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1
Content available Perturbation theory, M-essential spectra of 2 x 2 operator matrices and application to transport operators
Jeribi Aref, Moalla Nedra, Yengui Sonia
Journal of Mathematics and Applications
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2021
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Vol. 44
35--55
EN
In this article we give some results on perturbation theory of 2 x 2 block operator matrices on the product of Banach spaces. Furthermore, we investigate their M-essential spectra. Finally, we apply the obtained results to determine the M-essential spectra of two group transport operators with general boundary conditions in the Banach space Lp([-a, a] x [-1, 1]) x Lp([-a, a] x [-1, 1]), p ≥ 1 and a > 0.
2
Content available The stability conditions of the cubic damping Van der Pol-Duffing oscillator using the HPM with the frequency-expansion technology
El-Dib Y. O.
Journal of Applied Mathematics and Computational Mechanics
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2018
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Vol. 17, nr 3
31--44
EN
In this paper, we perform the frequency-expansion formula for the nonlinear cubic damping van der Pol’s equation, and the nonlinear frequency is derived. Stability conditions are performed, for the first time ever, by the nonlinear frequency technology and for the nonlinear oscillator. In terms of the van der Pol’s coefficients the stability conditions have been performed. Further, the stability conditions are performed in the case of the complex damping coefficients. Moreover, the study has been extended to include the influence of a forcing van der Pol’ oscillator. Stability conditions have been derived at each resonance case. Redoing the perturbation theory for the van der Pol oscillator illustrates more of a resonance formulation such as sub-harmonic resonance and super-harmonic resonance. More approximate nonlinear dispersion relations of quartic and quintic forms in the squaring of the extended frequency are derived, respectively.
3
Content available remote The Design of MPPT Controller in Photovoltaic System
Che Y., Zhang W., Li W.
Przegląd Elektrotechniczny
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2013
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R. 89, nr 3b
71--73
EN
In photovoltaic power system, the maximum power point changes under different circumstances, so it is meaningful to track the unique point to provide maximum power for the load. In this paper, we designed the main circuit and control circuit of the maximum power point tracking controller. This controller uses the observation and perturbation method to achieve the maximum power point tracking. At last we tested the efficiency of the controller, the experimental result demonstrates that the system tracks the maximum power point rapidly, works safely and reliably.
PL
W artykule przedstawiono projekt elektronicznego sterownika do śledzenia punktu mocy maksymalnej. Budowę urządzenia oparto na teorii obserwacji i perturbacji. Zawarte wyniki eksperymentalne potwierdzają skuteczność śledzenia i szybkość reakcji na zmiany w systemie PV.
4
Content available Homotopy perturbation method in the heat conduction problems
Hetmaniok E., Nowak I., Słota D., Wituła R.
Zeszyty Naukowe. Matematyka Stosowana / Politechnika Śląska
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2011
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z. 1
109--120
EN
In this paper an application of the homotopy perturbation method for solving the steady state and unsteady state heat conduction problem is presented.
PL
W artykule przedstawiono zastosowanie homotopijnej metody perturbacyjnej do rozwiązania zagadnień ustalonego oraz nieustalonego przewodzenia ciepła.
5
Ocena wpływu perturbacji parametrów zadania brzegowego na rozwiązanie równania Helmholtza
Winkler A.
Zeszyty Naukowe. Budownictwo / Politechnika Śląska
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2005
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z. 104
395-402
PL
Niniejszy artykuł jest prezentacją nowego systemu algebraicznego oraz jego aplikacji do teorii perturbacji cząstkowych równań różniczkowych. Nowa metoda zastosowania została do rozwiązania zadania brzegowego dla równania Helmholtza. Wprowadzone zostały zaburzenia parametrów równania oraz warunków początkowych i brzegowych. W nowym systemie klasyczne problemy perturbacyjne opisywane równaniami różniczkowymi mogą być rozwiązane w sposób tak prosty jak zwykłe równania różniczkowe stosowane w akustyce, matematyce czy technice. Nie są konieczne dodatkowe przekształcenia analityczne.
EN
This paper presents applications of the new algebraic system in the theory of perturbed partial differential equations. New method is applied to solve boundary problems for Helmholtz equation. Perturbation of equation parameters as well as for initial and boundary conditions are considered. Classical perturbation problems described by differential equations are solved in the new algebraic system as easy as usual differential problems of applied acoustics, mathematics and techniques. Additional analytical transformations are not applied acoustics, mathematics and techniques. Additional analytical transformations are not required.
6
The application of the finite element method in diagnostics of electrical drives
Fiser R., Ferkolj S.
Journal of Technical Physics
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2002
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Vol. 43, no 4
399-403
EN
The paper presents the application of the finite element method for predicting the performance of induction motor having asymmetry of stator and/or rotor winding due to the different combination and propagation of faults gained during heavy-duty operation. Quantities like magnetic vector potential, flux density, force components, rotor and stator currents, mutual and leakage inductance are determined very precisely. The detailed insight in magnetic field distribution of a squirrel cage induction motor, forms the basis for further evaluation of its operational behaviour. Increasing anomaly in magnetic field distribution due to the increasing stage of faults propagation results in a degradation of steady-state and dynamic performance of the induction motor and can be evaluated with computer simulation eliminating expensive and time-consuming laboratory tests.
7
Comparison of thermodynamic functions calculated by means of various methods
Avsec J., Marcic M.
Journal of Technical Physics
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2002
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Vol. 43, no 3
309-321
EN
The paper deals with the Lennard-Jones fluid and presents the mathematical model of computating thermodynamic functions of state in the liquid and gas domain by means of statistical thermodynamics. To calculate the thermodynamic properties of a real fluid, we used the Johnson-Zollweg-Gubbins model based on the modified Benedict-Webb-Rubin equation of state, the Chunxi-Yigui-Jiufang equation of state based on the simple perturbation theory, and the complex Tang-Tong-Lu model based on the solution of the Ornstein-Zernike equation obtained by means of the perturbation theory. The analytical results are compared with the thermodynamical data, and with the results obtained from classical thermodynamics.
8
Gauge symmetry in models of high temperature superconductors
Przeszowski J.
Journal of Technical Physics
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2001
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Vol. 42, no 4
389-396
EN
Gauge symmetry which appears in the slave-mode approach to the t-J model of high temperature superconductivity is presented. The mean field analysis of these microscopic models lead to the continuum gauge field systems with infinitely strong coupling constant. The viability of the perturbative calculations (with finite coupling constant) are illustrated with a particularly simple field theory model. Exact resummation of the perturbation series is discussed for the Heisenberg model of strongly interacting spins in 1 + 1 dimensions which is approximated by the Schwinger model.
9
Calculation of thermophysical properties for solids with application of statistical thermodynamics
Avsec J., Marcic M.
Journal of Technical Physics
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2001
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Vol. 42, no 3
327-336
EN
The paper deals with a mathematical model for calculation of the thermodynamic properties of solids. The mathematical model, based upon statistical thermodynamics, is designed to assess the impact of atom vibration, electron excitation and the effect of intermolecular energy between atoms in a crystal. To calculate the configuration integral, the perturbation theory was used with the Van der Waals model as perturbation. The temperature-variable coefficients were introduced into the model presented in this paper. Finally, the model was compared with the experimental data proving a good matching.
10
Calculation of thermodynamical properties in liquid-gas region
Avsec J., Marcic M.
Journal of Technical Physics
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2000
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Vol. 41, no 3
241-252
EN
The paper presents the mathematical model used for the computation of thermodynamic functions of state in the liquid and gas domain, with the aid of statistical thermodynamics of Lennard-Jones fluid. To calculate the thermodynamic properties of a real fluid, we used the Johnson-Zollweg-Gubbins model based on the modified Benedict-Webb-Rubin equation of state, the Chunxi-Yigui-Jiufang equation of state based on the simple perturbation theory, and the complex Tang-Tong-Lu model based on the solution of the Ornstein-Zernike equation obtained by means of the perturbation theory. The analytical results are compared with the thermodynamical data, and with the results obtained from classical thermodynamics. \\@ng\
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