Autor: Katunin, A. - Katalog OPAC zbiorów

Skocz do pozycji: 1.

Tytuł:: Analysis of critical percolation clusters of mixtures of conducting and dielectric polymers
Autorzy:: Katunin, A.
Powiązania:: https://bibliotekanauki.pl/articles/122371.pdf
Data publikacji:: 2016
Wydawca:: Politechnika Częstochowska. Wydawnictwo Politechniki Częstochowskiej
Tematy:: electrical percolation
critical percolation cluster
chemical distance distribution
Minkowski-Bouligand dimension
conducting polymers
przesączania elektryczne
krytyczne przesączenia klastra
chemiczna dystrybucja odległości
wymiar Minkowskiego-Bouliganda
polimery przewodzące
Opis:: The paper deals with the analysis of critical percolation clusters that have resulted from the numerical simulation of mixtures of various conducting polymers in a dielectric medium. The conducting particles in the electrical percolation problem are modelled following the hard-core/double soft-shell model which considered realistic values of particles dimensions, electrical conductivity and hopping distances. The new formulation of the chemical distance distribution in the percolation clusters is developed and several representative examples using this formulation are presented. In order to verify the fractal nature of the obtained critical percolation clusters the Minkowski-Bouligand dimension formulation was applied. Approximation of obtained results confirms the fractal nature of analysed clusters.
Źródło:: Journal of Applied Mathematics and Computational Mechanics; 2016, 15, 1; 59-69
2299-9965
Pojawia się w:: Journal of Applied Mathematics and Computational Mechanics
Dostawca treści:: Biblioteka Nauki

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Skocz do pozycji: 2.

Tytuł:: Spatial damage identification in composite plates using multiwavelets
Autorzy:: Katunin, A.
Powiązania:: https://bibliotekanauki.pl/articles/122453.pdf
Data publikacji:: 2013
Wydawca:: Politechnika Częstochowska. Wydawnictwo Politechniki Częstochowskiej
Tematy:: multiwavelets
multiwavelet transform
damage identification
composite plate
identyfikacja uszkodzeń
płyta kompozytowa
Opis:: The wavelet transform is one of the most effective tools for many tasks concerning signal and image processing, however it is difficult to obtain all of the necessary properties in one scalar wavelet. This leads to the development of new types of transforms such as a multiwavelet transform, which possesses more than one scaling and wavelet function and makes a possibility to combine these functions in order to obtain necessary properties. In the present study the CL2, LV and DGHM multiwavelets were used for an identification of spatial damage in a composite plate based on the analysis of its modal shapes. The obtained results show that some properties of the multiwavelet transform may improve the damage identification algorithm and replace the classical wavelet-based methods
Źródło:: Journal of Applied Mathematics and Computational Mechanics; 2013, 12, 3; 69-78
2299-9965
Pojawia się w:: Journal of Applied Mathematics and Computational Mechanics
Dostawca treści:: Biblioteka Nauki

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Skocz do pozycji: 3.

Tytuł:: On the convergence of multicomplex M-J sets to the Steinmetz hypersolids
Autorzy:: Katunin, A.
Powiązania:: https://bibliotekanauki.pl/articles/122672.pdf
Data publikacji:: 2016
Wydawca:: Politechnika Częstochowska. Wydawnictwo Politechniki Częstochowskiej
Tematy:: generalized M-J sets
multicomplex M-J sets
convergence
Steinmetz hypersolid
uogólniony zbiór Mandelbrot-Julia
analiza fraktalna
konwergencja
Opis:: In this paper, the analysis of generalized multicomplex Mandelbrot-Julia (henceforth abbrev. M-J) sets is performed in terms of their shape when a degree of an iterated polynomial tends to infinity. Since the multicomplex algebras result from a tensor product of complex algebras, the dynamics of multicomplex systems described by iterated polynomials is different with respect to their complex and hypercomplex analogues. When the degree of an iterated polynomial tends to infinity the M-J sets tend to the higher dimensional generalization of the Steinmetz solid, depending on the dimension of a vector space, where a given generalization of M-J sets is constructed. The paper describes a case of bicomplex M-J sets with appropriate visualizations as well as a tricomplex one, and the most general case - the muticomplex M-J sets, and their corresponding geometrical convergents.
Źródło:: Journal of Applied Mathematics and Computational Mechanics; 2016, 15, 3; 67-74
2299-9965
Pojawia się w:: Journal of Applied Mathematics and Computational Mechanics
Dostawca treści:: Biblioteka Nauki

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Skocz do pozycji: 4.

Tytuł:: Stress concentration at the circular hole of cyclically bent layered composite plate within the framework of a moment theory of thermoviscoelasticity
Autorzy:: Katunin, A.
Powiązania:: https://bibliotekanauki.pl/articles/122724.pdf
Data publikacji:: 2014
Wydawca:: Politechnika Częstochowska. Wydawnictwo Politechniki Częstochowskiej
Tematy:: moment theory of thermoviscoelasticity
self-heating effect
composite plate
teoria momentów termolepkosprężystości
efekt samorozgrzania
płyta kompozytowa
Opis:: In the continuum mechanics there is a class of problems that cannot be solved directly or the solutions of these problems are affected by large errors when the classical equations of thermoviscoelasticity are considered. The paper discusses a special case of such problems - the cyclic bending of a composite plate with a circular hole subjected to the stationary self-heating, which was solved within the framework of a moment theory of thermoviscoelasticity.
Źródło:: Journal of Applied Mathematics and Computational Mechanics; 2014, 13, 3; 75-83
2299-9965
Pojawia się w:: Journal of Applied Mathematics and Computational Mechanics
Dostawca treści:: Biblioteka Nauki

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Skocz do pozycji: 5.

Tytuł:: Three-dimensional octonion wavelet transform
Autorzy:: Katunin, A.
Powiązania:: https://bibliotekanauki.pl/articles/122330.pdf
Data publikacji:: 2014
Wydawca:: Politechnika Częstochowska. Wydawnictwo Politechniki Częstochowskiej
Tematy:: octonion wavelet transform
spatial data processing
octonionic wavelets
Opis:: The necessities of processing of spatial data require developing new feature-sensitive tools such as extensions of the wavelet transform. Considering the advantages of the application of complex wavelets and their extension to quaternionic wavelets for twodimensional data structures, the new octonion discrete wavelet transform for the analysis of three-dimensional data structures was introduced in this paper. The construction of the wavelet pyramid as well as octonionic wavelets were presented.
Źródło:: Journal of Applied Mathematics and Computational Mechanics; 2014, 13, 1; 33-38
2299-9965
Pojawia się w:: Journal of Applied Mathematics and Computational Mechanics
Dostawca treści:: Biblioteka Nauki

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Skocz do pozycji: 6.

Tytuł:: Percolation thresholds of 3D all-sided percolation clusters in non-cubic domains
Autorzy:: Katunin, A.
Powiązania:: https://bibliotekanauki.pl/articles/122722.pdf
Data publikacji:: 2016
Wydawca:: Politechnika Częstochowska. Wydawnictwo Politechniki Częstochowskiej
Tematy:: 3D percolation
percolation threshold
all-sided percolation cluster
percolation in parallelepiped domain
Monte Carlo simulation
próg perkolacji
model perkolacji izolatora
symulacja Monte Carlo
Opis:: The critical 3D all-sided percolation clusters in aL×L×L and aL×aL×L threedimensional domains with a side length L and an aspect ratio a obtained from continuous percolation problem were analysed in this paper. The simulations of continuous percolation were performed in parallelepiped domains starting from a = 1 and ending at a = 10 using the Monte Carlo algorithm. The resulting percolation thresholds for the simulated domains and percolation clusters as well as variability of number of cells in a domain and in a percolation cluster with variation of a were analysed. The obtained results are useful for evaluation of a content of electrically conducting particles in the dielectric matrix of a composite developed for aircraft lightning strike protection purposes.
Źródło:: Journal of Applied Mathematics and Computational Mechanics; 2016, 15, 4; 63-69
2299-9965
Pojawia się w:: Journal of Applied Mathematics and Computational Mechanics
Dostawca treści:: Biblioteka Nauki

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Skocz do pozycji: 7.

Tytuł:: On the symmetry of bioctonionic Julia sets
Autorzy:: Katunin, A.
Powiązania:: https://bibliotekanauki.pl/articles/122886.pdf
Data publikacji:: 2013
Wydawca:: Politechnika Częstochowska. Wydawnictwo Politechniki Częstochowskiej
Tematy:: Julia sets
hypercomplex fractals
bioctonions
hypercomplex algebra
Opis:: The hypercomplex fractals obtained from generalizations of J- and M-sets, apart from their visual aesthetics, play an important role in the mathematical description in various fields of physics. The generalizations of J- and M-sets to the four-dimensional Euclidean space are well known and well described. However, very few studies were done for the higher-dimensional generalizations. The paper discusses the J-sets generalization to the hypercomplex algebra of bioctonions and completes the previous studies in this domain. The symmetry properties were studied for quadratic mapping of the bioctonionic J-sets. The discussion of limitations of the further generalizations of J-sets to higher hypercomplex spaces was also provided.
Źródło:: Journal of Applied Mathematics and Computational Mechanics; 2013, 12, 2; 23-28
2299-9965
Pojawia się w:: Journal of Applied Mathematics and Computational Mechanics
Dostawca treści:: Biblioteka Nauki

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Skocz do pozycji: 8.

Tytuł:: On a visualization of the convergence of the boundary of generalized Mandelbrot set to (n-1)-sphere
Autorzy:: Katunin, A.
Fedio, K.
Powiązania:: https://bibliotekanauki.pl/articles/122318.pdf
Data publikacji:: 2015
Wydawca:: Politechnika Częstochowska. Wydawnictwo Politechniki Częstochowskiej
Tematy:: generalized Mandelbrot set
fractals
convergence
generalized sphere
Opis:: In this article we analyze the generalized Mandelbrot set in higher-order hypercomplex number spaces following both the Cayley-Dickson construction algebraic spaces and the spaces defined by Clifford algebras. The particular case of the generalized 3D quasi-Mandelbrot set was also considered. In particular, we investigated the increase of power of the iterated variable and proved that when this power tends to infinity, the Mandelbrot set is convergent to the unit circle. The same is true for the generalized Mandelbrot sets in higher-dimensional hypercomplex number spaces, i.e. when the power of iterated variable tends to infinity, the generalized Mandelbrot set is convergent to the unit (n-1)- sphere. The results of our investigation were visualized for the generalized Mandelbrot set in a complex number space and the generalized quasi-Mandelbrot set in a 3D Euclidean space.
Źródło:: Journal of Applied Mathematics and Computational Mechanics; 2015, 14, 1; 63-69
2299-9965
Pojawia się w:: Journal of Applied Mathematics and Computational Mechanics
Dostawca treści:: Biblioteka Nauki

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