Non-stationary Structure Research Articles

Multiresolution models for nonstationary spatial covariance functions

Many geophysical and environmental problems depend on estimating a spatial process that has nonstationary structure. A nonstationary model is proposed based on the spatial field being a linear combination of multiresolution (wavelet) basis functions and random coefficients. The key is to allow for a limited number of correlations among coefficients and also to use a wavelet basis that is smooth. When approximately 6% nonzero correlations are enforced, this representation gives a good approximation to a family of Matern covariance functions. This sparseness is important not only for model parsimony but also has implications for the efficient analysis of large spatial data sets. The covariance model is successfully applied to ozone model output and results in a nonstationary but smooth estimate.

Spatiotemporal structures in a transversely extended semiconductor system

A semiconductor system with an N-shaped current-voltage characteristic can generate nonstationary structures that are inhomogeneous in the direction transverse to the current flow. In samples of semiinsulating GaAs with a large cross section, this effect is explained by a loss of stability of the regime of uniform domain motion.

Possible problems of scale dependency in applications of the three‐dimensional fractional advection‐dispersion equation to natural porous media

A three‐dimensional (3‐D) analysis of transport and macrodispersion at the Macrodispersion Experiment (MADE) site [Boggs et al., 1993] using the Fractional Advection‐Dispersion Equation (FADE) developed by Meerschaert et al. [1999, 2001] shows that the Levy dispersion process is scale dependent. Levy dispersion may be superior to Gaussian dispersion on a sufficiently small scale; on larger scales, both theories are likely to suffer from the fact that because of depositional structures most flow fields display an evolving, nonstationary structure. Motion in such fields is advection‐dominated, displays a lot of memory and therefore is not modeled well by Markov random processes which underlie the derivation of both the Gaussian and Levy advection‐dispersion equations [Berkowitz et al., 2002]. To improve plume simulation of an advection‐dominated transport process, one would have to bring in more advective irregularity while simultaneously decreasing the Levy dispersion coefficient. Therefore, on a 3‐D basis, first‐order Levy dispersion has limitations similar to Gaussian dispersion. However, this and related theories, such as the continuous time random walk (CTRW) formalism, are in the early stages of development and thus may be fruitful areas for further research.

ROLE OF LOCALIZED STREAMWISE STRUCTURES IN THE PROCESS OF TRANSITION TO TURBULENCE IN BOUNDARY LAYERS AND JETS (REVIEW)

Results of the analysis of specific features of the laminar–turbulent transition in various subsonic shear flows, which are caused by localized stationary and nonstationary streamwise structures, are presented. One mechanism of flow turbulization is considered, which involves the origination and development of secondary high‐frequency disturbances in regions of flow instability generated by its modulation by streamwise structures. It is shown that this process is identical in different types of shear flows (boundary layers and jets) and in flows of the type of localized streamwise structures (stationary or nonstationary).

Field Interaction with Inhomogeneous Non-Stationary Planer Structures of Finite Size: Solution of Inverse Problems

Field Interaction with Inhomogeneous Non-Stationary Planer Structures of Finite Size: Solution of Inverse Problems

Stationary and Nonstationary Wave Structures that Arise in Stabilization of Detonation Over a Compression Surface

The paper reports results of numerical simulations of flow structures with oblique detonation waves that arise in supersonic flow of a uniformly mixed mixture of hydrogen with air over two–dimensional compression surfaces (wedge and cone). In the first series of calculations, the internal structure of the detonation front was not resolved but the physical processes in the remaining flow region were simulated with allowance for nonequilibrium chemical reactions. This flow is shown to have a complex wave structure, and the dependence of this structure on the parameters of the problem is studied. In the second series of calculations, nonstationary wave structures at the detonation front were obtained. These nonstationary waves are compared with the structure of the spin head in a nonstationary spin detonation.

Calculation of eddy currents in moving structures by a sliding mesh-finite element method

In this paper we present some theoretical and numerical results concerning the simulation of eddy currents in nonstationary structures. Both 2D and 3D models are considered. The approximation is based on the sliding-mesh mortar method combined with node elements in 2D and edge elements in 3D. An implicit Euler scheme is used to discretize in time.

Calculation of eddy currents with edge elements on non-matching grids in moving structures

In this paper we present a nonconforming nonoverlapping domain decomposition method to approximate the eddy current problem, formulated in terms of the electric field variable, in nonstationary structures. This approximation, that allows for nonmatching grids at the sliding interface, is based on the mortar element method combined with edge elements in space and finite differences in time. Numerical results illustrate how the method works and the influence of the free part movement on the electric field distribution.

Short-Term Effects of Air Pollution on Childhood Respiratory Illness in Piraeus, Greece, 1987–1992: Nonparametric Stochastic Dynamic Analysis

The short-term effects of air pollution on childhood respiratory illness are analyzed for the city of Piraeus, Greece during the 1987–1992 period using a distinct, nonparametric, stochastic dynamical system approach. This approach accounts for the time continuity of the phenomenon, including contemporaneous, lagged, and unstructured cumulative effects. It also accounts for the presence of autocorrelation and nonstationary structures in the series and aims at revealing the potentially subtle relationships among the examined pollutants (smoke, CO, SO2, NO2, O3), meteorological factors (temperature, humidity), and hospital admissions. The approach is also capable of assessing the individual effects of any isolated pollutant, as well as the total effects of all measured pollutants. The study is based upon 4042 hospital admissions, and its results indicate statistically significant effects of each individual pollutant, as well as meteorological factor, on hospital admissions. It is interesting that these effects appear stronger for the second half of the examined period, despite declines in the observed mean concentrations for most pollutants. The total effects of the four pollutants (excluding O3) are characterized by multiple coherence measures of 18.37 and 21.66% in the first and second halves of the examined period, respectively, and are confirmed as statistically significant.

Chemical waves and localized chaos in a model of heterogeneous catalytic reaction in a porous particles

A mathematical model of an oscillatory chemical reaction in a porous catalyst particle is considered. The model describes an oscillatory medium uniformly distributed throughout the volume of a spherical particle. The dynamical interaction of the reaction with the diffusive flow of the gaseous reagent inside the pores generates nonstationary dissipative structures in the oscillatory medium on the surface of the catalyst. Depending on the pressure in the gaseous phase, the model produces specific chemical waves and localized spatio-temporal chaos.

A Variance Components Model for Analyzing Repeated Measures Designs with Non-Stationary Error Structure

When data are collected in the form of multiple measurements on several subjects, they are often analyzed as repeated measures data with some stationary error structure assumed for the errors. For data with non-stationary error structure, the multivariate model is often used. The multivariate model imposes restrictions that are often not met in practice by data of such type. At the same time, they ignore valuable information in the data that are related to time dependencies and time relations. In this paper, we propose a model that is a reparametrization of the multivariate model and is suitable to analyze general repeated measures designs with non-stationary error structure. The model is shown to be a variance components model whose components are estimated using the method of maximum likelihood. Several other properties of the model are derived and discussed including tests of significance. Finally, an example on neurological data is included to demonstrate its application in biological sciences.

Helical structures in an anisotropic electron plasma

Exact solutions are found that represent nonlinear nonstationary structures of a helical symmetry in a plasma with anisotropic electron pressure. These are solutions to the system of the equations of vortex electron anisotropic hydrodynamics (VEAH) which describe a nonlinear evolution of the Weibel instability. The symmetry properties of VEAH equations are also studied and an optimal system of one-dimensional sub-groups is constructed that allows one to find other exact nonlinear solutions.

Longitudinal data analysis: non-stationary error structures and antedependent models

Non-stationary covariance structures had not been analyzed in detail for longitudinal data mainly because the existing applications did not require their use. Data from the Iowa Cochlear Implant Project showed this type of structure and the problem needed to be addressed. We propose a linear model for longitudinal data in which the correlation structure includes the Box-Cox transformation of the time scale. This transformation can produce nonstationary covariance structures within subjects, with stationarity as a special case. Restricted maximum likelihood methods for parameter estimation (REML) are discussed and the method is applied to speech recognition data from the Iowa Cochlear Implant Project. The growth curve for this audiologic performance measure is shown. Possible extensions for the model are suggested. © 1998 John Wiley & Sons, Ltd.

Growth curve models with non-stationary errors

The estimation of growth curves has been extensively studied in both parametric and stationary situations. In this paper we propose the use of a transformation of the time scale that can produce non-stationary covariance structure, with stationarity as a special case. First, we estimate the parameters of the covariance structure using nonlinear least squares, and with these estimators we estimate the average growth curve non-parametrically. We conduct Monte Carlo studies to assess the influence of the number of subjects and the number of observations per subject on the estimation. © 1998 John Wiley & Sons, Ltd.

Fast ‘‘stretched‐space’’ method for generating synthetic vertical sheets of nonstationary stochastic atmospheric structure for infrared background scene simulation

Fast ‘‘stretched‐space’’ method for generating synthetic vertical sheets of nonstationary stochastic atmospheric structure for infrared background scene simulation

Calculation of the process of blast wave diffraction in a cylindrical channel

We performed a numerical investigation of the process of transition of a spherical leading front into a plane one in a cylindrical channel. The processes of the collision of reflected shock waves, formation of a nonstationary grating-like structure of flow, and of the overtaking interaction of shock waves are investigated. We found that in the presence of hot gas layers on the walls of the channel a plane head front is not formed.

Deterministic spontaneous appearance of traffic jams in slightly inhomogeneous traffic flow.

This paper shows, based on numerical investigations of the kinetic model of traffic flow, what a process of a formulation of a traffic jam shows qualitatively new peculiarities seen in a slightly inhomogeneous traffic flow. A traffic jam on a highway can spontaneously appear in a deterministic way; i.e., even if fluctuations in traffic flow are negligible. This effect may be usual for a highway, where traffic flow is always slightly inhomogeneous due to entering traffic to on-ramps and leaving traffic to off-ramps. Such deterministic self-formation of traffic jams is caused by the local breakdown effect, which results in a dynamical local restructuring. Summarizing the results of this article along with two related studies, the whole possible range of density can be divided into four regions: (1) a stable state of traffic flow where any short-time perturbations fade in time; (2) a metastable state, where traffic jams can appear if localized fluctuations occur whose amplitudes exceed the critical value; (3) an unstable state where complex nonhomogeneous nonstationary structures that cover the whole road are formed; and (4) a metastable state where anticlusters and local dipole layers can be formed if localized fluctuations occur whose amplitudes exceed the critical value.

Optimal detection using bilinear time-frequency and time-scale representations

Bilinear time-frequency representations (TFRs) and time-scale representations (TSRs) are potentially very useful for detecting a nonstationary signal in the presence of nonstationary noise or interference. As quadratic signal representations, they are promising for situations in which the optimal detector is a quadratic function of the observations. All existing time-frequency formulations of quadratic detection either implement classical optimal detectors equivalently in the time-frequency domain, without fully exploiting the structure of the TFR, or attempt to exploit the nonstationary structure of the signal in an ad hoc manner. We identify several important nonstationary composite hypothesis testing scenarios for which TFR/TSR-based detectors provide a natural framework; that is, in which TFR/TSR-based detectors are both optimal and exploit the many degrees of freedom available in the TFR/TSR. We also derive explicit expressions for the corresponding optimal TFR/TSR kernels. As practical examples, we show that the proposed TFR/TSR detectors are directly applicable to many important radar/sonar detection problems. Finally, we also derive optimal TFR/TSR-based detectors which exploit only partial information available about the nonstationary structure of the signal.

Study of local scaling in the stable atmospheric boundary layer for the evaluation of turbulence parameters

A renewed interest in the dynamic and thermal structure of the atmospheric boundary layer (ABL) has recently revived, due to the contribution that this layer can provide to the improvement of skill of weather prediction and climate simulation in the most advanced general circulation models. The attention is particularly focused on non-stationary and non-homogeneous turbulent structures of this transition layer, for which many parametrization schemes, based on local-and non-local-closure assumptions, have been proposed. However, also stationary, non-homogeneous, continous-turbulence conditions can give rise to some complication in the ABL parametrization when air stability becomes stronger and stronger. In this situation, the governing scales of the classical non-local Monin-Obukhov similarity theory are no more representative, and new local scales must be derived from local forcings of the flux. This paper summarizes a few relevant points of the local-similarity theory and shows the results of a local-scaling analysis obtained by observation data of wind and temperature profiles in the ABL in the northern Po Valley

Applications of positive time-frequency distributions to speech processing

Much of our current knowledge and intuition of speech is derived from analyses involving assumptions of short-time stationarity (e.g., the speech spectrogram). Such methods are, by their very nature, incapable of revealing the true nonstationary nature of speech. A careful consideration of the theory of time-frequency distributions (TFDs), however, allows the construction of methods that reveal far more of the nonstationarities of speech, thereby highlighting just what it is that conventional approaches miss. We apply two iterative methods for generating positive time-frequency distributions (TFDs) to speech analysis. Both methods make use of multiple sources of information (e.g., multiple spectrograms) to yield a high-resolution estimate of the joint time-frequency energy density of speech. Plosive events and formant harmonic structure are simultaneously preserved in these TFDs. Rapidly time-varying formants are also resolved by these TFDs, and harmonic structure is revealed, independent of sweep rate; this result is quite different from that seen with conventional speech spectrograms. The speech features observed in these distributions demonstrate that conventional sliding window techniques lose or distort much of the rich nonstationary structure of speech. Examples for synthetic formants and real speech are provided. The differences between joint distributions and conditional distributions are also illustrated. >