Calculation of Generalized Polynomial-Chaos Basis Functions and Gauss Quadrature Rules in Hierarchical Uncertainty Quantification

Stochastic spectral methods are efficient techniques for uncertainty quantification. Recently they have shown excellent performance in the statistical analysis of integrated circuits. In stochastic spectral methods, one needs to determine a set of orthonormal polynomials and a proper numerical quadrature rule. The former are used as the basis functions in a generalized polynomial chaos expansion. The latter is used to compute the integrals involved in stochastic spectral methods. Obtaining such information requires knowing the density function of the random input {\it a-priori}. However, individual system components are often described by surrogate models rather than density functions. In order to apply stochastic spectral methods in hierarchical uncertainty quantification, we first propose to construct physically consistent closed-form density functions by two monotone interpolation schemes. Then, by exploiting the special forms of the obtained density functions, we determine the generalized polynomial-chaos basis functions and the Gauss quadrature rules that are required by a stochastic spectral simulator. The effectiveness of our proposed algorithm is verified by both synthetic and practical circuit examples.Comment: Published by IEEE Trans CAD in May 201

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

A Fast Frequency Sweep – Green’s Function Based Analysis of Substrate Integrated Waveguide

In this paper, a fast frequency sweep technique is applied to the analysis of Substrate Integrated Waveguides performed with a Green’s function technique. The well-known Asymptotic Waveform Evaluation technique is used to extract the Padè approximation of the frequency response of Substrate Integrated Waveguides devices. The analysis is extended to a large frequency range by adopting the Complex Frequency Hopping algorithm. It is shown that, with this technique, CPU time can be reduced of almost one order of magnitude with respect to a point by point computation

The gravitational-wave memory from eccentric binaries

The nonlinear gravitational-wave memory causes a time-varying but nonoscillatory correction to the gravitational-wave polarizations. It arises from gravitational waves that are sourced by gravitational waves. Previous considerations of the nonlinear memory effect have focused on quasicircular binaries. Here, I consider the nonlinear memory from Newtonian orbits with arbitrary eccentricity. Expressions for the waveform polarizations and spin-weighted spherical-harmonic modes are derived for elliptic, hyperbolic, parabolic, and radial orbits. In the hyperbolic, parabolic, and radial cases the nonlinear memory provides a 2.5 post-Newtonian (PN) correction to the leading-order waveforms. This is in contrast to the elliptical and quasicircular cases, where the nonlinear memory corrects the waveform at leading (0PN) order. This difference in PN order arises from the fact that the memory builds up over a short "scattering" time scale in the hyperbolic case, as opposed to a much longer radiation-reaction time scale in the elliptical case. The nonlinear memory corrections presented here complete our knowledge of the leading-order (Peters-Mathews) waveforms for elliptical orbits. These calculations are also relevant for binaries with quasicircular orbits in the present epoch which had, in the past, large eccentricities. Because the nonlinear memory depends sensitively on the past evolution of a binary, I discuss the effect of this early-time eccentricity on the value of the late-time memory in nearly circularized binaries. I also discuss the observability of large "memory jumps" in a binary's past that could arise from its formation in a capture process. Lastly, I provide estimates of the signal-to-noise ratio of the linear and nonlinear memories from hyperbolic and parabolic binaries.Comment: 25 pages, 8 figures. v2: minor changes to match published versio

Gravitational Wave Bursts from Cosmic Superstring Reconnections

We compute the gravitational waveform produced by cosmic superstring reconnections. This is done by first constructing the superstring reconnection trajectory, which closely resembles that of classical, instantaneous reconnection but with the singularities smoothed out due to the string path integral. We then evaluate the graviton vertex operator in this background to obtain the burst amplitude. The result is compared to the detection threshold for current and future gravitational wave detectors, finding that neither bursts nor the stochastic background would be detectable by Advanced LIGO. This disappointing but anticipated conclusion holds even for the most optimistic values of the reconnection probability and loop sizes.Comment: 26 pages, 6 figures; v2: references added and typos correcte

On Time-Variant Distortions in Multicarrier Transmission with Application to Frequency Offsets and Phase Noise

Phase noise and frequency offsets are due to their time-variant behavior one of the most limiting disturbances in practical OFDM designs and therefore intensively studied by many authors. In this paper we present a generalized framework for the prediction of uncoded system performance in the presence of time-variant distortions including the transmitter and receiver pulse shapes as well as the channel. Therefore, unlike existing studies, our approach can be employed for more general multicarrier schemes. To show the usefulness of our approach, we apply the results to OFDM in the context of frequency offset and Wiener phase noise, yielding improved bounds on the uncoded performance. In particular, we obtain exact formulas for the averaged performance in AWGN and time-invariant multipath channels.Comment: 10 pages (twocolumn), 5 figure