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1
Content available Spectral and integral methods of determining parameters in selected electric arc models with a forced sinusoid current circuit
Sawicki A., Haltof M.
Archives of Electrical Engineering
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2016
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Vol. 65, nr 1
87--103
EN
The paper discusses problems arising in attempts to accurately represent dynamic processes of an electric arc by means of simple mathematical models. It describes the properties of the universal Pentegov model, employing any shape of static voltagecurrent characteristics of an arc. Next, it presents spectral and integral measuring methods for determining arc parameters in the Mayr, Cassie and Pentegov models of the electric arc with a forced sinusoid current circuit, with the raising static characteristics of hyperbolic-flat and hyperbolic-linear shape. The influence is discussed of the random power supply disturbances on errors of determining the mathematical model parameters.
2
Content available remote LES and DNS of the Flow with Heat Transfer in Rotating Cavity
Tuliszka-Sznitko E., Majchrowski W.
Computational Methods in Science and Technology
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2010
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Vol. 16, No. 1
105-114
EN
In the present paper we summarized our numerical investigations on the flow with heat transfer in rotating cavity performed by DNS (Direct Numerical Simulation) and LES (Large Eddy Simulation). We considered different geometrical configurations and different flow and thermal conditions. All presented computations have been performed in Poznań Supercomputing and Networking Center. The objective of our investigations was to analyze the coherent structures of transitional and turbulent flows and to compute statistical parameters, i.e. turbulent heat fluxes, the Reynolds stress tensor components, the turbulent Prandtl number and others. In the LES we used a version of the dynamic Smagorinsky eddy viscosity model proposed by Meneveau et al. (A Lagrangian dynamic subgrid-scale model of turbulence, J. Fluid Mech., vol. 319, 1996), in which the Smagorinsky coefficient at a given position x depends on the history of the flow along the fluid particle pathline.
3
Content available An influence matrix technique for multi-domain solution of the Navier-Stokes equations in a vorticity-streamfunction formulation
Bogusławski A., Kubacki S.
Journal of Theoretical and Applied Mechanics
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2009
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Vol. 47 nr 1
17-40
EN
The paper presents new multi-domain algorithms based on the influence matrix technique applied together with the non-overlapping iterative domain decomposition method for solution of the incompressible Navier- Stokes equations in vorticity-streamfunction formulation. The spectral Chebyshev collocation method and the influence matrix algorithm are applied for solution of the Stokes problem in each subdomain resulting from time discretization of the Navier-Stokes equations, while the patching conditions (continuity of the solution and continuity of its first order derivative) at the interfaces between subdomains are satisfied using the iterative domain decomposition algorithm.
PL
W pracy przedstawiono nowy iteracyjny algorytm dekompozycji obszaru obliczeniowego oparty na metodzie macierzy wpływu w zastosowaniu do równań Naviera- -Stokesa dla przepływu czynnika nieściśliwego w sformułowaniu wirowość-funkcja prądu. Spektralna metoda kolokacji wykorzystująca szeregi wielomianów Czebyszewa oraz metoda macierzy wpływu została zastosowana do rozwiązania zagadnienia Stokesa, będącego rezultatem dyskretyzacji równań Naviera-Stokesa w funkcji czasu, w każdym z podobszarów obszaru obliczeniowego, natomiast warunek ciągłości rozwiązania i jego pierwszej pochodnej na powierzchniach rozdziału pomiędzy podobszarami został uzyskany przy pomocy metody iteracyjnej.
4
Content available remote Dirichlet/Dirichlet and Dirichlet/Dirichlet-Neumann/Neumann non-overlapping iterative domain decomposition methods
Kubacki S., Bogusławski A.
TASK Quarterly : scientific bulletin of Academic Computer Centre in Gdansk
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2008
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Vol. 12, No 1-2
85-104
EN
A new iterative non-overlapping domain decomposition method is proposed for solving the one- and two-dimensional Helmholtz equation on parallel computers. The spectral collocation method is applied to solve the Helmholtz equation in each subdomain based on the Chebyshev approximation, while the patching conditions are imposed at the interfaces between subdomains through a correction, being a linear function of the space coordinates. Convergence analysis is performed for two applications of the proposed method (DDLC and DDNNLC algorithms - the meaning of these abbreviations is explained below) based on the works of Zanolli and Funaro et al. Numerical tests have been performed and results obtained using the proposed method and other iterative algorithms have been compared. Parallel performance of the multi-domain algorithms has been analyzed by decomposing the two-dimensional domain into a number of subdomains in one spatial direction. For the one-dimensional problem, convergence of the iteration process was quickly obtained using the proposed method, setting a small value of the ? constant in the Helmholtz equation. Another application of the proposed method may be an alternative to other iterative schemes when solving the two-dimensional Helmholtz equation.
5
Content available The motion planning problem and exponential stabilization of a heavy chain. Part II
Grabowski P.
Opuscula Mathematica
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2008
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Vol. 28, no. 4
481-505
EN
This is the second part of paper [8], where a model of a heavy chain system with a punctual load (tip mass) in the form of a system of partial differential equations was interpreted as an abstract semigroup system and then analysed on a Hilbert state space. In particular, in [8] we have formulated the problem of exponential stabilizability of a heavy chain in a given position. It was also shown that the exponential stability can be achieved by applying a stabilizer of the colocated-type. The proof used the method of Lyapunov functionals. In the present paper, we give other two proofs of the exponential stability, which provides an additional intrinsic insight into the exponential stabilizability mechanism. The first proof makes use of some spectral properties of the system. In the second proof, we employ some relationships between exponential stability and exact observability.
6
Content available remote Analysis of left cardiac ventricle shape variations based on examination of ultrasound images
Przytulska M.
Machine Graphics and Vision
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2007
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Vol. 16, No. 3/4
275-292
EN
The changes in the shape of the left cardiac ventricle within full heart evolution cycle in norm and in pathology are described using a kinetic model programmed and verified on real clinical data. In the model, information is represented by the so-called shape coefficients. The time series of the shape coefficients as well as of differential and normalized shape coefficients of the left heart ventricle have been obtained experimentally. They are then analyzed using three different approaches: spectral analysis, direct analysis of shape coefficients and direct visualization of contractions. In each of those cases, the aim of the analysis is detection and recognition of various types of abnormalities, as well as evaluation of the distance between the detected pathology and the norm.
7
Content available remote Examination of left cardiac ventricle's contractility based on spectral analysis of ultrasound imaging
Przytulska M., Kulikowski J. L.
Biocybernetics and Biomedical Engineering
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2007
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Vol. 27, no. 4
17-28
EN
A method of left cardiac ventricle's contractility abnormalities recognition and assessment, based on computer-aided analysis of sequences of ultrasonographic images is presented. The method is based on an analytical model of ventricle's shape time-variations during a single or several heart evolution cycles. An approach to ventricle's contractility abnormalities detection and evaluation based on a concept of spectral analysis of the shape coefficients' time-variations is proposed. The shape coefficients can be obtained by a computer-aided analysis of sequences of ultrasonographic cardiac images. The contraction process is characterized by spectral indicators: the contraction-depth ratio and the smoothness ratio. The results of preliminary testing of the method on clinical data are presented.
8
Content available Well-posedness and stability analysis of hybrid feedback systems using Shkalikov's theory
Grabowski P.
Opuscula Mathematica
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2006
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Vol. 26, no. 1
45-97
EN
The modern method of analysis of the distributed parameter systems relies on the transformation of the dynamical model to an abstract differential equation on an appropriately chosen Banach or, if possible, Hilbert space. A linear dynamical model in the form of a first order abstract differential equation is considered to be well-posed if its right-hand side generates a strongly continuous semigroup. Similarly, a dynamical model in the form of a second order abstract differential equation is well-posed if its right-hand side generates a strongly continuous cosine family of operators. Unfortunately, the presence of a feedback leads to serious complications or even excludes a direct verification of assumptions of the Hille-Phillips-Yosida and/or the Sova-Fattorini Theorems. The class of operators which are similar to a normal discrete operator on a Hilbert space describes a wide variety of linear operators. In the papers [12, 13] two groups of similarity criteria for a given hybrid closed-loop system operator are given. The criteria of the first group are based on some perturbation results, and of the second, on the application of Shkalikov's theory of the Sturm-Liouville eigenproblems with a spectral parameter in the boundary conditions. In the present paper we continue those investigations showing certain advanced applications of the Shkalikov's theory. The results are illustrated by feedback control systems examples governed by wave and beam equations with increasing degree of complexity of the boundary conditions.
9
Content available Zmiany widm w bliskiej podczerwieni (NIR) w poziomach organicznych pod drzewostanami bukowymi i świerkowymi
Chodak M.
Inżynieria Środowiska / Akademia Górniczo-Hutnicza im. S. Staszica w Krakowie
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2006
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T. 11, z. 1
79-86
PL
Metody spektralne wykorzystujące różne zakresy promieniowania elektromagnetycznego mogą być stosowane do badania jakości materii organicznej gleb. Celem niniejszej pracy było porównanie widm NIR materiału organicznego o różnym stopniu rozkładu pochodzącego z poziomów organicznych gleb leśnych pod drzewostanami bukowymi, świerkowymi i mieszanymi oraz próba powiązania obserwowanych zmian spektralnych z przemianami chemicznymi materii organicznej. Porównane zostały drugie pochodne zarejestrowanych widm. Widma NIR zmieniały się stopniowo w poziomach organicznych wraz z głębokością. Wartości absorbancji względnej pików przypisywanych określonym strukturom odzwierciedlały przypuszczalnie zmiany w ilości tych struktur w poszczególnych poziomach próchnicy nadkładowej oraz wskazywały na różnice pomiędzy poszczególnymi drzewostanami wynikające prawdopodobnie z różnic w składzie chemicznym ściółki. Analiza widm wykazała wzrost absorbancji pików 2320 nm i 2360 nm wskazujący na wzrost ilości struktur alifatycznych w poziomach organicznych. Wartości absorbancji względnej pików 1680, 2140 i 2170 nm, przypisywane strukturom aromatycznym, spadały wraz z głębokością, wskazując na spadek ilości tych struktur w poziomach organicznych wraz z głębokością. Stwierdzono, że wykalibrowanie widm NIR przy użyciu standardowych metod analitycznych (tj. powiązanie kształtu widma NIR z zawartością określonych substancji lub struktur oznaczoną z wykorzystaniem innych metod) może pozwolić na zastosowanie spektroskopii NIR do ilościowego badania przemian struktur chemicznych materii organicznej w procesie humifikacji
EN
Spectral methods utilizing different ranges of electromagnetic radiation may be applied to study soil organic matter quality. The objective of this study was to compare near infrared (NIR) spectra of organic layers under beech, spruce and mixed forest stands and to assign the observed spectral changes to chemical alterations of organic matter. Compared were second derivatives of the NIR spectra. The NIR spectra changed gradually in organic layers. The changes of intensities of the peaks, which may be assigned to certain chemical structures, reflected the changes in abundance of these structures and indicated differences among the studied stands resulting probably from different chemical composition of organic matter under different stands. The analysis of spectra indicated an increase of relative absorbance of the peaks at 2320 nm and 2360 nm within organic horizons, suggesting an increase of aliphatic compounds. On the contrary, the relative absorbance of the peaks at 1680 nm, 2140 nm and 2170 nm decreased within the organic horizons suggesting relative decrease of aromatic structures with depth. It was concluded that calibration of NIR spectra with standard chemical methods might enable application of NIR spectroscopy for quantitative assessment of chemical changes of soil organic matter during humification process
10
Content available remote Kinetics of hydrogen absorption in getter materials for a cylindrical tank: analytical and numerical resolutions
Gondor G., Laydi R., Laxcellent Ch.
Computer Methods in Materials Science
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2006
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Vol. 6, No. 1
1-8
EN
The kinetics of hydrogen absorption in getter materials are studied. The dissociation of hydrogen molecules on the surface, penetration of hydrogen atoms into the material and bulk diffusion are taken into account. This paper extended the investigation on a wall (1D cartesian case) performed by Liu et al. to a hollow cylinder more closed to technological application. The resolution of the equation system is solved in an analytical way (Bessel and Euler functions) or by finite difference methods. For a given time period, the filling rate of hydrogen absorbed in the container can be estimated.
PL
W artykule opisano badania kinetyki absorpcji wodoru w materiałach pochłaniających.. Rozważono dysocjację molekuł wodoru na powierzchni oraz wnikanie atomów wodoru do materiału i dyfuzję objętościową. Opisane badania rozszerzają wcześniejsze wyniki uzyskane przez Liu i in. dla płyty (przypadek Kartezjański ID) na wnętrze cylindra, czyli przypadek bliższy zastosowaniom technologicznym. Rozwiązanie układu równań przeprowadzono analitycznie (za pomocą funkcji Bessela i Eulera) oraz metodą różnic skończonych (opisano schemat jawny I niejawny). W konsekwencji możliwe było określenie szybkości napełniania zbiornika wodorem w zadanym przedziale czasu.
11
Spectral ray tracer: a class of accurate two-point ray tracers
Dębski W., Ando M.
Acta Geophysica Polonica
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2004
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Vol. 52, nr 1
1-14
EN
The recent development of high resolution seismic tomography and the in-creasing necessity for high precision seismic (acoustic) source locations calls for robust and very precise numerical methods of estimating of seismic (acoustic) wave travel times and propagation ray paths. This paper deals with two issues. First of all we present a ray path tracing algorithm based on the parameterization of ray paths by a series of Chebyshev polynomials. This pseudo-spectral method combined with the accurate Gauss-Lobbato integration procedure allows to reach a very high relative accuracy of travel time calculation, of the order of t/t 10(-7). The pseudo-spectral representation of sought ray paths turns the ray tracing problem into a numerical optimization task which, depending on the requirements, can be solved by a properly chosen optimizer. The used numerical representation designates the developed algorithm for tomography/location applications when no sharp interfaces occur. Secondly, we consider the question of the accuracy of the ray path tracing and travel time calculations. Achieving the highest tracing accuracy in terms of both accurate travel time estimation and precise spatial tracing (ray path geometry) requires a very careful analysis of all classes of errors. Some of them are caused by the numerical approximation (discretization) of the (continuous) physical law underlying a chosen computational algorithm. We demonstrate that these errors can degrade the ray tracing accuracy even by two orders of magnitude. To suppress this type of inaccuracy we propose to use a damping mechanism which introduces a kind of "tension" to the numerically generated ray paths. When properly applied, it suppresses the artificial spatial oscillations caused by the approximation errors and improves the ray tracing accuracy. The damping mechanism can also be regarded as the a priori requirement to keep the physical ray path trajectory as simple (smooth) as possible.
12
Content available Pseudospectral approximation compared with control volume formulation and finite differences- some test cases
Tyliszczak A., Bogusławski A.
TASK Quarterly : scientific bulletin of Academic Computer Centre in Gdansk
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2000
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Vol. 4, No 2
193-202
EN
The paper presents comparison of the pseudospectral method with low-order approximation for two test cases. The first test case is quasi one-dimensional supersonic flow through converging-diverging nozzle for which exact solution exists. The comparison of the error of pseudospectral approximation and upwind finite-differences using Steger-Warming flux splitting method shows high accuracy of the pseudospectral method even for few collocation points. The same conclusion is formulated for the second test case, namely incompressible flow in two-dimensional driven cavity solved by control volume formulation with modified QUICK upwinding scheme and SIMPLEC algorithm for pressure correction. As usually conclusions concerning accuracy of numerical methods are flow case dependent, but the two examples shown give some idea about the accuracy and resolution of spectral approximation versus standard CFD schemes.
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