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1
Content available Analysis of a multiphase free boundary problem
Abdelouahab Ahlem, Bensid Sabri
Opuscula Mathematica
|
2024
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Vol. 44, no. 5
631--649
EN
In this paper, we investigate a free boundary problem relevant in several applications, such as tumor growth models. Our problem is expressed as an elliptic equation involving discontinuous nonlinearities in a specified domain with a moving boundary. We establish the existence and uniqueness of solutions and provide a qualitative analysis of the free boundaries generated by the nonlinear term (inner boundaries). Furthermore, we analyze the dynamics of the outer region boundary. The final result demonstrates that under certain conditions, our problem is solvable in the neighborhood of a radial solution.
2
Content available A new improved of incorporating photovoltaic energy into the production of green hydrogen
Benchenina Yacine, Zemmit Abderrahim, Bouzaki Mohammed Moustafa, Belhouchet Khaled
Diagnostyka
|
2024
|
Vol. 25, No. 2
art. no. 2024210
EN
The integration of renewable energies, particularly photovoltaic energy, into green hydrogen production presents a highly promising prospect in the energy sector. Nonetheless, these energy sources face challenges due to their inherent instability and susceptibility to various atmospheric factors such as temperature and illumination. Therefore, it's imperative to tackle these challenges before renewable energy can be widely adopted as a primary source in hydrogen production. To address this, we propose constructing an autonomous photovoltaic system using MATLAB software. This system will employ a DC-DC boost converter to connect the PV array to the load. Furthermore, to enhance the efficiency of photovoltaic power generation, we will implement the perturbation and observation maximum power point tracking (MPPT) approach. The research endeavor extends towards integrating this optimized system with an electrolysers developed a sophisticated electrolyte model utilizing MATLAB Simulink software, paving the way for hydrogen gas production.
3
Content available Spectrum localization of a perturbed operator in a strip and applications
Gil Michael
Opuscula Mathematica
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2021
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Vol. 41, no. 3
395–-412
EN
Let A and A be bounded operators in a Hilbert space. We consider the following problem: let the spectrum of A lie in some strip. In what strip the spectrum of A lies if A and Ä are “close”? Applications of the obtained results to integral operators and matrices are also discussed. In addition, we apply our perturbation results to approximate the spectral strip of a Hilbert-Schmidt operator by the spectral strips of finite matrices.
4
Content available An effect of electrokinetics phenomena on nonlinear wave propagation in bubbly liquids
Panahov G., Abbasov E., Bakhtiyarov S., Museibli P.
International Journal of Applied Mechanics and Engineering
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2021
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Vol. 26, no. 3
177--186
EN
A study of nonlinear waves in liquid-gas mixtures with the consideration of internal effects is an important problem of both the fundamental and the applied fluid mechanics. Investigation of nonlinear waves in the gas-liquid mixtures with allowance for internal effects is an important task of both fundamental and applied fluid mechanics. These problems often arise in industrial processes such as oil and gas production, hydrocarbons pipeline transportation, gas-saturated fluids flow in pipelines, etc. In this work, we investigate the effect of the internal electric field on the nonlinear wave propagation in a bubbly liquid. Numerical simulations have been conducted to study the nonlinear waves described by the nonlinear Burgers-Korteweg-de Vries equation. The numerical simulations showed that the electrokinetic processes significantly affect the wave propagation process. The amplitude of the waves gradually decreases when the size of the gas bubble is decreasing and the electrical potential increases. A good agreement of obtained results with our previous predictions is found.
5
Content available Comparison of direct and perturbation approaches to analysis of infinite-dimensional feedback control systems
Grabowski Piotr
International Journal of Applied Mathematics and Computer Science
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2021
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Vol. 31, no. 2
195--218
EN
For general boundary control systems in factor form some necessary and sufficient conditions for generation of an analytic exponentially stable semigroup are proposed in both direct and perturbation forms for comparison. The direct approach is applicable to operators with the numerical range satisfying certain additional conditions. In particular, it applies to operators similar to convexoids and therefore it generalizes previous results known for hyponormal operators. The perturbation result (indirect approach) is derived and formulated as an exponential stability robustness result using the frequence-domain considerations. It is expressed in terms of some estimates of the resolvent growth over the open right complex half-plane and compared with some recent results. The analysis is illustrated in detail with examples of an unloaded and loaded electric RC-transmission line with proportional negative feedback.
6
Content available remote A new acoustic traveltime approximation for attenuating transversely isotropic media
Xiao Han, Wang Deli
Acta Geophysica
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2021
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Vol. 69, no. 5
1611--1621
EN
Attenuation is one of the most important quantities in describing seismic wave propagation, which is also anisotropic because of the dispersion relationship between the seismic wave and the symmetry direction. Transverse isotropic media with titled symmetry-axis (TTI) is a widespread approximation of the Earth’s surface. For 2D TTI attenuating media, we frstly use the acoustic assumption to simplify the exact eikonal equation for the complex-valued quasi P-wave traveltime. Then we design a perturbation method to obtain the new approximation by solving the acoustic attenuating eikonal equation of TTI media and use Shanks transform to increase precision. Compared with former studies, the new approximation considers the symmetryaxis angles of the media as a factor, which will improve its robustness. The approximation is tested in several medium to demonstrate its efectiveness. The energy velocity which derived by the steepest-descent method is used to calculate the exact complex-valued traveltime. We test the accuracy of the approximations developed with and without Shanks transform in the following. Finally, we discussed the possibility to apply this approximation to the methods like fast marching methods.
7
Content available Moment Lyapunov exponents and stochastic stability of a thin-walled beam subjected to eccentric axial loads
Janevski G., Kozić P., Pavlović R.
Journal of Theoretical and Applied Mechanics
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2012
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Vol. 50 nr 1
61-83
EN
The Lyapunov exponent and moment Lyapunov exponents of two degrees-of-freedom linear systems subjected to white noise parametric excitation are investigated. The method of regular perturbation is used to determine the explicit asymptotic expressions for these exponents in the presence of small intensity noises. The Lyapunov exponent and moment Lyapunov exponents are important characteristics for determining the almost-sure and moment stability of a stochastic dynamic system. As an example, we study the almost-sure and moment stability of a thinwalled beam subjected to an eccentric stochastic axial load. The validity of the approximate results for moment Lyapunov exponents is checked by the numerical Monte Carlo simulation method for this stochastic system.
PL
W artykule zbadano wykładniki Lapunowa i momentowe wykładniki Lapunowa układów o dwóch stopniach swobody poddanych parametrycznemu wymuszeniu białym szumem. Zastosowano regularną metodę perturbacyjną do wyznaczenia jawnych wyrażeń na te wykładniki w obecności szumów o małej intensywności. Wykładniki Lapunowa i momentowe wykładniki Lapunowa są ważnymi wielkościami w określaniu prawie pewnej i momentowej stateczności stochastycznej układu dynamicznego. Jako przykład rozważono cienkościenną belkę poddaną mimośrodowemu obciążeniu osiowemu o charakterze losowym. Poprawność otrzymanych wyników przybliżenia momentowych wykładników Lapunowa sprawdzono w drodze symulacji numerycznej przy wykorzystaniu metody Monte Carlo.
8
Content available remote Ecological status of shallow Lake Gorbacz (NE Poland) in its final stage before drying up
Zieliński P., Ejsmont-Karabin J., Grabowska M., Karpowicz M.
Oceanological and Hydrobiological Studies
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2011
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Vol. 40, No.2
1-12
EN
The article assesses the ecological status of shallow Gorbacz Lake (NE Poland) in the last stage before complete drying up. For last few years hydrological regime of the lake catchment has been changed dramatically which was caused by functioning nearby peat mine and longer autumn drought periods for following years. Progressing macrophytes succession leaded complete emergent macrophytes overgrowth of the lake beginning from 2000. The analyses include records of previous samples and data for morphology, water quality, phytoplankton, zooplankton and macrophytes. The trophic status of Gorbacz Lake was verified compare to the previous studies. The results indicate that even with minimum amount of water Gorbacz Lake itself still keeps its dystrophic character with increasing of water color and of DOC, biogenic substances, chlorophyll a concentrations. Humic State Index (HSI) and hydrochemical dystrophy index (HDI) confirm the dystrophic status of the lake with values 71.3 and 76.2 respectively. Both typical phytoplankton representatives of eutrophic and dystrophic waters were recorded. Very high diversity of desmids in the telmatoplankton, indicates the observed process of shallowing in the reservoir. Planktonic crustacean fauna was represented by small filtrators. Rotifera community was strongly dominated by Trichocerca simonei. The article concludes with the main causes of the observed changes and some future remarks for the lake state.
9
Content available A computer code for eliminating secularity in perturbed systems
Hien T. D.
Pomiary Automatyka Kontrola
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2009
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R. 55, nr 6
385-388
EN
In the paper an efficient algorithm is formulated to eliminate inherent secular effects in solving engineering problems by the perturbation technology. Basing upon the modified data-window concept, a computer procedure written in Fortran is worked out in the standard form and can be applied to deal with a large class of nonlinear and/or stochastic engineering systems of dynamics, control, identification and optimization. An illustrating numerical example related to a structural dynamics system with random parameters is presented.
PL
W pracy sformułowano skuteczny algorytm wyeliminowania efektów sekularnych, swoistych w rozwiązywaniu zagadnień inżynierskich drogą perturbacyjną. Bazując na zmodyfikowanym pojęciu okien-danych, opracowano w języku Fortran podprogram komputerowy. Będący w standardowej formie, kod ten może być stosowany w szerokiej klasie nieliniowych lub/i stochastycznych układów dynamiki, kontroli, identyfikacji czy optymalizacji. Przedstawiono ilustrujący przykład dotyczący dynamiki konstrukcyjnego układu z parametrami losowymi.
10
Content available remote Kinetic determination of gibberellic acid applying the BZ oscillating chemical system
Dong Y.
Chemia Analityczna
|
2006
|
Vol. 51, No. 3
447-452
EN
A new analytical method for the determination of gibberellic acid (GA) has been proposed. It is based on the perturbation effect caused by different amounts of GA on the BZ chemical oscillating system: the Mn(II)-catalysed reaction between L-serine, potassium bromate. and malonic acid in acidic medium. The method utilises a linear relationship between the change in the oscillating period and GA concentration. Such a procedure has been used in this work for the first time. The obtained calibration curve was linear in GA concentration range 1.0 x 10 -8-1.0 10 -6 mol L-1,with the regression coefficient of 0.9998.
PL
Zaproponowano nowąanalitycznąmetodę oznaczania kwasu gibberellowego (GA). Metoda jest oparta na wpływie różnych zawartości GA na chemiczny system oscylacyjny BZ, w którym reakcja między L-seryną, bromianem potasu i kwasem malonowym, zachodząca w środowisku kwaśnym, jest katalizowana przez Mn(II). Opracowana metoda wykorzystuje liniową zależność między okresem oscylacji i stężeniem GA. Takie podejście zostało zastosowane po raz pierwszy w tej pracy. Krzywa kalibrowania była liniowa w zakresie stężeń 1.0 x 10 -8-1.0 10 -6 mol L-1 i miała współczynnik korelacji - 0,9998.
11
Zastosowania metody perturbacji do oszacowania wartości własnych układów dynamicznych o parametrach niepewnych
Skrzypczyk J., Liszka T.
Zeszyty Naukowe Katedry Mechaniki Stosowanej / Politechnika Śląska
|
2004
|
z. 23
369-374
PL
Metoda perturbacji pozwala na szybkie oszacowanie wartości własnych w układach poddanych zaburzeniom. Uogólniając tą metodę na liczby przedziałowe można wykorzystać ją do oszacowania wszystkich wartości własnych przedziałowego zadania własnego [A]x=Alfa[B]x a także zadania własnego drugiego stopnia Alfa2[A]x + Alfa[B]x+[C]x = 0. W teorii konstrukcji tą metodę możemy wykorzystać do oszacowania częstości drgań własnych wielowymiarowych układów dynamicznych o parametrach niepewnych oraz częstości drgań swobodnych w układach z tłumieniem.
EN
Method of perturbation makes possible quick estimation of eigenvalues of systems imposed on a perturbations. Extension of this method over interval numbers gives possibility to estimate all eigenvalues of interval generalized eigenvalue problem [A]x=Alpha[B]x end second degree eigenvalue problem Alpha2[A]x +Alpha[B]x + [C]x = 0, In theory of structures this method can be used for eigenfrequency estimation of multidimensional dynamic systems with interval parameters end frequency of free vibration in systems with damping.
12
Metody perturbacyjne - nowa arytmetyka
Skrzypczyk J.
Zeszyty Naukowe Katedry Mechaniki Stosowanej / Politechnika Śląska
|
2004
|
z. 23
363-368
PL
Celem pracy jest przedstawienie systemu algebraicznego ze specjalnie zdefiniowanymi operacjami dodawania i mnożenia, które czynią rozwiązywanie problemów perturbacyjnych tak prostymi, jak rozwiązywanie zwykłych, klasycznych zadań matematyki stosowanej, fizyki teoretycznej i techniki. Nie są przy tym wymagane dodatkowe przekształcenia analityczne.
EN
The aim of the paper is to present a new algebraic system with specifically defined addition and multiplication operations. The new numbers called perturbation numbers are introduced. It's proved that the new algebraic system is imbedded into the system of real numbers. Some additional properties as subtraction, inversion and division are presented too. Some elementary formulations of matrices and vectors of new numbers are introduced, as well as some basic properties of perturbation matrices, inverse matrices and solution properties of linear equations in the new algebraic system of perturbation elements. Classical perturbation problems can be solved in the new algebraic system as easy as usual problems of applied mathematics, theoretical physics and techniques. Additional analytical transformations are not required.
13
Content available remote On some basic finite difference inequalities
Pachpatte B. G.
Fasciculi Mathematici
|
2004
|
Nr 34
65-71
EN
In this paper we establish some basic finite difference inequalities which can be used as tools in the study of qualitative properties of the solutions of finite difference equations and numerical analysis.
14
Content available Elasto-plastic limit loads of cylinder-cone configurations
Dinkler D., Knoke O.
Journal of Theoretical and Applied Mechanics
|
2003
|
Vol. 41 nr 3
443-457
EN
The paper presents a procedure for computation of the limit loads of imperfection-sensitive shells including plastic deformations. On the basis of strain energy of shells, the worst case scenario for critical perturbations at fixed load levels is investigated. Limit loads of cylindrical and conical shells under combined actions are compared to European design rules. The concept is applied to more general buckling cases of combined shell structures.
PL
W pracy przedstawiono metodę wyznaczania obciążeń granicznych dla powłok wrażliwych na niedoskonałości, z uwzględnieniem odkształceń plastycznych. Opierajac się na energii odksztalcenia powłok rozważono przypadek najgorszego scenariusza krytycznych perturbacji przy ustalonych poziomach obciążeń. Wartości obciążeń granicznych dla powłók cylindrycznych i stożkowych porównano z przyjętymi w Europie metodami projektowania. Koncepcja została zastosowana do analizy bardziej ogólnych przypadków utraty stateczności konstrukcji powłokowych.
15
Content available Two-Dimensional Automatic Control Modeling of a Posture Control System
Park K. S., Kim U. H.
International Journal of Occupational Safety and Ergonomics
|
1998
|
Vol. 4, No. 4
485--498
EN
A posture control model has been developed on the basis of the 2-dimensional feedback control theory. Human postural characteristics were investigated in 5 healthy participants. Tests were performed with eyes open and eyes closed. After 5 s of quiet standing, each participant was unexpectedly pulled forward by 30 mm at his pelvis height and then released. Postural sway was measured over 20 s at a rate of 100 per second. Transfer functions to represent the posture control characteristic were identified by the least squares' method. These showed good results of the model's fitness, predictability, and stability. The response of the eyes-closed condition to perturbation is more oscillatory than that of the eyes-open condition. It seems that the model identified could be applicable to ergonomics, sports, or clinical situations.
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