Pole Parameters Research Articles

The κ resonance in s wave πK scatterings

A new unitarization approach incorporated with chiral symmetry is established and applied to study the πK elastic scatterings. We demonstrate that the κ resonance exists, if the scattering length parameter in the I=1/2, J=0 channel does not deviate much from its value predicted by chiral perturbation theory. The mass and width of the κ resonance is found to be M κ =594±79 MeV, Γ κ =724±332 MeV, obtained by fitting the LASS data up to 1430 MeV. Better determination to the pole parameters is possible if the chiral predictions on scattering lengths are taken into account.

Estimation of the location and exponent of the spectral singularity of a long memory process

Abstract. We consider the estimation of the location of the pole and memory parameter ω0 and d of a covariance stationary process with spectral density image We investigate optimal rates of convergence for the estimators of ω0 and d, and the consequence that the lack of knowledge of ω0 has on the estimation of the memory parameter d. We present estimators which achieve the optimal rates. A small Monte‐Carlo study is included to illustrate the finite sample performance of our estimators.

Frequency response of pressure pulsations and source identification in a suction manifold

A complicated suction manifold geometry is modelled as a simplified cylindrical annular cavity to study gas pulsations in a multi-cylinder compressor. Linear acoustic plane wave theory and a four pole parameter formulation are used to derive and solve the governing inhomogeneous equation for the forced pressure response in the manifold. By matching the lowest natural frequency of the idealized annular cavity model to that of the actual system using finite element modelling, the best possible match between the free response characteristics of the complicated and idealized manifolds is obtained. A simulation procedure for estimating gas pressure pulsations in the annular cavity connected to an anechoic inlet pipe is then described. Complicated interactions between multiple cylinder valve ports are shown to produce interesting changes in the frequency response for changes in the operating speed, and hence, the flow rate characteristics through the valves. By including a delay time for opening the valve in the mass flow rate profiles and considering the difference between the experimental and simulation results, the variable stroke of the piston and the delay times for opening the valve are estimated without solving the valve dynamic and thermodynamic equations. It is shown that the estimate of the gas pulsation in the suction manifold, which was identified using an iterative procedure, is in good agreement with the experimental result in the case of lower mass flow rate. By applying mass flow rate sinks at each valve as identified, the correlation between analytical and experimental results is shown to be much better than if the idealized, kinematically obtained source functions are used instead.

Determination of the Δ++ magnetic dipole moment

Abstract We study the elastic and radiative π+p scattering within a full dynamical model which incorporates the finite width effects of the Δ++. The scattering amplitudes are invariant under contact transformations of the spin 3/2 field and gauge-invariance is fulfilled for the radiative case. The pole parameters of the Δ++ obtained from the elastic cross section are mΔ=(1211.2±0.4) MeV and ΓΔ=(88.2±0.4) MeV. From a fit to the most sensitive observables in radiative π+p scattering, we obtain μΔ=(6.14±0.51)e/2mp for the magnetic dipole moment of the Δ++.

Estimation of EOP from VLBI: Direct Approach

AbstractThe currently adopted strategy of EOP estimation from VLBI is to estimate six parameters: UT1, UT1 rate, pole positions and nutation offsets for each 24-hour session independently. Then the resulting time series of raw Earth orientation parameters are filtered and a regression analysis is performed in order to obtain nutation coefficients, polhode of the pole and other physical parameters. Thus, the latter parameters are obtained indirectly in two stages. An alternative approach of direct estimation of the final Earth orientation parameters is presented. Pole coordinates and UT1 are considered as a sum of three components: the low-period component which is modeled by a cubic spline, the harmonic component which includes forced nutation, precession and sub-daily variations of EOP, and the stochastic component which is modeled by a linear spline with segment length 1-2 hours. All parameters are obtained in a single LSQ solution using all available data.

Conversion of Single- and Multilevel Breit-Wigner Resonance Parameters to Pole Representation Parameters

One reliable and convenient way of processing the cross sections in the resolved energy region is by use of the generalized pole representation, whereby the Doppler-broadening calculation can be carried out rigorously using the analytical approach. So far, its applications have been limited to cases with resonance parameters specified by the Reich-Moore formalism. Although such an approach can in principle be extended to all three remaining representations of resolved resonance parameters specified by the ENDF data format, there is no computational tool for handling such a task at present. Given that Breit-Wigner formalisms are probably the most widely used by any evaluated nuclear data library to represent cross sections, a special effort needs to be made to convert the single- and multilevel Breit-Wigner resonance parameters to pole parameters. The FORTRAN computer code BW2PR has been developed for this purpose. Extensive calculations have been performed to demonstrate that the proposed method ensures the conservation of the information contained originally in Breit-Wigner resonance parameters. This will make it possible to apply the exact Doppler-broadening method to a larger collection of nuclides.

Exact Solution for One-Dimensional Acoustic Fields in Ducts With Polynomial Mean Temperature Profiles

The purpose of this paper is to present closed form expressions for sound propagation in ducts with polynomial mean temperature profiles. It is shown that using appropriate transformations, the one-dimensional wave equation for ducts with an axial mean temperature gradient can be reduced to a standard differential equation whose form depends upon the specific mean temperature profile in the duct. The solutions are obtained in terms of Bessel and Neumann functions. The analysis neglects the effects of mean flow and therefore the solutions obtained are valid only for mean mach numbers that are less than 0.1. The developed solution is used to investigate the sound propagation in a quarter wave tube with an axial mean temperature gradient. The expressions for the four pole parameters are also presented.

GAS PULSATIONS IN THIN, CURVED OR FLAT CAVITIES DUE TO MULTIPLE MASS FLOW SOURCES WITH SPECIAL ATTENTION TO MULTI-CYLINDER COMPRESSORS

If compressor manifolds are thin compared to the smallest wavelength of interest, the general procedure developed by the authors [1, 2] for the analysis of curved, thin muffler elements can be applied to the analysis of gas pulsations in multi-cylinder compressor head cavities. The procedure for single-input/single-output systems is extended to systems of multi-inputs. Four pole parameters and transfer functions for each input/output set are obtained separately. The pressure response at the output port excited by each input is calculated by multiplying the input volume flow rate for each compressor valve with the respective transfer functions. The total pressure response is obtained by superposition of the pressure response excited by each input. A rectangular box type compressor head cavity with refrigerant discharged from a two-cylinder compressor and a thin cylindrical head cavity of a four cylinder automotive air conditioning compressor are analyzed as application examples.

TWO- DIMENSIONAL ANALYSIS OF THIN SHELL- OR PLATE-LIKE MUFFLER ELEMENTS OF NON-UNIFORM THICKNESS

A general procedure for the analysis of curved, thin muffler elements, which can efficiently utilize the limited space in hermetically sealed compressors or compact engine installations [1], is extended to take non-uniform thickness into account. The inhomogeneous 2-D wave equation for the non-uniform thickness case is derived in two dimensional curvilinear coordinates defined on a curved surface by the application of Hamilton's principal. Four pole parameters are formulated form the pressure response solutions using the modal series expansion method and orthogonality property. The analyses of two types of curved, thin muffler elements with thickness variation in only one direction are demonstrated as examples. Analytical results are verified by comparison with the results obtained from a finite element program. Good agreement was achieved as long as the thickness of the muffler element is sufficiently small compared to the wavelength range of interest.

TWO DIMENSIONAL ANALYSIS OF THIN, SHELL OR PLATE LIKE MUFFLER ELEMENTS

A general procedure for the analysis of curved or flat, thin two dimensional muffler elements is developed. These thin elements can efficiently utilize the limited space of hermetically sealed compressors or small engine compartments. The two dimensional inhomogenous wave equation is developed in two dimensional curvilinear co-ordinates by the application of Hamilton's principle. Four pole parameters are formulated form the pressure response solutions using the modal series expansion method. The eigenvalues and transfer functions of three types of thin muffler elements connected to an anechoic pipe are given as examples: the flat rectangular box, the thin annular cylindrical shell, and the flat circular box. A verification is made by comparing results for an annular cylindrical muffler element with results obtained from a three-dimensional model; good agreement was achieved as long as the thickness of the muffler element is sufficiently small compared to the wavelength range of interest.

Analysis of mimo mechanical systems using the vectorial four pole parameter method

Formulas are derived to predict the frequency response characteristics of a multiple-input/multiple-output (MIMO) linear system consisting of several subsystems by using those of each subsystem. The method is called here the vectorial four pole parameter technique, since the basic concept and procedure are the same as for the conventional (scalar) four pope parameter method for a single-input/single-output (SISO) system. Compatibility of the formulas with Newtonian mechanics is confirmed by two examples: one system constructed by two subsystems in series and another system in parallel. Since two poles are defined under clamped conditions while the other two poles are under free boundary conditions, it is often difficult in practice to measure all of the four poles directly from an excitation test. A method of indirect estimation of the two poles defined under boundary conditions which are difficult to realize is presented, in which the reciprocity and transmissibility theorems are used. Experimental results for a beam structure with two-input and two-output connections are presented as an illustration of the vectorial four pole parameter approach.

The Azores triple junction evolution since 10 Ma from an aeromagnetic survey of the Mid-Atlantic Ridge

In the past two decades several models have been presented to describe the evolution and the present structure of the Azores Triple Junction. These models were mainly based on morphological analysis of sea bottom topography, sparse magnetic profiling, sidescan sonar surveying over the plateaus and global plate kinematic considerations for the North Atlantic. In this paper we follow a different approach: from a detailed aeromagnetic survey covering both sides of the Mid-Atlantic Ridge between 37°N and 40°30′N the magnetic anomalies up to anomaly 5 are accurately identified, allowing careful modelling of the kinematics of this region for the past 10 Ma and thus establishing a coherent framework for the design of geophysical models for the Azores Triple Junction. The analysis of magnetic anomalies and the use of Fourier domain inversion techniques show that the ridge is made up of six segments, each one varying in length from 50 to 60 km. The more continuous section of the ridge can be defined from the first four northern segments, although the North Azores Fracture Zone right-offsets the ridge at 39°30′N, 29°40′W. The fifth and sixth segments are, respectively, right-offset by the Acor Fracture Zone (at 38°23′N, 30°15′W) and by the Princess Alice Fracture Zone (at 38°00′N, 30°50′W). Anomaly identifications using a two-dimensional model and plate tectonics reconstruction techniques allowed the calculation of rotation pole parameters. The results thus obtained reveal that, at least between anomalies 5 and 3 ( ∼ 10–3.85 Ma), the Azores displayed an independent motion relative to the neighbouring plates and after anomaly 2A (2.45 Ma) the Azores moved attached to the Eurasian plate. The triple junction (Azores-North America-Africa, or Eurasia-North America-Africa) moved northward from ∼ 38°00′N, 30°50′W to ∼ 38°20′N, 30°15′W (between 4 and 3A) and probably to 38°50′N, 30°00′W at anomaly 2A time. A detailed reconstruction model is presented.

Pole-parameter analysis: a novel approach for the design of filters

The paper introduces pole parameter analysis (PPA) as a novel approach useful in obtaining the realisable transfer functions to meet the prescribed specifications of a filter. Analytical expressions are obtained for the design parameters and performance indices, in terms of pole parameters omega /sub p/ and theta /sub p/ that are introduced as the basis of PPA. Details have been given for the second order case and extensions to higher order filters are indicated. Perspectives obtained through this approach indicate the possibilities of generating new families of transitional filters. A practically useful class of higher order filters which make use of (second order) identical section filters (ISFs) in cascade is studied in detail. ISFs are also desirable in limiting the component-spread in the fabrication using IC technology. The elegant manner in which the effect of component-spread can be incorporated at the design stages using the PPA approach is also discussed.

Development of a General Procedure to Formulate Four Pole Parameters by Modal Expansion and Its Application to Three-Dimensional Cavities

If an acoustic system has one or more large dimensions compared to the shortest wave length of interest, the pressure responses which are necessary to formulate four pole parameters have to be obtained by solving the continuous wave equation of the system. In this paper, a general procedure is established to derive four pole parameters from the pressure response solutions utilizing modal series expansion. As an example, four pole parameters of a cylindrically annular cavity are obtained. The validity of the procedure is proven by applying it also to a one-dimensional pipe whose four pole parameters are available by direct method. The comparison is made in terms of four pole parameters and pressure profiles along the pipe. The comparison allows interesting observations with regard to the equivalence of the two approaches. The theory was further generalized to be applied to more complex acoustic systems, namely multiply connected systems. A cylindrically annular cavity connected by two pipes to a small lumped parameter cavity is taken as an example of the application. Noise control by either mode cancellation or wave cancellation is explored.

High‐resolution inversion for South Atlantic Plate kinematics using joint altimeter and magnetic anomaly data

We present an inversion for plate kinematics that solves for finite rotation parameters using fracture zone (FZ) and magnetic anomaly location data jointly. We define misfit functions that incorporate properties unique to each data type; in particular, the FZ misfit function does not depend upon alignment of conjugate FZ traces in the same way as magnetic lineations under the finite rotations. This property is useful for FZ locations, in which the signals on conjugate sides of the ridge may include systematic differences, or where data from one side of the ridge are sparse or missing. Formal error bounds estimated for the pole parameters show that the magnetic and FZ data are complementary in their information content. Error bounds computed for the joint inversion are substantially smaller than for either the FZ or magnetics data used separately, indicating that simultaneous use of the data in an inversion is crucial. We apply this method to Seasat altimeter data and magnetic anomaly picks in the South Atlantic. We solve for finite poles corresponding to magnetic anomalies 5, 6, 8, 13, 21, 22, 25, 30, 33, 33r, and 34; these define a smooth path over the past 84 m.y. indicating that the plate motions have not been as erratic as found previously.

Analysis of gas pulsations in multiply connected three-dimensional acoustic cavities with special attention to natural mode or wave cancellation effects

The general four pole parameters for a system of two continuous three-dimensional cavities connected by n pipes are derived utilizing four pole parameters of each individual cavity in terms of its natural modes, frequencies, and modal damping. As an application example, a two-pipe connection is investigated and resulting natural mode or wave cancellations are discussed. Also, a four-pipe connection is analyzed to illustrate a method of combining the advantages of cancelling both a three-dimensional natural mode and certain plane waves in the feeder pipes.

General formulation of four pole parameters for three-dimensional cavities utilizing modal expansion, with special attention to the annular cylinder

Four poles for three-dimensional cavities were simulated in terms of eigenfunctions of these cavities, first for general curvilinear co-ordinates, then for the specific example of an annular cylindrical cavity. As an application example, this formulation was applied to an annular cylindrical cavity connected to an anechoic pipe, with a single and a double input. Various responses are illustrated. Many applications come to mind, for example in three-dimensional muffler theory, but application examples were chosen in such a way that they contribute to the understanding of pressure pulsations inside a shell enclosing a refrigeration compressor, with the acoustic input being the suction port of the compressor and the output being the evaporator pipe. The relative locations of input and output ports, pressure distributions in the cavity at resonance condition, and phase cancellations when two input ports are used, are discussed.

Towards a Globally Convergent Approximation of Optimal On-line Parameter Estimation

A possibly globally convergent approximation to the optimal continuous time non linear filter for n pole parameters and n states only is found by computing the first, second, and third order moment equations. Closure of the moment equations results from approximating fourth order moments by the Gaussian formula involving second order moments. Five necessary conditions for stability are given. The unique convergence point of the algorithm is shown to be the true pole parameter value in the scalar case. The new algorithm is asymptotically equivalent to the non-stationary version of the recursive prediction error method. The error incurred by the Gaussian approximation is shown to be small in several examples of the discrete time optimal nonlinear filter.

Investigations of relative plate motions in the South Atlantic using Seasat altimeter data

Fracture zones in the world's oceans appear clearly in the Seasat altimeter (geoid) data at wavelengths of about 100 km and less. In the North and South Atlantic these signatures are stable in form and amplitude from the ridge crest to crust tens of millions of years old and can be mapped across nearly the width of the basin. The signatures diminish in amplitude markedly on crust older than 70 to 80 m.y. B.P., apparently when thickly covered by sediments. Because fracture zone trajectories closely approximate plate motion flow lines, they may be used to infer the plate kinematic history of the ocean basin. In this paper I describe a new method for estimating the relative poles of opening, describing the history of motion between two plates by using fracture zone trajectories. The method is an iterative inversion whereby the trajectories of synthetic flow lines are linearized with respect to the pole parameters. When applied to the Seasat altimeter track data, a waveform inversion based upon this method is possible in which the altimeter data are modeled using a synthetic geoid fracture zone signal. This waveform inversion is applied to 17 prominent fracture zones in the central and South Atlantic to estimate the poles of opening between the South American and African plates. Altogether, 1022 Seasat fracture zone crossings are used; for each of these a waveform comparison is made. The new method is found to be robust and converges to a stable set of pole solutions even if the initial flow lines are small circles about a single pole that poorly approximates the observed trajectories. The solution poles document a Cenozoic change in plate motion near anomaly 13 time (36 m.y. B.P.) similar to that in the North Atlantic at anomaly 1.3–21 time (36–50 m.y. B.P.).

Three-dimensional acoustic analysis of circular expansion chambers with a side inlet and a side outlet

The effects of higher-order acoustic modes upon the performance of a circular expansion chamber with its inlet and outlet located on the cylinder wall are investigated. The sound distribution in the expansion chamber is obtained, theoretically, considering the influences of the diffracted sound pressure generated by the presence of end plates in the chamber. A theoretical method for the estimation of the transmission loss is suggested by using the derived four pole parameters, assuming that the chamber can be modeled as a piston-driven circular rigid cylinder. A series of experimental observations are taken for verification, and it is found that they are in good agreement with the theoretical results. The influences of those modes are studied for a variety of chamber lengths and combined inlet/outlet locations. As a result of this study, it is concluded that the diffracted sound pressure affects the performance of the expansion chamber considerably in the range above the cutoff frequency of the n=1, m=0 asymmetric mode, and that the plane-wave theory can hardly be adopted even in the low-frequency range where the fundamental mode prevails.