1,568 research outputs found
On non-vanishing and sign changes of the Fourier coefficients of Hilbert cusp forms
In this article, we study (simultaneous) non-vanishing, (simultaneous) sign
changes of Fourier coefficients of (two) Hilbert cusp forms, respectively
Strongly correlated quantum dynamics of multimode light coupled to a two-level atom in a cavity
We study a composite multimode light-two-level atom system in a cavity. We
show that coupling of the two-level atom to multiple modes of the light
destroys the Mott phase of the composite system thus making the system less
useful platform for developing concepts in quantum information processing
Primordial power spectrum: a complete analysis with the WMAP nine-year data
We have improved further the error sensitive Richardson-Lucy deconvolution
algorithm making it applicable directly on the un-binned measured angular power
spectrum of Cosmic Microwave Background observations to reconstruct the form of
the primordial power spectrum. This improvement makes the application of the
method significantly more straight forward by removing some intermediate stages
of analysis allowing a reconstruction of the primordial spectrum with higher
efficiency and precision and with lower computational expenses. Applying the
modified algorithm we fit the WMAP 9 year data using the optimized
reconstructed form of the primordial spectrum with more than 300 improvement in
\chi^2 with respect to the best fit power-law. This is clearly beyond the reach
of other alternative approaches and reflects the efficiency of the proposed
method in the reconstruction process and allow us to look for any possible
feature in the primordial spectrum projected in the CMB data. Though the
proposed method allow us to look at various possibilities for the form of the
primordial spectrum, all having good fit to the data, proper error-analysis is
needed to test for consistency of theoretical models since, along with possible
physical artefacts, most of the features in the reconstructed spectrum might be
arising from fitting noises in the CMB data. Reconstructed error-band for the
form of the primordial spectrum using many realizations of the data, all
bootstrapped and based on WMAP 9 year data, shows proper consistency of
power-law form of the primordial spectrum with the WMAP 9 data at all wave
numbers. Including WMAP polarization data in to the analysis have not improved
much our results due to its low quality but we expect Planck data will allow us
to make a full analysis on CMB observations on both temperature and
polarization separately and in combination.Comment: 19 pages, 5 figures, discussions extended, results unchanged, matches
the final version published in JCAP. Note: JCAP published version contains
minor typesetting errors (introduced by JCAP at the proof stage) in the plot
label
Primordial power spectrum from Planck
Using modified Richardson-Lucy algorithm we reconstruct the primordial power
spectrum (PPS) from Planck Cosmic Microwave Background (CMB) temperature
anisotropy data. In our analysis we use different combinations of angular power
spectra from Planck to reconstruct the shape of the primordial power spectrum
and locate possible features. Performing an extensive error analysis we found
the dip near represents the most prominent feature in the
data. Feature near is detectable with high confidence only
in 217 GHz spectrum and is apparently consequence of a small systematic as
described in the revised Planck 2013 papers. Fixing the background cosmological
parameters and the foreground nuisance parameters to their best fit baseline
values, we report that the best fit power law primordial power spectrum is
consistent with the reconstructed form of the PPS at 2 C.L. of the
estimated errors (apart from the local features mentioned above). As a
consistency test, we found the reconstructed primordial power spectrum from
Planck temperature data can also substantially improve the fit to WMAP-9
angular power spectrum data (with respect to power-law form of the PPS)
allowing an overall amplitude shift of . In this context low-
and 100 GHz spectrum from Planck which have proper overlap in the multipole
range with WMAP data found to be completely consistent with WMAP-9 (allowing
amplitude shift). As another important result of our analysis we do report the
evidence of gravitational lensing through the reconstruction analysis. Finally
we present two smooth form of the PPS containing only the important features.
These smooth forms of PPS can provide significant improvements in fitting the
data (with respect to the power law PPS) and can be helpful to give hints for
inflationary model building.Comment: 30 pages, 11 figures, 1 table, matches published version in JCA
Structural Vulnerability Analysis of Electric Power Distribution Grids
Power grid outages cause huge economical and societal costs. Disruptions in
the power distribution grid are responsible for a significant fraction of
electric power unavailability to customers. The impact of extreme weather
conditions, continuously increasing demand, and the over-ageing of assets in
the grid, deteriorates the safety of electric power delivery in the near
future. It is this dependence on electric power that necessitates further
research in the power distribution grid security assessment. Thus measures to
analyze the robustness characteristics and to identify vulnerabilities as they
exist in the grid are of utmost importance. This research investigates exactly
those concepts- the vulnerability and robustness of power distribution grids
from a topological point of view, and proposes a metric to quantify them with
respect to assets in a distribution grid. Real-world data is used to
demonstrate the applicability of the proposed metric as a tool to assess the
criticality of assets in a distribution grid
- …