• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제17권3호
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• pp.197-207
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• 2013

The Cahn-Hilliard equation was proposed as a phenomenological model for describing the process of phase separation of a binary alloy. The equation has been applied to many physical applications such as amorphological instability caused by elastic non-equilibrium, image inpainting, two- and three-phase fluid flow, phase separation, flow visualization and the formation of the quantum dots. To solve the Cahn-Hillard equation, many numerical methods have been proposed such as the explicit Euler's, the implicit Euler's, the Crank-Nicolson, the semi-implicit Euler's, the linearly stabilized splitting and the non-linearly stabilized splitting schemes. In this paper, we investigate each scheme in finite-difference schemes by comparing their performances, especially stability and efficiency. Except the explicit Euler's method, we use the fast solver which is called a multigrid method. Our numerical investigation shows that the linearly stabilized stabilized splitting scheme is not unconditionally gradient stable in time unlike the known result. And the Crank-Nicolson scheme is accurate but unstable in time, whereas the non-linearly stabilized splitting scheme has advantage over other schemes on the time step restriction.

• 제어로봇시스템학회:학술대회논문집
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• 제어로봇시스템학회 1989년도 한국자동제어학술회의논문집; Seoul, Korea; 27-28 Oct. 1989
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• pp.901-906
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• 1989

A robust stability problem for time delay systems is discussed by using a property of Lyapunov type operator equation. We propose a method to check the robust stability against the parameter perturbations occurring in both lumped parameter part and distributed delay element.

• 제어로봇시스템학회:학술대회논문집
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• 제어로봇시스템학회 2005년도 ICCAS
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• pp.22-25
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• 2005

In the paper, algorithms for disturbance observers are newly presented in the time-domain. Attention is paid to observing a ramp disturbance by introducing an integral term to the output equation of a constant disturbance observer. In order to reduce the sensitivity to the measurement noise, the disturbance observer is combined with the state observer. It will be shown that the estimation dynamics can be arbitrarily chosen by assigning the eigenvalues of a characteristic equation. Also, we provide the analysis of observer behaviors subject to non-ramp-style disturbances. Finally, we propose the generalized disturbance observer that accurately estimates disturbances of higher order in time series expansion.

• Nonlinear Functional Analysis and Applications
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• 제26권1호
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• pp.157-164
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• 2021

Recently we investigated a type of Hyers-Ulam stability of the Schrödinger equation with the symmetric parabolic wall potential that efficiently describes the quantum harmonic oscillations. In this paper we study a type of Hyers-Ulam stability of the Schrödinger equation when the potential barrier is a quartic wall in the solid crystal models.

• 대한전기학회:학술대회논문집
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• 대한전기학회 2003년도 하계학술대회 논문집 D
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• pp.2082-2084
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• 2003

A practical real-time LOS rate estimator is proposed to handle the time-varying measurement noise statistics. To calculate the optimal Kalman gain, the algebraic transformation method is taken into account. By using the algebraic transformation, the differential algebraic Riccati equation(DARE) regarding estimation error covariance is replaced by the simple algebraic Riccati equation(ARE). The proposed LOS estimation filter gain is only a function of relative range. Consequently, the proposed method is computationally very efficient and suitable for embedded environment.

• Bulletin of the Korean Chemical Society
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• 제27권10호
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• pp.1659-1663
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• 2006

A many-body master equation is constructed by incorporating stochastic terms responsible for chemical reactions into the many-body Smoluchowski equation. Two forms of Langevin-type of memory equations describing the time evolution of dynamical variables under the influence of time-independent perturbation with an arbitrary intensity are derived. One form is convenient in obtaining the dynamics approaching the steady-state attained by the perturbation and the other in describing the fluctuation dynamics at the steady-state and consequently in obtaining the linear response of the system at the steady-state to time-dependent perturbation. In both cases, the kinetics of statistical averages of variables is found to be obtained by analyzing the dynamics of time-correlation functions of the variables.

• Structural Engineering and Mechanics
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• 제54권4호
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• pp.809-827
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• 2015

In this paper, seismic energy response of inelastic steel structures under earthquake excitations is investigated. For this purpose, a numerical procedure based on nonlinear dynamic analysis is developed by considering material, geometric and connection nonlinearities. Material nonlinearity is modeled by the inversion of Ramberg-Osgood equation. Nonlinearity caused by the interaction between the axial force and bending moment is also defined considering stability functions, while the geometric nonlinearity caused by axial forces is described using geometric stiffness matrix. Cyclic behaviour of steel connections is taken into account by employing independent hardening model. Dynamic equation of motion is solved by Newmark's constant acceleration method in the time history domain. Energy response analysis of space frames is performed by using this proposed numerical method. Finally, for the first time, the distribution of the different energy types versus time at the duration of the earthquake ground motion is obtained where in addition error analysis for the numerical solutions is carried out and plotted depending on the relative error calculated as a function of energy balance versus time.

• 대한가정학회지
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• 제41권7호
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• pp.59-71
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• 2003

Koreans were started moving to Yunhaju in Russia for escaping from tyrannical rule and famine in 1860's in Korea. Social and political situation of Russia were made it very hard to get to know about Korean's life there so far. But it was known that Korean Diaspora has been kept traditional way of living in without contacts between Korea for 140 years. This study examined the dwellings of Korean Diaspora in Yunhaju through reviewing related documents and records firstly and had a time to visit places which Koreans lived since 1860's for example Posyet(equation omitted), Suifen(equation omitted), Ussuriisk(equation omitted), Vladivostok(equation omitted), Partizansk(equation omitted) and took interviews with Koreans who lived there pre 1930's. Results of research were as following : 1) A first place to settle down for Koreans in Yunhaju was Posye(equation omitted) and scattered as time goes by far away from there. 2) Koreans were helping each other for living and they had their own self managing organizations in village there. 3) The villages which was made in Yunhaju by Koreans in the beginning were similar to traditional ones in Korea. 4) It was verified that dwellings which was built by Koreans in Yunhaju were similar to ones in north area in Korea. At that time lots of Korean Diaspora came from north part and they kept their own traditional way of building houses there for a long time. 5) Korean Diaspora have been kept traditional heating system ‘Ondol’ in their various types of houses until now in Yunhaju. Moreover, it is known that Russians prefer to set ‘Ondol’ in their houses recently as a very special and expensive heating system. This study would be a very good opportunity to standing out Korean history of housing in Yunhaju as well as evaluating their identification as Koreans. For this, it is needed to take more deep research in specific areas which could see more various types of housing and could compare ones between two countries.

• 대한수학회보
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• 제60권6호
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• pp.1673-1685
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• 2023

Inspired by Hongjie Dong and Qi S. Zhang's article [3], we find that the analyticity in time for a smooth solution of the heat equation with exponential quadratic growth in the space variable can be extended to any complete noncompact Riemannian manifolds with Bakry-Émery Ricci curvature bounded below and the potential function being of at most quadratic growth. Therefore, our result holds on all gradient Ricci solitons. As a corollary, we give a necessary and sufficient condition on the solvability of the backward heat equation in a class of functions with the similar growth condition. In addition, we also consider the solution in certain L^p spaces with p ∈ [2, +∞) and prove its analyticity with respect to time.

• 대한조선학회논문집
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• 제43권1호
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• pp.22-31
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• 2006

Recent studies have shown that the short time solution of the equation of motion for the rolling of ships is important in deciding the possibility of capsize of ships due to the excessive heel. Since most of known solutions for nonlinear equations of motion are long time or steady periodic solutions, here a simple way is described to get the short time solutions of the Duffing equation, which was chosen for deriving a criterion for the capsize of the ship. With the small external rolling moment, we first assume the state of the small damping and near resonance. Then, for cases when the frequency of the external moment is higher than the resonant one, an inequality was derived as a criterion for the capsize. This gives the range of the initial condition and the magnitude of the external moment which should be avoided for a ship to be safe from capsize. Furthermore, from the linearized equation, it is also shown that a simple and self-explanatory solution can be obtained consistent with that for the case of no damping, which yields the well-known linear growth with time.