Analysis of NMR Spin-Relaxation Data Using an Inverse Gaussian Distribution Function

We investigate the electron-boson spectral density function, $I^2\chi(\omega,T)$, of CuO$_2$ plane in underdoped Bi$_2$Sr$_2$CaCu$_2$O$_{8+\delta}$ (Bi-2212) and underdoped YBa$_2$Cu$_3$O$_{6.50}$ (Y-123) using the Eliashberg formalism. We apply a new (in-plane) pseudogap model to extract the electron-boson spectral function. For extracting the spectral function we assume that the spectral density function consists of two components: a sharp mode and the broad Millis-Monien-Pines (MMP) mode. We observe that both the resulting spectral density function and the intensity of the pseudogap show strong temperature dependences: the sharp mode takes most spectral weight of the function and the peak position of the sharp mode shifts to lower frequency and the depth of pseudogap, $1-\tilde{N}(0,T)$, is getting deeper as temperature decreases. We observe also that the total spectral weight of the electron-boson density and the mass enhancement coefficient increase as temperature decreases. We estimate fictitious (maximum) superconducting transition temperatures, $T_c(T)$, from the extracted spectral functions at various temperatures using a generalized McMillan formula. The estimated (maximum) $T_c$ also shows a strong temperature dependence; it is higher than the actual $T_c$ at all measured temperatures and decreases with temperature lowering. Since as lowering temperature the pseudogap is getting stronger and the maximum $T_c$ is getting lower we propose that the pseudogap may suppress the superconductivity in cuprates.

Variability response functions for beams with nonlinear constitutive laws

We introduce a differential-geometric structure for spectral density functions of discrete-time random processes. This is quite analogous to the Riemannian structure of information geometry, which is used to study perturbations of probability density functions, and which is based on the Fisher information metric. Herein, we introduce an analogous Riemannian metric, which we motivate with a problem in prediction theory. It turns out that this problem also provides a prediction theoretic interpretation to the Itakura distortion measure, which relates to our metric. Geodesies and geodesic distances are characterized in closed form and, hence, the geodesic distance between two spectral density functions provides an explicit, intrinsic (pseudo)metric on the cone of density functions. Certain other distortion measures that involve generalized means of spectral density functions are shown to lead to the same Riemannian metric. Finally, an alternative Riemannian metric is introduced, which is motivated by an analogous problem involving smoothing instead of prediction.

The author focuses on the frequency domain approach, which provides a complete characterization of frequency. The standard characterization of frequency stability in the frequency domain is the spectral density function (SDF). The author describes SDFs that model sampled frequency stability data and that are related to the SDFs of the standard characterization. On the basis of standard techniques in spectral analysis, he outlines a systematic way of estimating SDFs typical of frequency stability data. The recommended procedure is to check for broadband bias in the periodogram using a sequence of data tapers and, if bias is in evidence, to design an autoregressive prewhitening filter to prewhiten the data. The author considers the relationship between the Allan variance and the SDF and outlines two nonparametric ways of translating stability measures between the two domains-one based upon pilot analysis and the other upon J. Rutman's bandpass variance (1978).< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Reduction of leakage and increase of resolution in power spectral density and coherence functions

Homogenization of spectral problem for locally periodic elliptic operators with sign-changing density function

This paper deals with a large class of nonstationary stochastic processes generated by passing white noise through a general linear time-varying filter. It is shown that such processes can be characterized in terms of a family of jointly wide-sense stationary processes. This formulation is used to define the spectral density function for the nonstationary processes considered in the paper. Then the spectral density function is used to give a suboptimal solution to the nonstationary Wiener filtering problem. This suboptimal solution is shown to be nearly optimal under conditions corresponding to a sufficiently small rate of variation. A numerical example compares this suboptimal Wiener filter solution to an optimal solution.

In this paper we present several results for three different canonical forms of linear prediction on a plane. These filters have causal, semicausal, and noncausal prediction geometries. Starting from their properties we consider the problem of realization of these filters from a given power spectral density function (SDF). Since it is not possible in general to obtain rational spectral factors of a two-dimensional SDF, we propose algorithms for obtaining rational approximations which are stable and converge to their limit (irrational) factors as the order of approximation is increased. It is also shown that the normal equations associated with the minimum variance two-dimensional prediction filters give a useful algorithm for obtaining rational approximations which are stable and converge to their unique limit filters. This result allows design of finite-order stable filters by solving a finite number of equations while realizing the given SDF arbitrarily closely.

Signal processing of flutter flight test data enables verification of aircraft flutter design, and the signal from a flutter flight test excited by atmospheric turbulence is a particularly important form of the flutter test. Owing to the randomness of atmospheric turbulence excitation, multi-channel analysis of turbulence responses at various positions in the same component can improve the analytical accuracy of flutter signal processing. The relationship between the maximum singular value of the multi-channel turbulence response power spectral density matrix and the system self-power spectral density function is elucidated herein using a frequency domain decomposition method. However, there is a contradiction in the power spectral density function between the spectral line density and the spectral line smoothing calculated based on the periodogram of the frequency domain decomposition. By applying an autoregressive spectral model, the power spectral density function of the turbulence response is calculated to achieve spectral line smoothing and sufficient spectral line density. Additionally, the power spectral density function is then used to construct the power spectral density function matrix of the multi-channel turbulence response, and the maximum singular value curve is calculated based on the singular value decomposition of each spectral pin. Finally, the modal parameters of the turbulence response signal are estimated via multi-modal frequency domain fitting. The developed approach is validated based on simulations and flutter flight test turbulence response signals.

Bayesian system reliability assessment method with maximum entropy as prior distribution is developed in the present analysis. The system reliability assessment model is established, and the method and process of system reliability assessment are put forward. The method is based on the theory of information entropy. The probability density function and distribution function of system reliability parameters are given by using maximum entropy method. Prior distribution of Bayesian analysis method is the distribution function. Likelihood function is given by a small amount of field test data. According to Bayesian methods, posterior distribution is determined by using prior distribution and likelihood function. The point estimation and interval estimation of system reliability parameters are calculated in order to evaluate the system reliability. The method solves better the problem of system reliability assessment for small sample cases, and is an optimum method for reliability assessment of large and complex systems.

Fokker—Planck—Langevin and extended diffusion models of internal rotation in molecules. I. symmetric internal rotor

Simulation of non-Gaussian surfaces with FFT

In the paper, two algorithms that allow identification of a parametric models of random time-series from binary-valued observations of their realizations, as well as from quantized measurements of their values, are proposed. The proposed algorithms are based on the idea of time-series decomposition either on a direct power spectral density or autocorrelation function approximation. They use the concepts of randomized search algorithms to recover the corresponding parametric models from calculated estimates of power spectral density or autocorrelation function. The considerations presented in the paper are illustrated with simulated identification examples in which linear and nonlinear block-oriented dynamic models of timeseries are identified from the binary-valued observations and quantized measurements.

Two Chebyshev recursion methods are presented for calculations with very large sparse Hamiltonians, the kernel polynomial method (KPM) and the maximum entropy method (MEM). They are applicable to physical properties involving large numbers of eigenstates such as densities of states, spectral functions, thermodynamics, total energies for Monte Carlo simulations and forces for tight binding molecular dynamics. this paper emphasizes efficient algorithms.

A method is presented for the determination of the transverse response of the idealized suspended span of an offshore pipeline to random seismic input. The method is based on spatial discretization of the pipe with nodal lumped masses. The earthquake is assumed to be a stationary random process characterized by a power spectral density function. The cross spectral density function between two random seismic excitations along the pipe length is defined with the help of a local earthquake power special density function, which is assumed to be the same for the two end supports of the pipeline, and a frequency dependent weighted function which decays exponentially with distance from the pipe supports. The solution is obtained in the frequency domain using the spectral approach and is presented in terms of r.m.s. displacements and stresses. The formulation adequately includes the pressure drag effect which tends to dampen the pipe motions. Utilizing this method of analysis, several idealized pipe sea bed configurations, in which the pipe is anchored between two end blocks and subjected to horizontal ground excitations normal to the pipe axis, have been analysed to predict the influence of certain important parameters on the response.