Nonstationary Formulation Research Articles

Estimating the total effect on a formation during borehole drilling

A stationary mathematical model describing the time-integrated effect on an oil-saturated reservoir during drilling is considered. Calculated results are compared with the solution of the problem in an exact nonstationary formulation. The formation of an invaded zone in straight borehole drilling in water-and oil-saturated reservoirs is studied by numerical modeling.

Statistical properties of ion channel records. Part II: Estimation from the macroscopic current

Macroscopic ion channel current is the summation of the stochastic records of individual channel currents and therefore relates to their statistical properties. As a consequence of this relationship, it may be possible to derive certain statistical properties of single channel records or even generate some estimates of the records themselves from the macroscopic current when the direct measurement of single channel currents is not applicable. We present a procedure for generating the single channel records of an ion channel from its macroscopic current when the stochastic process of channel gating has the following two properties: (I) the open duration is independent of the time of opening event and has a single exponential probability density function (pdf), (II) all the channels have the same probability to open at time t. The application of this procedure is considered for cases where direct measurement of single channel records is difficult or impossible. First, the probability density function (pdf) of opening events, a statistical property of single channel records, is derived from the normalized macroscopic current and mean channel open duration. Second, it is shown that under the conditions (I) and (II), a non-stationary Markov model can represent the stochastic process of channel gating. Third, the non-stationary Markov model is calibrated using the results of the first step. The non-stationary formulation increases the model ability to generate a variety of different single channel records compared to common stationary Markov models. The model is then used to generate single channel records and to obtain other statistical properties of the records. Experimental single channel records of inactivating BK potassium channels are used to evaluate how accurately this procedure reconstructs measured single channel sweeps.

Phenological and geographical patterns of walleye pollock (Theragra chalcogramma) spawning in the western Gulf of Alaska

Over 20 years of egg sampling data were used to reconstruct the geographical and phenological patterns of walleye pollock (Theragra chalcogramma) spawning aggregations in the Gulf of Alaska (GOA). The analyzed time series (1972, 1978–1979, 1981–2000) included a documented event of climate change (i.e., 1988–1989) and the rise and fall of the GOA pollock population abundance and harvests. We compared results from two generalized additive model (GAM) formulations: one assuming no change of egg distribution and phenology over the examined time series (stationary) and the other admitting such changes (nonstationary) across an epoch determined from the data. Results from both model formulations corroborate the existence of a high egg concentration in Shelikof Strait, historically the primary spawning area of pollock in the GOA. However, model results also highlight the presence of other secondary, and possibly transitory, centers of egg distribution at various locations along the shelf and slope regions of the GOA. In addition, results from the nonstationary (and statistically superior) formulation indicate that the abundance of the non-Shelikof aggregations has increased over time, along with a tendency for earlier occurrence and displacement toward shallower areas of the high egg density regions.

Effect of the initial temperature of a reactive medium on the critical conditions for thermal explosion

A nonstationary formulation of critical conditions for thermal explosion in the Thomas problem (asymmetric self-ignition) and the classical Frank-Kamenetskii problem (symmetric self-ignition) are numerically studied. By the example of the Thomas problem, it is shown that the thermal explosion limit depends on the form of the initial spatial temperature distribution of the medium. For the Frank-Kamenetskii problem, the effect of the initial spatial temperature distribution and the initial overheating of the reactant on the critical value of the Frank-Kamenetskii number is studied. The particular initial spatial temperature distribution is determined; the investigation of its evolution allows one to make a conservative estimate of the thermal explosion limit. The limitation of the classical criterion for thermal explosion is shown, and the limits of applicability of the stationary theory are numerically determined from the initial overheating. For engineering calculations, an analytical formula for conservatively estimating the critical conditions for thermal explosion as a function of the initial reactant overheating is obtained.

Handbook of Utility Theory: Principles, Vol. 1

Handbook of Utility Theory: Principles, Vol. 1, ed. Salvador Barbera, Peter J. Hammond, and Christian Seidl, 1998, Dordrecht, the Netherlands: Kluwer Academic Publishers. Reviewer: Gautam Vora, University of New Mexico This is the first volume in a two-volume set of recent developments in fundamental conceptual problems or their resolutions that are too recent to have achieved widespread understanding among social scientists. The editors selected several topics and invited contributions from researchers whose work had come to their attention. The intended readership is researchers working in economics, political science, ethics, and other major branches of the social sciences. The first volume, spanning approximately 700 pages, contains the following topics: (1) Preference and utility (G. B. Mehta), (2) Separability: A Survey (C. Blackorby, D. Primont, and R. R. Russell), (3) Recursive Utility and Dynamic Programming (P. A. Streufert), (4) Dual Approaches to Utility (M. Browning), (5) Objective Expected Utility (P. J. Hammond), (6) Subjective Expected Utility (P. J. Hammond), (7) Stochastic Utility (P. C. Fishbun), (8) Fuzzy Utility (M. Salles), (9) Lexicographic Utility and Orderings (J. E. Martinez-Legaz), (10) Utility Theory and Ethics (P. Mongin and C. d'Aspremont), (11) Measures of Economic Welfare (M. Ahlheim), (12) Changing Utility Functions (H. Shefrin), and (13) Causal Decision Theory (J. M. Joyce and A. Gibbard). Chapters 1 through 6 and 8 and 9 are extreme mathematical treatments of topics whose relevance to applications in finance, economics, insurance, and risk is difficult to fathom. The second volume is expected to contain the following 12 topics: (14) Alternatives to Expected Utility: Foundations and Concepts, (15) Alternatives to Expected Utility: Some Formal Theories, (16) State-Dependent Utility, (17) Extending Preferences to Sets of Alternatives, (18) Utility as a Tool in Non-Cooperative Game Theory, (19) Utility as a Tool in Cooperative Game Theory, (20) Utility in Social Choice, (21) Interpersonal Comparisons of Utility, (22) Experimental and Empirical Research I: Riskless Utility, (23) Experimental and Empirical Research I: Utility Under Risk, (24) Experimental and Empirical Research I: Utility Under Ambiguity, and (25) Utility Theory in Retrospect. A quick glance at the reference sections reveals that the editors have assembled an impressive array of authors, who have published voluminously in utility theory. As the title suggests, these articles present of utility theory; I deduce that articles in the second volume present applications. The presentation of principles in the volume under review is at an advanced level; i.e., these articles are written by specialists for specialists. A nonspecialist reader-say, a researcher in economics or psychology-is unlikely to find the articles inviting. This is not to say that he or she would not find some of them somewhat interesting. A critical synopsis of the chapters is given below. Mehta's article (Chapter 1) studies the problem of preference and utility. He finds general conditions for the existence and nonexistence of a real-valued (continuous, differentiable) utility representation on an ordered set. Blackorby, Primont, and Russell's article (Chapter 2) is a survey and lays out the fundamentals of separability theory, integrating literature with more recent developments. The presentation is in the context of the consumer theory, but it is general enough for applications to an agent with a well-behaved preference ordering. Streufert (Chapter 3) studies the tradeoff traditionally faced by the economist who wants to formulate a dynamic optimization problem for an agent's decision to forgo current benefits for the sake of future benefits. The economist must choose between a stationary formulation having an infinite number of time periods and a nonstationary formulation having a finite number of time periods. …

Interior ballistics of a powder-driven pulsed water cannon

Results of theoretical and experimental studies of the interior ballistics of a powder-driven pulsed cannon are presented. The liquid flow in the facility is considered in quasistationary and nonstationary formulations. Conditions for the applicability of the quasistationary approximation are determined. The effect of the compressibility of the liquid on the performance of the pulsed cannon is evaluated. Calculation results are compared with experimental data obtained on a particular installation.

Axisymmetric interaction of an acoustic wave with a thin elastic spherical shell stiffened by an elastic rib

In nonstationary formulation in the context of the classical theories of shells and curvilinear rods we solve the axisymmetric problem of scattering of sound on a spherical shell stiffened by a rib. We analyze the effect of the rib on the spectral density of the echo-signal. We give the results of computing the reflected pulse and classify the sequence of pulses of peripheral waves in the echo-signal.

The mechanics of a powder-drive water jet

We consider the processes in a powder-drive pulse water jet in which the acceleration of the water shell occurs as the result of the energy from burning powder. The one-dimensional motion of the fluid is described in the nonstationary formulation, while the combustion of the powder is described in a quasistationary formulation. The barriers are assumed rigid. In a numerical solution that is presented we use the method of complete computation. For a specific structure of the cannon we give the results of numerical computations. We discuss a simplified approach for estimating the parameters of the apparatus. Four figures. Bibliography: 5 titles.

Optimal restoration of multichannel images based on constrained mean-square estimation

In this paper, we present an efficient algorithm for the problem of multichannel image restoration. Existing multichannel techniques do not provide sufficient flexibility for the simultaneous suppression of the noise process and the preservation of sharp detailed structure in the estimate. The approach introduced overcomes this inefficiency by introducing the prototype Wiener structure in the smoothing process of the estimate. The corresponding algorithm is obtained from the optimization of the constrained mean-square-error (CMSE) criterion, which is interpreted as a structured regularized criterion. The CMSE estimate always has a meaningful structure and lies between the minimum mean-square error estimate and the pseudo-inverse solution. In addition, the CMSE approach enables the suppression of streak artifacts, which are often experienced due to the amplification of the noise process. In particular, the paper focuses on the selection of the regularization parameter, which can significantly affect the quality of the regularized estimate. Two selection techniques are introduced. The first technique develops the equivalence between the minimization of the weighted least-squares function and the solution of a set of nonlinear equations in the case of unstructured space-varying and nonstationary problem formulations. The second selection method is based on the Cramer-Rao bound on the expected variation of the stabilizing term. The CMSE approach is demonstrated through a multichannel restoration example and is compared to other restoration techniques.

Ignition of a radiating gas by an incandescent surface

The fundamental regularities of ignition of a radiating and absorbing gas by an incandescent surface are examined. In the case of an optically thin medium characteristic for high-temperature ignition, the problem is solved in the traditional stationary and nonstationary formulations [8]. It is shown that radiant heat transfer plays an essential part in the gas ignition process, in particular, the process can be accelerated and retarded in an optically thin gas medium because of radiant heat exchange. The case of an optically dense gasl kb/l o corresponds to radiant heat conduction, and therefore, does not result in a change in the ignition time but only to an increase in the scale of the lengthl o. For intermediate values ofl kb/l o the dependence of τ✩ on parameters governing the energetics of radiant heat transfer is complex in nature and can only be analyzed numerically in each specific case. The development of a suitable model of radiation heat exchange is the fundamental difficulty here.

Sound radiation by a system of piezoceramic spherical shells under pulse electrical excitation

Shell structures from piezoceramic materials operating under the effect of connectedness of the mechanical and electrical fields have recently found extensive practical application in modern engineering. The general theory of piezoceramic shells, underlying which are the Kirchhoff-Love hypotheses, is elucidated in [1-3]. Let us note that within the framework of the approach mentioned, dynamic processes have been studied in sufficient detail for wave fields steady in time. Such problems have not been examined in a nonstationary formulation.

Stability of heat transfer regimes at the front stagnation point of a body in a stream of dissociated gas

The formulation and solution of the stationary problem of heat transfer in the neighborhood of the front point of a body at constant temperature in a stream of dissociated air are given in [1]. In [2], the results are given of numerical solution of this problem in the nonstationary formulation; the establishment of a stationary heat transfer regime was established for all the calculated variants. In the present paper, we investigate the stability of stationary heat transfer regimes at the front stagnation point of a body in a stream of dissociated air using the Lyapunov functional method [3, 4] and the method of [2, 5], which is based on the use of Meksyn's method in boundary-layer theory [6, 7]. It is established that an arbitrarily strong growth of the Damkohler number does not lead to instability and multiplicity of the stationary regimes, in contrast to the case when a hot mixture of gases flows over the front point of a thermostat [2, 5, 8]. Numerical solution of the boundary-layer equations for a wide range of Damkohler numbers confirms the results of the approximate qualitative analysis and shows that in a number of cases the time of establishment of the stationary state is a nonmonotonic function of the Damkohler number.

Experimental comparison between stationary and nonstationary formulations of linear prediction applied to voiced speech analysis

The purpose of this paper is to present the theoretical differences and results of experimental comparison of the stationary (autocorrelation) and nonstationary (covariance) linear prediction formulations when applied to voiced speech analysis. In this experimental study three criterion used for comparison purposes are: 1) total minimum normalized squared error, 2) accuracy in estimating speech spectrum, and 3) accuracy in estimating formant parameters. The results of linear prediction pitch synchronous as well as pitch asynchronous analyses of synthetic and natural speech are given. Influence of analysis segment size and its position on the estimated formant parameters and total minimum normalized squared error have been investigated. For pitch synchronous analysis, nonstationarity is a better assumption than stationarity, but for pitch asynchronous analysis and large analysis segment size (20-25 ms) the performance of both formulations in representing the speech waveform is practically the same.

Experimental comparison of stationary and nonstationary formulations of linear prediction applied to voiced speech analysis

There are basically two formulations of linear prediction: (1) stationary, and (2) nonstationary. This paper presents the theoretical differences between the two formulations and gives the results of experimental comparison of the two formulations when applied to voiced speech analysis. In this experimental study three criteria are used for comparison purposes: (1) total minimum normalized squared error (η) [Makhoul, “Spectral Analysis of Speech by Linear Prediction,” IEEE Trans. Audio Electroacoust. (June 1973)], (2) accuracy in estimating speech spectrum, and (3) accuracy in estimating formant parameters. This paper presents the results of linear prediction pitch synchronous as well as pitch asynchronous analysis of synthetic and natural speech. Influence of analysis segment size and its position on the estimated formant parameters and η have been investigated. Nonstationary formulation performs better in case of pitch synchronous analysis than pitch asynchronous analysis. We have found that, for pitch synchronous analysis, nonstationarity is a better assumption than stationarity, but for pitch asynchronous analysis and large analysis segment size (20–25 msec) the performance of both formulations in representing the speech waveform is practically the same.

Variationally computed antenna impedances and accuracy of resulting current distributions

The difference between a stationary and a nonstationary impedance formulation is shown to become zero if a complex current distribution produces zero tangential electric field along the metallic surface of the antenna. This difference between the two impedances is used as a criterion for establishing the accuracy for a given approximate current distribution. Illustrative examples consider dielectric-coated antennas in free space and insulated antennas in a magnetoionic medium.