662 research outputs found
Synthesis of high molecular weight poly(p-benzamide)s
The polymerization of aromatic para-amino acid ester derivatives was studied using model compounds. Mechanistic and kinetic experiments led to the discovery of some side reactions. Finally, high molecular weight poly(p-benzamide)s were synthesized and characterized. The use of highly reactive pentafluorophenol ester lead to polymers up to molecular weights of around 50 000 Da. Poly(benzamides) carrying both N-alkyl or N-benzyl groups on the amine could be polymerized to high molecular weight
Bayesian Analysis of Inflation II: Model Selection and Constraints on Reheating
We discuss the model selection problem for inflationary cosmology. We couple
ModeCode, a publicly-available numerical solver for the primordial perturbation
spectra, to the nested sampler MultiNest, in order to efficiently compute
Bayesian evidence. Particular attention is paid to the specification of
physically realistic priors, including the parametrization of the
post-inflationary expansion and associated thermalization scale. It is
confirmed that while present-day data tightly constrains the properties of the
power spectrum, it cannot usefully distinguish between the members of a large
class of simple inflationary models. We also compute evidence using a simulated
Planck likelihood, showing that while Planck will have more power than WMAP to
discriminate between inflationary models, it will not definitively address the
inflationary model selection problem on its own. However, Planck will place
very tight constraints on any model with more than one observationally-distinct
inflationary regime -- e.g. the large- and small-field limits of the hilltop
inflation model -- and put useful limits on different reheating scenarios for a
given model.Comment: ModeCode package available from
http://zuserver2.star.ucl.ac.uk/~hiranya/ModeCode/ModeCode (requires CosmoMC
and MultiNest); to be published in PRD. Typos fixe
Tomography and weak lensing statistics
We provide generic predictions for the lower order cumulants of weak lensing maps, and their correlators for tomographic bins as well as in three dimensions (3D). Using small-angle approximation, we derive the corresponding one- and two-point probability distribution function for the tomographic maps from different bins and for 3D convergence maps. The modelling of weak lensing statistics is obtained by adopting a detailed prescription for the underlying density contrast that involves hierarchal ansatz and lognormal distribution. We study the dependence of our results on cosmological parameters and source distributions corresponding to the realistic surveys such as LSST and DES. We briefly outline how photometric redshift information can be incorporated in our results. We also show how topological properties of convergence maps can be quantified using our results
Principal Component Analysis of Weak Lensing Surveys
We study degeneracies between cosmological parameters and measurement errors
from cosmic shear surveys using a principal component analysis of the Fisher
matrix. We simulate realistic survey topologies with non-uniform sky coverage,
and quantify the effect of survey geometry, depth and noise from intrinsic
galaxy ellipticities on the parameter errors. This analysis allows us to
optimise the survey geometry. Using the shear two-point correlation functions
and the aperture mass dispersion, we study various degeneracy directions in a
multi-dimensional parameter space spanned by Omega_m, Omega_Lambda, sigma_8,
the shape parameter Gamma, the spectral index n_s, along with parameters that
specify the distribution of source galaxies. If only three parameters are to be
obtained from weak lensing data, a single principal component is dominant and
contains all information about the main parameter degeneracies and their
errors. The variance of the dominant principal component of the Fisher matrix
shows a minimum for survey strategies which have small cosmic variance and
measure the shear correlation up to several degrees [abridged].Comment: 13 pages, 17 figures. A&A in press, matches the version to be
publishe
Evolution of hierarchical clustering in the CFHTLS-Wide since z~1
We present measurements of higher order clustering of galaxies from the
latest release of the Canada-France-Hawaii-Telescope Legacy Survey (CFHTLS)
Wide. We construct a volume-limited sample of galaxies that contains more than
one million galaxies in the redshift range 0.2<z<1 distributed over the four
independent fields of the CFHTLS. We use a counts in cells technique to measure
the variance and the hierarchical moments S_n = /^(n-1)
(3<n<5) as a function of redshift and angular scale.The robustness of our
measurements if thoroughly tested, and the field-to-field scatter is in very
good agreement with analytical predictions. At small scales, corresponding to
the highly non-linear regime, we find a suggestion that the hierarchical
moments increase with redshift. At large scales, corresponding to the weakly
non-linear regime, measurements are fully consistent with perturbation theory
predictions for standard LambdaCDM cosmology with a simple linear bias.Comment: 17 pages, 11 figures, submitted to MNRA
Cosmic Shear Tomography and Efficient Data Compression using COSEBIs
Context. Gravitational lensing is one of the leading tools in understanding
the dark side of the Universe. The need for accurate, efficient and effective
methods which are able to extract this information along with other
cosmological parameters from cosmic shear data is ever growing. COSEBIs,
Complete Orthogonal Sets of E-/B-Integrals, is a recently developed statistical
measure that encompasses the complete E-/B-mode separable information contained
in the shear correlation functions measured on a finite angular range. Aims.
The aim of the present work is to test the properties of this newly developed
statistics for a higher-dimensional parameter space and to generalize and test
it for shear tomography. Methods. We use Fisher analysis to study the
effectiveness of COSEBIs. We show our results in terms of figure-of-merit
quantities, based on Fisher matrices. Results. We find that a relatively small
number of COSEBIs modes is always enough to saturate to the maximum information
level. This number is always smaller for 'logarithmic COSEBIs' than for 'linear
COSEBIs', and also depends on the number of redshift bins, the number and
choice of cosmological parameters, as well as the survey characteristics.
Conclusions. COSEBIs provide a very compact way of analyzing cosmic shear data,
i.e., all the E-/B-mode separable second-order statistical information in the
data is reduced to a small number of COSEBIs modes. Furthermore, with this
method the arbitrariness in data binning is no longer an issue since the
COSEBIs modes are discrete. Finally, the small number of modes also implies
that covariances, and their inverse, are much more conveniently obtainable,
e.g., from numerical simulations, than for the shear correlation functions
themselves.Comment: 17 pages, 15 figure
Cosmological parameters from combined second- and third-order aperture mass statistics of cosmic shear
We present predictions for cosmological parameter constraints from combined
measurements of second- and third-order statistics of cosmic shear. We define
the generalized third-order aperture mass statistics and show that it
contains much more information about the bispectrum of the projected matter
density than the skewness of the aperture mass. From theoretical models as well
as from LCDM ray-tracing simulations, we calculate and and
their dependence on cosmological parameters. The covariances including shot
noise and cosmic variance of M_ap^2, M_ap^3 and their cross-correlation are
calculated using ray-tracing simulations. We perform an extensive Fisher matrix
analysis, and for various combinations of cosmological parameters, we predict
1-sigma-errors corresponding to measurements from a deep 29 square degree
cosmic shear survey. Although the parameter degeneracies can not be lifted
completely, the (linear) combination of second- and third-order aperture mass
statistics reduces the errors significantly. The strong degeneracy between
Omega_m and sigma_8, present for all second-order cosmic shear measures, is
diminished substantially, whereas less improvement is found for the
near-degenerate pair consisting of the shape parameter Gamma and the spectral
index n_s. Uncertainties in the source galaxy redshift z_0 increase the errors
of all other parameters.Comment: Revised version, 15 pages, 10 figures, in press at A&A. Some changes
were made including an extension of the analysis. Matches the published
versio
Application of Bayesian model averaging to measurements of the primordial power spectrum
Cosmological parameter uncertainties are often stated assuming a particular
model, neglecting the model uncertainty, even when Bayesian model selection is
unable to identify a conclusive best model. Bayesian model averaging is a
method for assessing parameter uncertainties in situations where there is also
uncertainty in the underlying model. We apply model averaging to the estimation
of the parameters associated with the primordial power spectra of curvature and
tensor perturbations. We use CosmoNest and MultiNest to compute the model
Evidences and posteriors, using cosmic microwave data from WMAP, ACBAR,
BOOMERanG and CBI, plus large-scale structure data from the SDSS DR7. We find
that the model-averaged 95% credible interval for the spectral index using all
of the data is 0.940 < n_s < 1.000, where n_s is specified at a pivot scale
0.015 Mpc^{-1}. For the tensors model averaging can tighten the credible upper
limit, depending on prior assumptions.Comment: 7 pages with 7 figures include
Crossing Statistic: Bayesian interpretation, model selection and resolving dark energy parametrization problem
By introducing Crossing functions and hyper-parameters I show that the
Bayesian interpretation of the Crossing Statistics [1] can be used trivially
for the purpose of model selection among cosmological models. In this approach
to falsify a cosmological model there is no need to compare it with other
models or assume any particular form of parametrization for the cosmological
quantities like luminosity distance, Hubble parameter or equation of state of
dark energy. Instead, hyper-parameters of Crossing functions perform as
discriminators between correct and wrong models. Using this approach one can
falsify any assumed cosmological model without putting priors on the underlying
actual model of the universe and its parameters, hence the issue of dark energy
parametrization is resolved. It will be also shown that the sensitivity of the
method to the intrinsic dispersion of the data is small that is another
important characteristic of the method in testing cosmological models dealing
with data with high uncertainties.Comment: 14 pages, 4 figures, discussions extended, 1 figure and two
references added, main results unchanged, matches the final version to be
published in JCA
End Capping Ring-Opening Olefin Metathesis Polymerization Polymers with Vinyl Lactones
The selective placement of a functional group at the chain end of a ring-opening metathesis polymer using ruthenium carbene initiators has been a significant limitation. Here we demonstrate a highly effective and facile end-capping technique for ROMP with living ruthenium carbene chain ends using single-turnover olefin metathesis substrates. Vinylene carbonate and 3H-furanone are introduced as functionalization and termination agents for the ruthenium-initiated ring-opening metathesis polymerization. This leads directly to the formation of functional polymer end groups without further chemical transformation steps. Aldehyde and carboxylic acid end groups can be introduced by this new method which involves the decomposition of acyl carbenes to ruthenium carbides. The high degrees of chain-end functionality obtained are supported by ^1H NMR spectroscopy, MALDI-ToF mass spectrometry, and end-group derivatization
- …