Efficient wideband electromagnetic scattering computation for frequency dependent lossy dielectrics using WCAWE

This paper presents a model order reduction algorithm for the volume electric field integral equation (EFIE) formulation, that achieves fast and accurate frequency sweep calculations of electromagnetic wave scattering. An inhomogeneous, two-dimensional, lossy dielectric object whose material is characterized by a complex permittivity which varies with frequency is considered. The variation in the dielectric properties of the ceramic BaxLa4Ti 2+xO 12+3x in the <1 GHz frequency range is investigated for various values of x in a frequency sweep analysis. We apply the well-conditioned asymptotic waveform evaluation (WCAWE) method to circumvent the computational complexity associated with the numerical solution of such formulations. A multipoint automatic WCAWE method is also demonstrated which can produce an accurate solution over a much broader bandwidth. Several numerical examples are given on order to illustrate the accuracy and robustness of the proposed methods

Geometry and Singularities of the Prony mapping

Prony mapping provides the global solution of the Prony system of equations $$\Sigma_{i=1}^{n}A_{i}x_{i}^{k}=m_{k},\ k=0,1,...,2n-1.$$ This system appears in numerous theoretical and applied problems arising in Signal Reconstruction. The simplest example is the problem of reconstruction of linear combination of $\delta$-functions of the form $g(x)=\sum_{i=1}^{n}a_{i}\delta(x-x_{i})$, with the unknown parameters $a_{i},\ x_{i},\ i=1,...,n,$from the "moment measurements"$m_{k}=\int x^{k}g(x)dx.$Global solution of the Prony system, i.e. inversion of the Prony mapping, encounters several types of singularities. One of the most important ones is a collision of some of the points$x_{i}.$ The investigation of this type of singularities has been started in \cite{yom2009Singularities} where the role of finite differences was demonstrated. In the present paper we study this and other types of singularities of the Prony mapping, and describe its global geometry. We show, in particular, close connections of the Prony mapping with the "Vieta mapping" expressing the coefficients of a polynomial through its roots, and with hyperbolic polynomials and "Vandermonde mapping" studied by V. Arnold.Comment: arXiv admin note: text overlap with arXiv:1301.118

Cosmology with gamma-ray bursts: II Cosmography challenges and cosmological scenarios for the accelerated Universe

Context. Explaining the accelerated expansion of the Universe is one of the fundamental challenges in physics today. Cosmography provides information about the evolution of the universe derived from measured distances, assuming only that the space time ge- ometry is described by the Friedman-Lemaitre-Robertson-Walker metric, and adopting an approach that effectively uses only Taylor expansions of basic observables. Aims. We perform a high-redshift analysis to constrain the cosmographic expansion up to the fifth order. It is based on the Union2 type Ia supernovae data set, the gamma-ray burst Hubble diagram, a data set of 28 independent measurements of the Hubble param- eter, baryon acoustic oscillations measurements from galaxy clustering and the Lyman-{\alpha} forest in the SDSS-III Baryon Oscillation Spectroscopic Survey (BOSS), and some Gaussian priors on h and {\Omega}M . Methods. We performed a statistical analysis and explored the probability distributions of the cosmographic parameters. By building up their regions of confidence, we maximized our likelihood function using the Markov chain Monte Carlo method. Results. Our high-redshift analysis confirms that the expansion of the Universe currently accelerates; the estimation of the jerk parameter indicates a possible deviation from the standard {\Lambda}CDM cosmological model. Moreover, we investigate implications of our results for the reconstruction of the dark energy equation of state (EOS) by comparing the standard technique of cosmography with an alternative approach based on generalized Pad\'e approximations of the same observables. Because these expansions converge better, is possible to improve the constraints on the cosmographic parameters and also on the dark matter EOS. Conclusions. The estimation of the jerk and the DE parameters indicates at 1{\sigma} a possible deviation from the {\Lambda}CDM cosmological model.Comment: 10 pages, 7 figures, accepted for publication in A &

Wideband Characteristic Basis Functions in Radiation Problems

In this paper, the use of characteristic basis function (CBF) method, augmented by the application of asymptotic waveform evaluation (AWE) technique is analyzed in the context of the application to radiation problems. Both conventional and wideband CBFs are applied to the analysis of wire and planar antennas

Wideband Characteristic Basis Functions in Radiation Problems

In this paper, the use of characteristic basis function (CBF) method, augmented by the application of asymptotic waveform evaluation (AWE) technique is analyzed in the context of the application to radiation problems. Both conventional and wideband CBFs are applied to the analysis of wire and planar antennas