coherence of fullerenes in a near-field interferometer
We study C70 fullerene matter waves in a Talbot-Lau interferometer as a
function of their temperature. While the ideal fringe visibility is observed at
moderate molecular temperatures, we find a gradual degradation of the
interference contrast if the molecules are heated before entering the
interferometer. A method is developed to assess the distribution of the
micro-canonical temperatures of the molecules in free flight. This way the
heating-dependent reduction of interference contrast can be compared with the
predictions of quantum theory. We find that the observed loss of coherence
agrees quantitatively with the expected decoherence rate due to the thermal
radiation emitted by the hot molecules.Comment: 11 pages, 9 figure
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