Small Number Of Poles Research Articles

Joint Stochastic Spline and Autoregressive Identification Aiming Order Reduction Based on Noisy Sensor Data.

This article introduces the spline approximation concept, in the context of system identification, aiming to obtain useful autoregressive models of reduced order. Models with a small number of poles are extremely useful in real time control applications, since the corresponding regulators are easier to design and implement. The main goal here is to compare the identification models complexity when using two types of experimental data: raw (affected by noises mainly produced by sensors) and smoothed. The smoothing of raw data is performed through a least squares optimal stochastic cubic spline model. The consecutive data points necessary to build each polynomial of spline model are adaptively selected, depending on the raw data behavior. In order to estimate the best identification model (of ARMAX class), two optimization strategies are considered: a two-step one (which provides first an optimal useful model and then an optimal noise model) and a global one (which builds the optimal useful and noise models at once). The criteria to optimize rely on the signal-to-noise ratio, estimated both for identification and validation data. Since the optimization criteria usually are irregular in nature, a metaheuristic (namely the advanced hill climbing algorithm) is employed to search for the model optimal structure. The case study described in the end of the article is concerned with a real plant with nonlinear behavior, which provides noisy acquired data. The simulation results prove that, when using smoothed data, the optimal useful models have significantly less poles than when using raw data, which justifies building cubic spline approximation models prior to autoregressive identification.

Collinear velocity relaxation of two spheres in a viscous incompressible fluid.

Collinear velocity relaxation of two spheres immersed in a viscous incompressible fluid is studied on the basis of an approximate expression for the retarded hydrodynamic interaction. After a sudden impulse applied to one sphere, the other one instantaneously starts to move as well, with amplitude determined by the added mass effect. The velocities of both spheres eventually decay with a t^{-3/2} long-time tail, but the relative velocity decays with a t^{-5/2} long-time tail. The three relaxation functions are approximated by simple expressions involving only a small number of poles in the complex square root of frequency plane.

„Tygodnik Polski” (Harbin 1922-1942) jako źródło do dziejów polskiej emigracji w Chinach

Tygodnik Polski (Harbin 1922–1942) as a Source for the History of Polish Emigration in China Harbin, a city located in Manchuria in the Far East, became an important centre of Polish emigration in the first half of the 20th century. It was inhabited by a few thousand Polish expatriates, who could attend Polish churches and schools and had Polish social, economic and cultural organisations here. They also published books and periodicals. The longest existing periodical was Tygodnik Polski, a weekly founded by priest Władysław Ostrowski. In spite of financial difficulties and a small number of Poles in Manchuria, Tygodnik survived for 20 years (1922–1942), becoming an important source documenting the life of the Polish community in that area. Among Polish periodicals issued in Asia, it was published for the longest time and was the only Polish periodical in Asia for some time. The aim of the presented paper is to supplement the existing state of research with new information regarding the publication, edition, character and mission of the weekly. Among raised problems, the issues of upbringing and education were highlighted. The research was based on an analysis of annual volumes of Tygodnik Polski.

Stress-stress correlator in \u03d54 theory: poles or a cut?

We explore the analytical properties of the traceless stress tensor 2-point function at zero momentum and small frequency (relevant for shear viscosity and hydrodynamic response) in hot, weakly coupled λϕ4 theory. We show that, rather than one or a small number of poles, the correlator has a cut along the negative imaginary frequency axis. We briefly discuss this result’s relevance for constructing 2’nd order hydrodynamic models of hot relativistic field theories.

Solving Burgersʼ equation using optimal rational approximations

We solve viscous Burgersʼ equation using a fast and accurate algorithm—referred to here as the reduction algorithm—for computing near optimal rational approximations.Given a proper rational function with n poles, the reduction algorithm computes (for a desired L∞-approximation error) a rational approximation of the same form, but with a (near) optimally small number m≪n of poles. Although it is well known that (nonlinear) optimal rational approximations are much more efficient than linear representations of functions via a fixed basis (e.g. wavelets), their use in numerical computations has been limited by a lack of efficient, robust, and accurate algorithms. The reduction algorithm presented here computes reliably (near) optimal rational approximations with high accuracy (e.g., ≈10−14) and a complexity that is essentially linear in the number n of original poles. A key tool is a recently developed algorithm for computing small con-eigenvalues of Cauchy matrices with high relative accuracy, an impossible task for standard algorithms without extended precision.Using the reduction algorithm, we develop a numerical calculus for rational representations of functions. Indeed, while operations such as multiplication and convolution increase the number of poles in the representation, we use the reduction algorithm to maintain an optimally small number of poles.To demonstrate the efficiency, robustness, and accuracy of our approach, we solve Burgersʼ equation with small viscosity ν. It is well known that its solutions exhibit moving transition regions of width O(ν), so that this equation provides a stringent test for adaptive PDE solvers. We show that optimal rational approximations capture the solutions with high accuracy using a small number of poles. In particular, we solve the equation with local accuracy ϵ=10−9 for viscosity as small as ν=10−5.

Evaluation of Aerial Remote Sensing Techniques for Vegetation Management in Power-Line Corridors

This paper presents an evaluation of airborne sensors for use in vegetation management in power-line corridors. Three integral stages in the management process are addressed, including the detection of trees, relative positioning with respect to the nearest power line, and vegetation height estimation. Image data, including multispectral and high resolution, are analyzed along with LiDAR data captured from fixed-wing aircraft. Ground truth data are then used to establish the accuracy and reliability of each sensor, thus providing a quantitative comparison of sensor options. Tree detection was achieved through crown delineation using a pulse-coupled neural network and morphologic reconstruction applied to multispectral imagery. Through testing, it was shown to achieve a detection rate of 96%, while the accuracy in segmenting groups of trees and single trees correctly was shown to be 75%. Relative positioning using LiDAR achieved root-mean-square-error (rmse) values of 1.4 and 2.1 m for cross-track distance and along-track position, respectively, while direct georeferencing achieved rmse of 3.1 m in both instances. The estimation of pole and tree heights measured with LiDAR had rmse values of 0.4 and 0.9 m, respectively, while stereo matching achieved 1.5 and 2.9 m. Overall, a small number of poles were missed with detection rates of 98% and 95% for LiDAR and stereo matching.

Design of the Rotary Magnetic Position Sensor With the Sinusoidally Magnetized Permanent Magnet

This paper proposes a rotary magnetic position sensor (RMPS) which has a sinusoidally magnetized permanent magnet (PM) with a small number of poles. To make the sinusoidal magnetic flux density distribution from the PM, a magnetizing fixture is designed by adjusting its pole shape. The magnetization process is analyzed using the Preisach model and two-dimensional finite-element method (FEM). The simulation result of the magnetization is compared with the experimental one. Also, the ability of position detection from two sinusoidal signals is shown

Continued fraction representation of the Fermi-Dirac function for large-scale electronic structure calculations

An efficient and accurate contour integration method is presented for large-scale electronic structure calculations based on the Green function. By introducing a continued fraction representation of the Fermi-Dirac function derived from a hypergeometric function, the Matsubara summation is generalized with respect to distribution of poles so that the integration of the Green function can converge rapidly. Numerical illustrations, evaluation of the density matrix for a simple model Green function and a total energy calculation for aluminum bulk within density functional theory, clearly show that the method provides remarkable convergence with a small number of poles, indicating that the method can be applied to not only the electronic structure calculations, but also a wide variety of problems.

The application of complex layer analysis to the vibrating fluid-loaded elastic plate

Structural acoustics’ canonical problem—the locally driven fluid-loaded elastic plate attracted David Crighton’s attention over much of his career, and was the subject of his 1998 Rayleigh Medal Lecture to the British Institute of Acoustics. During this lecture he showed it ‘‘to contain a great richness of effects.’’ This presentation further elucidates the problem using an approach we refer to as complex layer analysis (CLA). CLA replaces the fluid half-space into which the plate radiates by a layer of acoustic fluid of finite thickness H=H0(1+iη) that is a complex number. By formulating the fluid-structure interaction problem in this manner the Fourier transformed surface pressure-velocity relationship which usually contains branch point singularities is approximated as a rational function of the transform variable. With the branch cut singularity removed, the resulting inverse Fourier transform is easily evaluated analytically, using contour integration, as a sum over a small number of poles. Each pole corresponds to a wave propagating in the fluid/structure system. The location of these poles is found analytically using a perturbation technique. Results for the radiation from a line-driven plate show excellent agreement with published results. This approach permits explicit evaluation and differentiation between the surface waves, i.e., the fluid-loaded structural waves and those associated with the acoustic field as affected by the plate’s structural parameters. [Work supported by CDNSWC ILIR Program.]

Characterization of gamma-tubulin in Artemia: isoform composition and spatial distribution in polarized cells of the larval epidermis.

Microtubule arrangement is influenced by gamma-tubulin, a soluble protein of the eukaryotic cell cytosol and a component of microtubule-organizing centers. In this study, affinity purified antibodies to gamma-tubulin were prepared and their specificity demonstrated by immunostaining of Western blots and in competitive ELISAs. When employed to label mouse fibroblasts, one or two brightly stained dots appeared in each cell, a pattern characteristic of centrosomes. Antibody 9, raised to a conserved amino-terminal peptide of gamma-tubulin, was used with TU-30 (from P. Dráber) to characterize gamma-tubulin in the crustacean, Artemia franciscana. Cell-free protein extracts from Artemia contained gamma-tubulin and it purified with alpha/beta-tubulin through several preparative steps. Probing of Western blots prepared from two-dimensional gels yielded a single isoform of gamma-tubulin in Artemia with a pI of about 5.6. Immunostaining with TAT, a general antibody to alpha-tubulin, demonstrated that Artemia possess two morphological types of immune blood cells (hemocytes) with distinctive microtubule arrays. Both the compact spherical hemocytes and the flatter, spreading cells exhibited fluorescent dots, often in pairs, when labelled with antibodies to gamma-tubulin. Microtubules in polarized cells of the epidermis were also brightly stained with antibody to alpha-tubulin, revealing interphase arrangements, anastral mitotic spindles and midbodies. Antibody 9 and TU-30 gave punctate staining patterns in interphase epidermal cell layers and they occasionally labelled midbodies. Unexpectedly, gamma-tubulin was seen only rarely at both poles of mitotic spindles in epidermal cells. The complete absence of asters and the apparent lack of gamma-tubulin at all but a small number of poles indicate that formation and structure of the mitotic spindle in epidermal cells of Artemia are unusual.

Radiation and scattering of waves on an elastic half-space; A non-commutative matrix Wiener-Hopf problem

Many problems in linear elastodynamics; or dynamic fracture mechanics; can be reduced to Wiener-Hopf functional equations defined in some region of a complex transform plane. Apart from a few simple cases; the inherent coupling between shear and compressional body motions gives rise to coupled systems of equations; and so the resulting Wiener-Hopf kernels are of matrix form. The key step in the solution of a Wiener-Hopf equation; which is to decompose the kernel into a product of two factors with particular analyticity properties; can be accomplished explicitly for scalar kernels. However; apart from special matrices which yield commutative factorizations; no procedure has yet been devised to exactly factorize general matrix kernels. It is the aim of this article to show that a new procedure for obtaining approximate factors of matrix kernels is applicable to the class of matrix kernels found in elasticity. This is performed; for ease of exposition; by way of a simple but non-trivial example: a linear elastic half-space; occupying the region y > 0; where ( x; y; z) are cartesian coordinates; has a free boundary on x > 0; y = 0; and has imposed time-harmonic displacements on x < 0; y = 0. Via the substitution of a scalar function in the kernel by its Padé approximant; an approximate solution to this boundary value problem is obtained explicitly for three different forcing cases. The approximate factorization technique described herein is simple to apply; is shown to converge to the exact result as the Padé number increases; and a maximum error bound is easily obtained. Numerical evaluation of the explicit results reveals that convergence to the exact solution is extremely rapid (i.e. only a small number of poles and zeros are required in the Padé approximant); which is confirmed by a global energy balance calculation; and so numerical calculations are extremely rapid. The outgoing cylindrically spreading compressional and shear wave coefficients are evaluated for several values of Poisson's ratio; v; and the outgoing Rayleigh wave is determined for all values of v (< 0.5).

Transient effects in diffusion-controlled absorption by a nonuniform sink of arbitrary constitution

The time-dependent rate coefficient for absorption of diffusing particles by a nonuniform sink of arbitrary constitution is studied on the basis of the Smoluchowski equation. It is shown that the amplitude of the long-time tail can be expressed in terms of the asymptotic rate coefficient. The time-dependent rate coefficient is expressed as the sum of the asymptotic steady-state coefficient and an integral of purely decaying exponentials with a positive weight function. It is shown that the rate coefficient can be represented accurately over a wide range of time by an approximation to its Laplace transform, characterized by a small number of poles in the complex square root of frequency plane.

Slow dynamics of linear relaxation systems

Linear relaxation, occurring in dielectrics, viscoelastic fluids, and many other systems, is often characterized by a broad continuous spectrum. We show that the relaxation behavior may be analyzed effectively by means of N-point Padé approximants, applied in the complex plane of the square root of frequency. The method leads to a compact analytic expression for the Laplace transform of the relaxation function, characterized by a small number of poles and their residues in the square root of frequency plane. We study the method in detail for a model of diffusion in three dimensions with a single or double radial potential barrier, and demonstrate its use in the analysis of the viscoelastic relaxation spectrum of polyisobutylene.

Semiclassical complex angular momentum analysis of low-energy H+-He differential cross sections

A semiclassical complex angular momentum (CAM) description of low-energy elastic collisions is presented. The scattering amplitude is divided into two parts: the direct part is described by non-orbiting semiclassical trajectories, while the orbiting part is described by a small number of poles of the S matrix. The system H+-He was studied in some detail.

Approximation of a transfer function with high Q-factor poles by a special transfer function with decreased Qs

This paper presents a method for the approximation of a transfer function with high Q-factor poles by a transfer function whose poles have a lower Q-factor. The ratio of this new transfer function to the given transfer function approximates unity with a minimum deviation over the whole ω-axis. The method is based on rearranging all poles of a given transfer function, lowering the Q of the high Q-factor poles and increasing the Q of the low Q-factor poles by interdependent movement in the s-plane. The resulting transfer function with decreased maximum £-factor has the same order as the original transfer function and a limit on the amount of Q-factor lowering is shown to exist. The function obtained can be used as a first (and in many cases, sufficient) step of the approximation process. Further reduction of the approximation error is obtained by generating more complicated transfer functions. In these functions the multiplicity of all poles which are the poles of the first-step transfer function with decreased Q is increased simultaneously. The error decreases in a geometric progression with each step. The rapid growth of approximating-function complexity restricts the application of the proposed method to transfer functions with a small number of poles. A method for determining the poles and zeros of the approximating function is described and an example of approximation is given.

Adjusting Poles and Zeros of Dielectric Dispersion to Fit Reststrahlen of PrCl3and LaCl3

The dielectric dispersion function of a medium can be defined by the locations of the poles and zeros of that function in the complex-frequency plane. In this form the dispersion function is not restricted by special characteristics of any specific physical model from which dispersion might be derived. The locations of these poles and zeros are subject to several more or less fundamental physical restrictions which are described in this paper. The connections between the locations of the poles and zeros, the frequencies and damping constants of certain optical modes, and the Lyddane-Sachs-Teller relation are discussed. Adjustments of locations of poles and zeros, consistent with the physical restrictions, were performed to obtain least-squares fits of reststrahlen data from Pr${\mathrm{Cl}}_{3}$ and La${\mathrm{Cl}}_{3}$ using a small number of poles and zeros. In this way, approximate dispersion functions for the two dielectric tensor components of each crystal were obtained at room temperature and at lower temperatures.

Automatic Resolution of Speech Spectra into Elemental Spectra

The acoustic output for a given configuration and excitation of the vocal tract during speech production can be described in a relatively compact manner by a transfer function characterized by a reasonably small number of poles and zeros. Thus the spectrum of a speech sound (log amplitude vs frequency) may be considered to be the sum of several elemental spectra, each associated with one pole or zero. The spectrum envelope of any vowel, for example, could be approximated reasonably accurately by combinations of spectra drawn from a catalog of 30 to 40 curves that represent simple resonances at a number of different frequencies. A digital computer has been programed to perform such an approximation on spectra of vowel and some consonant sounds sampled periodically in time. Successive comparisons are made between a particular speech spectrum and spectra constructed from a catalog of elementary curves that are stored in the memory. The computer is programed to converge rapidly from a first approximation of the spectrum based on previous examinations of adjacent samples towards the synthesized spectrum that yields the best fit with the input spectrum, and reads out numbers that identify the particular elemental spectra that are finally selected. [Supported by U. S. Army (S.C.), U. S. Air Force (O.S.R., A.R.D.C.), and U. S. Navy (Office of Naval Research), and by Air Force Cambridge Research Center Contract AF 19(604)-2061.]