• Kyungpook Mathematical Journal
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• v.58 no.3
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• pp.533-546
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• 2018

The object of this work is to study the existence of solutions for a class of p(x)-Kirchhoff type problem under no-flux boundary conditions with dependence on the gradient. We establish our results by using the degree theory for operators of ($S_+$) type in the framework of variable exponent Sobolev spaces.

• Journal of the Korea Institute of Information and Communication Engineering
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• v.8 no.7
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• pp.1410-1417
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• 2004

In this paper, we propose that the chaotic behavior analysis in the chaotic mobile robot embedding Arnold, equation, Chua's equation and hyper-chaos equation. In order to analysis of chaotic behavior in the mobile robot, we apply not only qualitative analysis such as time-series, embedding phase plane, but also quantitative analysis such as Lyapunov exponent in the mobile robot with obstacle.

• Proceedings of the Korean Institute of Electrical and Electronic Material Engineers Conference
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• 1999.05a
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• pp.57-61
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• 1999

Electrical stress makes insulating materials aged finally resulting in the dielectric failure. It becomes more and more important to recognize the degree of aging and the life time of the insulating materials since it is directly concerned with the reliability of the insulation system. In this paper, the life time of the Cross-linked Polyethylene(XLPE), the insulation layer in the 154kV-grade power cable, is expected and calculated using statistical and mathematical methods. The simulated results are compared with experimental ones and the life exponent of the material is obtained.

• Journal of KIEE
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• v.10 no.1
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• pp.7-15
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• 2000

Source separation is a statistical method, the goal of which is to separate the linear instantaneous mixtures of statistically independent sources without resorting to any prior knowledge. This paper addresses a source separation algorithm which is able to separate the mixtures of sub- and super-Gaussian sources. The nonlinear function in the proposed algorithm is derived from the generalized Gaussian distribution that is a set of distributions parameterized by a real positive number (Gaussian exponent). Based on the relationship between the kurtosis and the Gaussian exponent, we present a simple and efficient way of selecting proper nonlinear functions for source separation. Useful behavior of the proposed method is demonstrated by computer simulations.

• Structural Engineering and Mechanics
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• v.52 no.3
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• pp.525-540
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• 2014

The Lyapunov exponent and moment Lyapunov exponents of Hill's equation with frequency and damping coefficient fluctuated by correlated wideband random processes are studied in this paper. The method of stochastic averaging, both the first-order and the second-order, is applied. The averaged $It\hat{o}$ differential equation governing the pth norm is established and the pth moment Lyapunov exponents and Lyapunov exponent are then obtained. This method is applied to the study of the almost-sure and the moment stability of the stationary solution of the thin simply supported beam subjected to time-varying axial compressions and damping which are small intensity correlated stochastic excitations. The validity of the approximate results is checked by the numerical Monte Carlo simulation method for this stochastic system.

• Journal of Mechanical Science and Technology
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• v.18 no.7
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• pp.1246-1257
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• 2004

The objective of this paper is to characterize dynamic pressure traces measured at self-excited combustion instabilities occurring in two combustion systems of different hardware. One system is a model lean premixed gas turbine combustor and the other a fullscale bipropellant liquid rocket thrust chamber. It is commonly observed in both systems that low frequency waves at around 300㎐ are first excited at the onset of combustion instabilities and after a short duration, the instability mode becomes coupled to the resonant acoustic modes of the combustion chamber, the first longitudinal mode for the lean premixed combustor and the first tangential mode for the rocket thrust chamber. Low frequency waves seem to get excited at first since flame shows the higher heat release response on the lower frequency perturbations with the smaller phase differences between heat release and pressure fluctuations. Nonlinear time series analysis of pressure traces reveals that even stable combustion might have chaotic behavior with the positive maximum Lyapunov exponent. Also, pressure fluctuations under combustion instabilities reach a limit cycle or quasi-periodic oscillations at the very similar run conditions, which manifest that a self-excited high frequency instability has strong nonlinear characteristics.

• Proceedings of the Korean Society of Propulsion Engineers Conference
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• 2017.05a
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• pp.508-512
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• 2017

In this study, we carried out the study on the combustion characteristics of HTPB/AP propellants with Al and Zr as fuel metal in order to develop the solid propellant with high burning rate. The major combustion characteristics of propellant were investigated as measuring of the burning rate and pressure exponent, and the HTPB/AP solid propellants were prepared with introducing Butacene as burning rate catalyst for the enhancement of burning rate. The propellant with Al and Zr was demonstrated the improvement of propellant performance and combustion characteristic.

• The Journal of the Korea institute of electronic communication sciences
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• v.8 no.11
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• pp.1691-1696
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• 2013

In this paper, an analysis of behavior is performed in the circular hybrid energy harvesting device. This analysis of behavior is to confirm with or without an existence of nonlinear system because its system is required to produce the more energy. To do this, first of all the phase portrait is reconstructed through Taken's embedding method, and then Poincare map is organized by using phase portrait and finally Lyapunov exponent is analyzed.

• Journal of the Korean Ceramic Society
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• v.35 no.8
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• pp.850-856
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• 1998

The dynaamic fatigue behavior of alumina ceramics was observed at room temperature using four-point bending method. Dynamic fatigue fracture strength was observed as function of down speed and notch length. The crack growth exponent of the specimens was calculated from the fracture strength and lifetime in dynamic fatigue test. After loading the stresses in the range of 0% to 105% compared with the average in-ert strength the value of residual fracture strength was measured for unnotched and 0.5mm notched speci-mens at the 0.001 and 0.0005 mm/min down speed respectively. After the 95% stress of the average inert strength was applied repeatedly the value of rsidual fracture strength was measured for 0.5mm notched specimens at the 0.001 and 0.0005 mm/min down speed respectively. The material constant A was found to be almost the same and not to depend on the loading mode or the down speed for unnotched and notched specimen. The value of fracture strength with time calculated from the constants n and A was in good agreement with the measured value.

• Journal of the Korean Data and Information Science Society
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• v.23 no.3
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• pp.595-604
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• 2012

In this article, we consider chaotic behavior happened in nonsmooth dynamical systems. To quantify such a behavior, a computation of Lyapunov exponents for chaotic orbits of a given nonsmooth dynamical system is focused. The Lyapunov exponent is a very important concept in chaotic theory, because this quantity measures the sensitive dependence on initial conditions in dynamical systems. Therefore, Lyapunov exponents can decide whether an orbit is chaos or not. To measure the sensitive dependence on initial conditions for nonsmooth dynamical systems, the calculation of Lyapunov exponent plays a key role, but in a theoretical point of view or based on the definition of Lyapunov exponents, Lyapunov exponents of nonsmooth orbit could not be calculated easily, because the Jacobian derivative at some point in the orbit may not exists. We use an algorithmic calculation method for computing Lyapunov exponents using time series for a two dimensional piecewise smooth dynamic system.