• Title/Summary/Keyword: oscillatory solutions

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Optimum Design Methodology of the Damped Oscillatory Impulse Current Generator Considering a Nonlinear Load (비선형 부하를 고려한 감쇠 진동형 임펄스 전류발생기의 설계 기법)

  • Chang, Sug-Hun;Lee, Jae-Bok;Shenderey, S.V.;Myung, Sung-Ho;Cho, Yuen-Gue
    • The Transactions of The Korean Institute of Electrical Engineers
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    • v.57 no.12
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    • pp.2255-2262
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    • 2008
  • This paper presents a design parameter calculation methodology and its realization to construction for the damped oscillatory impulse current generator(ICG) modelled as damping factor $\alpha$. Matlab internal functions, "fzero" and "polyfit" are applied to find a which are solutions of second order nonlinear equation related with three wave parameters $T_{1},T_{2}$ and $I_{os}$. The calculation results for standard impulse current waveforms such as 4/10${\mu}s$, 8/20${\mu}s$ and 30/80${\mu}s$ show very good accuracy and this results make it possible to extend to generalization in the design of damped oscillatory lCG with any capacitor. 8/20${\mu}s$ ICG based on the calculated design circuit parameters is fabricated in consideration of the nonlinear load(MOV) variation. Comparisons of the tested waveforms with the designed estimation show error within 10% for the waveform tolerance recommended in IEC 60060-1 and IEEE std. C62.45.

Electromagnetic Field Analysis and Measurements of Cylindrical Linear Oscillatory Actuator using Transfer Relations Theorem (전자기 전달관계를 이용한 원통형 직선 왕복구동 액추에이터의 전자기 특성 해석 및 실험)

  • Jang, Seok-Myeong;Kim, Hyun-Kyu;Choi, Jang-Young;Lee, Sung-Ho
    • Proceedings of the KIEE Conference
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    • 2008.04c
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    • pp.89-91
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    • 2008
  • This paper deals with the thrust calculations and the measurements of a cylindrical Linear Oscillatory Actuator (LOA) sing Transfer Relations Theorem (TRT), namely, Melcher's methodology. Using transfer relations derived in terms of a magnetic vector potential and a two-dimensional (2-d) cylindrical coordinate system, this paper derives analytical solutions for the magnetic vector potential, magnetic fields due to Permanent Magnets (PMs) and stator winding currents and the thrust. The analytical results are validated by non-linear Finite Element (FE) analyses. In particular, test results such as thrust and back-emf measurements are given to confirm the analysis.

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ADAPTIVE MESH REFINEMENT FOR WEIGHTED ESSENTIALLY NON-OSCILLATORY SCHEMES

  • Yoon, Dae-Ki;Kim, Hong-Joong;Hwang, Woon-Jae
    • Bulletin of the Korean Mathematical Society
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    • v.45 no.4
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    • pp.781-795
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    • 2008
  • In this paper, we describe the application procedure of the adaptive mesh refinement (AMR) for the weighted essentially non-oscillatory schemes (WENO), and observe the effects of the derived algorithm when problems have piecewise smooth solutions containing discontinuities. We find numerically that the dissipation of the WENO scheme can be lessened by the implementation of AMR while the accuracy is maintained. We deduce from the experiments that the AMR-implemented WENO scheme captures shocks more efficiently than the WENO method using uniform grids.

Bifurcation analysis of budding yeast cell cycle

  • Nguyen, Cuong;Yoon, Chang-No;Kim, Hak-Yong;Han, Seung-Kee
    • Proceedings of the Korean Society for Bioinformatics Conference
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    • 2004.11a
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    • pp.50-56
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    • 2004
  • Bifurcation analysis of cell cycle regulation in the budding yeast is performed basedon the mathematical model by Chen et al [Molecular biology of cell, 11:369-391, 2000]. On the bifurcation diagram, locations of both stable and unstable solutions of the nonlinear differential equations are presented by taking the mass of cell as a controlparameter. Based on the bifurcation diagram, dynamic mechanism underlying the 'start' transition, initiation of a new round of cell cycle, and the 'finish' transition, completion of cell cycle and returning back to the initial state, is discussed: the 'start' transition is a transition from a stable fixed solution for a small mass and to an oscillatory state for a large mass, and the 'finish' transition is a switching back to the stable fixed solution from the oscillatory state. To understand the role of the genes during the cell cycle regulation, bifurcation diagrams for the mutants are compared with that of the wild type.

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OSCILLATION OF SECOND ORDER UNSTABLE NEUTRAL DIFFERENCE EQUATIONS WITH CONTINUOUS ARGUMENTS

  • TIAN YU;ZHANG ZHENGUO;GE WEIGAO
    • Journal of applied mathematics & informatics
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    • v.20 no.1_2
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    • pp.355-367
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    • 2006
  • In this paper, we consider the oscillation second order unstable neutral difference equations with continuous arguments $\Delta^2_{/tau}(\chi(t)-p\chi(t-\sigma))=f(t,\chi(g(t)))$ and obtain some criteria for the bounded solutions of this equation to be oscillatory.

Nonlinear vibration of oscillatory systems using semi-analytical approach

  • Bayat, Mahmoud;Bayat, Mahdi;Pakar, Iman
    • Structural Engineering and Mechanics
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    • v.65 no.4
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    • pp.409-413
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    • 2018
  • In this paper, He's Variational Approach (VA) is used to solve high nonlinear vibration equations. The proposed approach leads us to high accurate solution compared with other numerical methods. It has been established that this method works very well for whole range of initial amplitudes. The method is sufficient for both linear and nonlinear engineering problems. The accuracy of this method is shown graphically and the results tabulated and results compared with numerical solutions.

OSCILLATION CRITERIA FOR SECOND-ORDER NONLINEAR DIFFERENCE EQUATIONS WITH 'SUMMATION SMALL' COEFFICIENT

  • KANG, GUOLIAN
    • Bulletin of the Korean Mathematical Society
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    • v.42 no.2
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    • pp.245-256
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    • 2005
  • We consider the second-order nonlinear difference equation (1) $$\Delta(a_nh(x_{n+1}){\Delta}x_n)+p_{n+1}f(x_{n+1})=0,\;n{\geq}n_0$$ where ${a_n},\;{p_n}$ are sequences of integers with $a_n\;>\;0,\;\{P_n\}$ is a real sequence without any restriction on its sign. hand fare real-valued functions. We obtain some necessary conditions for (1) existing nonoscillatory solutions and sufficient conditions for (1) being oscillatory.

BOUNDED OSCILLATION OF SECOND ORDER UNSTABLE NEUTRAL TYPE DIFFERENCE EQUATIONS

  • Thandapani, E.;Arul, R.;Raja, P.S.
    • Journal of applied mathematics & informatics
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    • v.16 no.1_2
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    • pp.79-90
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    • 2004
  • In this paper the authors present sufficient conditions for all bounded solutions of the second order neutral difference equation ${\Delta}^2(y_n\;-\;py_{n-{\kappa}})\;-\;q_nf(y_{n-e})\;=\;0,\;n\;{\in}\;N$ to be oscillatory. Examples are provided to illustrate the results.