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Showing papers on "Parametric statistics published in 1974"


Journal ArticleDOI
TL;DR: In this paper, the behavior of parametric transmitting arrays in their far field is studied, neglecting higher-order interaction effects, in the form of normalized curves and simplified equations which can be used for the preliminary design of such devices.
Abstract: Since Westervelt's original proposal [J. Acoust. Soc. Am. 35, 535–537(1963)] that nonlinear acoustic interactions may be used to produce relatively narrow beams of sound at relatively low frequencies, a great deal of effort has gone into the study of parametric transmitting arrays, both experimentally and theoretically. In this paper, the behavior of such arrays in their farfield is studied, neglecting higher‐order interaction effects. Results are presented in the form of normalized curves and simplified equations which can be used for the preliminary design of such devices.

76 citations


Journal ArticleDOI
TL;DR: In this paper, a set of model equations for the parametric instability that consist of damped harmonic oscillators coupled with a stochastic oscillatory driver is considered, and a solution for the average response of the oscillators is derived.
Abstract: A set of model equations for the parametric instability that consist of damped harmonic oscillators coupled with a stochastic oscillatory driver is considered. With the assumption that the autocorrelation time of the stochastic part of the driver is very short, a solution for the average response of the oscillators is derived. This solution holds for arbitrary damping rates, unlike the results of previous authors. Threshold levels and growth rates for the parametric decay and oscillating two‐stream instabilities are found as a function of driver bandwidth.

67 citations


Journal ArticleDOI
TL;DR: In this article, an explicit expression for the steady-state periodic response of a linear dynamical system subjected to combined parametric and forcing excitations of periodic nature is given in terms of the fundamental matrix of the homogeneous system.
Abstract: A linear dynamical system subjected to combined parametric and forcing excitations of periodic nature is governed by a system of inhomogeneous differential equations with periodic coefficients. Presented here is an explicit expression for the steady-state periodic response of such a system, given in terms of the fundamental matrix of the homogeneous system. Based upon this expression, specific analytic formulas of the steady-state response can be derived for some physical systems. For a general system where such an analytical determination is not feasible, the derived expression allows us to devise a straightforward numerical procedure which is particularly suited for computer evaluation and which is equally suited for high-order systems.

60 citations


Journal ArticleDOI
TL;DR: In this paper, the authors present a set of Feynman-Dyson rules in parametric space for the construction of ultraviolet-and infrared-divergence-free FPNs.
Abstract: Concise and practical formulas for Feynman-parametric integrals are assembled and presented in the form of Feynman-Dyson rules in parametric space. These rules enable us to write down $S$-matrix elements directly in terms of some parametric functions. They are particularly useful for construction of ultraviolet- and infrared-divergence-free Feynman-parametric integrals in a form suitable for numerical integration.

42 citations



Journal ArticleDOI
TL;DR: In this paper, an analytical method for the study of orthogonal-flux systems and parallel-fluctuated systems is presented, which is applied to study and compare controllable inductors.
Abstract: Analytical methods for the study of orthogonal-flux systems and parallel-flux systems are presented. The analyses are applied to study and compare orthogonal-flux and parallel-flux controllable inductors. It is found that the two systems have a great qualitative similarity but differ in the magnitudes of similar effects. This paper lays the ground work to be used in the study of parametric power converters or parametric voltage regulators to be presented in subsequent papers.

37 citations


Journal ArticleDOI
TL;DR: In this article, two types of parametric transformers referred to as the "chain type" and "cross-winding type" are described, which are related in the sense that they have identical magnetic circuits, but they differ in their windings arrangement.
Abstract: The paper describes the two types of parametric transformers referred to as the "chain type" and "cross-winding type". They are related in the sense that they have identical magnetic circuits, but they differ in their windings arrangement. These transformers utilize the principle of parametric oscillations to develop an output voltage and transfer energy from the input circuit to the output circuit without direct mutual coupling. The two types belong to two different categories in which the MMF's of the input and output circuits act either at right angle to one another (orthogonal) or along the same line (co-linear) in the common regions. The operation of each type is described by two simultaneous nonlinear differential equations and the magnetization characteristics which relate the MMF's and fluxes in the input and output sides of the transformer. The experimental results on a small unit show that the cross-winding type is more efficient and has a higher output to weight ratio than the chain type.

27 citations


Book ChapterDOI
TL;DR: This chapter discusses three cases related to the blending of patches: (1) blending at a common border, (2) blending between two nonadjacent patches, and (3) blending a given patch to the borders of another patch.

25 citations


Journal ArticleDOI
TL;DR: A quantitative experimental confirmation of a recent theory for large-signal parametric instabilities in IMPATT diode circuits is described and a graphical technique is given that is useful for analyzing circuit stability.
Abstract: This paper describes a quantitative experimental confirmation of a recent theory for large-signal parametric instabilities in IMPATT diode circuits. The relevant parts of the theory are presented in a concise form. A graphical technique is given that is useful for analyzing circuit stability. A sufficient (though not necessary) condition for well-behaved circuits is also studied, and several diagrams are presented that may prove useful to circuit designers.

23 citations


Journal ArticleDOI
TL;DR: In this paper, a non-linear two degrees of freedom dynamical system subjected to parametric excitation is studied and the relationship between the parametric frequency and the natural frequencies of the system are such that the first generalized coordinate is excited into parametric resonance while both generalized coordinates are excited into combination resonance at the same time.
Abstract: A non-linear two degrees of freedom dynamical system subjected to parametric excitation is studied. The relationship between the parametric frequency and the natural frequencies of the system are such that the first generalized coordinate is excited into parametric resonance while both generalized coordinates are excited into combination resonance at the same time. The unstable zone and response of the system under multi-resonant condition are then compared with the unstable zones and responses of the system where each type of resonance is treated on an individual basis, assuming the other type of resonance does not occur.

22 citations


Journal ArticleDOI
TL;DR: In this article, a parametric approach towards the classification of relaxation methods is presented, and a comparison of one of these methods with the other methods already available is made with the comparison of the two methods.

Journal ArticleDOI
01 Jan 1974
TL;DR: In this article, an analysis of the four-photon parametric amplification in an unbiased Josephson junction is presented, and the analysis is extended to multiple (series-connected) junctions and subharmonic pumping.
Abstract: An analysis is presented describing four-photon parametric amplification in an unbiased Josephson junction. Central to the theory is the model of the Josephson effect as a nonlinear inductance. Linear, small signal analysis is applied to the two-fluid model of the Josephson junction. The gain, gain-bandwidth product, high frequency limit, and effective noise temperature are calculated for a cavity reflection amplifier. The analysis is extended to multiple (series-connected) junctions and subharmonic pumping.

Journal ArticleDOI
D.A. Woodford1
TL;DR: In this paper, it was shown that several of the most common time-temperature parameters express one variable as the product of functions of two others, and the optimum value of the appropriate constant is obtained from the equation of a straight line.


Journal ArticleDOI
TL;DR: In this article, a theory of the stabilization of an inverted pendulum by means of externally imposed random oscillations of the point of support in a vertical line is described, and two conditions for stability in the upright position are derived.

Journal ArticleDOI
01 Jul 1974
TL;DR: In this article, the parametric resonance in a system having two modes of the same frequency is studied, and the simultaneous occurence of the instabilities of the first and second kind is examined, by using a generalized perturbation procedure.
Abstract: The parametric resonance in a system having two modes of the same frequency is studied. The simultaneous occurence of the instabilities of the first and second kind is examined, by using a generalized perturbation procedure. The region of instability in the first approximation is obtained by using the Sturm's theorem for the roots of a polynomial equation.

Journal ArticleDOI
TL;DR: In this paper, the external value of a parametric problem of mathematical programming is considered as a function of a parameter and the directional derivatives of different orders of this function are investigated.
Abstract: THE EXTERNAL value of a parametric problem of mathematical programming is considered as a function of a parameter. The directional derivatives of different orders of this function are investigated.

Journal ArticleDOI
TL;DR: Numerical results for two example problems are presented using the Univac 1108 digital computer, revealing the economic advantages and disadvantages of the integrated approach to the identification and optimization problems.
Abstract: This study is concerned with the simultaneous identification and optimization of static systems. The necessity and the advantages of an integrated approach to the identification and optimization of the system model is established theoretically as well as computationally. A parametric approach to the integrated problem is proven to converge to the integrated problem solution. The general methodology of decomposition of large-scale systems is extended by implementingfeasible decomposition of the joint problem. A multilevel approach is then utilized to successfully solve example problems. Handling the system constraints via a penalty-function technique is shown to be an efficient approach when using the parametric formulation of the joint problem. Numerical results for two example problems are presented using the Univac 1108 digital computer, revealing the economic advantages and disadvantages of the integrated approach to the identification and optimization problems.


Journal ArticleDOI
TL;DR: A hybrid technique combining the rapid gradient generation capability of the method of gradients with the rapid convergence characteristics of finite-dimensional, variable-metric function minimization algorithms is presented.


Journal ArticleDOI
TL;DR: In this paper, the steady-state parametric interactions of a three-wave system where one of the waves is a backward-traveling wave were studied. But the results showed that the backward traveling wave is not quite so efficient an amplification process as suggested by a previous investigation.
Abstract: We studied the steady‐state parametric interactions of a three‐wave system where one of the waves is a backward‐traveling wave. This situation is shown to lead to complications not previously discussed. Analytical expressions are given for the intensity of the backward‐traveling wave as a function of the pump wave intensity and of parameters characterizing the nonlinear medium. This result shows that backward‐traveling parametric interaction is not quite so efficient an amplification process as suggested by a previous investigation.

Journal ArticleDOI
R. Alan Gregory1
TL;DR: In this paper, a continuous thermal parametric pumping system is compared to a conventional adsorption system with thermal regeneration, and well-defined mathematical models are used to find the operating conditions which maximize the separation and throughput of each system.
Abstract: A continuous thermal parametric pumping system is compared to a conventional adsorption system with thermal regeneration. Well-defined mathematical models are used to find the operating conditions which maximize the separation and throughput of each system. Under practical operating conditions, the model equations indicate parametric pumping can process a larger volume feed stream at equivalent separations than conventional adsorption for the solute/adsorbent system studied. At equilibrium conditions equivalent results are obtained but parametric pumping requires more energy.


Proceedings ArticleDOI
01 Jan 1974
TL;DR: In this article, the authors survey some of the fundamentals underlying these phenomena results and demonstrate their behavior and their application by presenting experimental results and data collected from a waveguide propagation in shallow water.
Abstract: Over the p ast decade, nonlinear acoustics has experienced an unprecedented expansion in theory, experiment, and application. This vigorous activity has its roots in Westervelt's theoretical discovery of the parametric acoustic arra,y (1960). This type of transducer utilizes the nonlinear properties of the water itself to produce a low frequency, superdirective radiation from the parametric interaction of two high frequency generating waves, The superdirective radiation so created is a wide band entity having no spatial diffraction lobes. Several practical applications of parametric arrays are now emerging; these include bathymetric profiling, the location of artifacts in marine archeolotg, ultrasonic imaging and biomedical diagno_s_tics, and measurements on waveguide propagation in shallow water. and will demonstrate their behavior and their application by presenting experimental This paper will survey some of the fundamentals underlying these phenomena results.

Journal ArticleDOI
TL;DR: The parametric cubic splines interpolating to such closed curves as the circle and ellipse are derived in a form where their parameters are given by simple algebraic expressions and the error in approximation of the given curves is precisely determined.
Abstract: The parametric cubic splines interpolating to such closed curves as the circle and ellipse are derived in a form where their parameters are given by simple algebraic expressions.

Journal ArticleDOI
TL;DR: In this article, an analysis of the parallel-flux parametric voltage regulator has been performed and it has been shown that it offers all the desirable characteristics of the orthogonal-fluctual parametric regulator and several additional advantages, such as higher energy transfer capability and higher efficiency in material utilization.
Abstract: An analysis of the parallel-flux parametric voltage regulator shows that it offers all the desirable characteristics of the orthogonal-flux parametric voltage regulator and that it offers several additional advantages. The most striking additional advantage is a much higher energy transfer capability, which implies higher efficiency in material utilization.

Journal ArticleDOI
TL;DR: In this paper, the authors report some experimental results on the parametric interaction of codirected saw in photoconducting CdS, which takes place through the 2nd-order electric field associated with the bunching of carriers.
Abstract: We report some experimental results on the parametric interaction of codirected saw in photoconducting CdS This interaction takes place through the 2nd-order electric field associated with the bunching of carriers Below threshold conditions, we directly observed both parametric attenuation and amplification with a 30 dB dynamic range At the highest electric level of the pump available on our apparatus, 16 dBm, the parametric gain is about 10 dB Beyond the threshold conditions, we observed only a parametric attenuation


01 Dec 1974
TL;DR: In this article, a new class of two-sample test statistics is defined, and sufficient conditions for its asymptotic normality under a broad class of alternatives are obtained.
Abstract: : A new class of two-sample test statistics is defined. Sufficient conditions for its asymptotic normality under a broad class of alternatives are obtained. Asymptotic efficiencies relative to the parametric competitors for shift in location and change of scale are also obtained. These results are extended to the situations where the sample sizes are random and the observations come in pairs and each pair has the same but unknown bivariate distribution. As a particular case, the asymptotic normality of the Spearman's rank correlation coefficient is established in Section 5 under all alternatives. In a straight forward manner the two-sample results are extended to the c-sample case and the asymptotic efficiency of the test criterion, in order to test for the equality of the underlying distributions is evaluated when the alternatives involve shifts in location parameters or changes in scale parameters.