• Korean Journal of Mathematics
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• 제19권2호
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• pp.191-203
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• 2011

The interface between fluids of different densities is unstable under acceleration by a shock wave. A previous small amplitude linear theory for the compressible Euler equation failed to provide a quantitatively correct prediction for the growth rate of the unstable interface. In this paper, to include dominant nonlinear effects in a large amplitude regime, we present high-order perturbation equations of the Euler equation, and boundary conditions for the contact interface and shock waves.

• 전기의세계
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• 제20권4호
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• pp.12-16
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• 1971

The electrical detector and computer systems for traffic flow and speed measurement are demonstrated in this paper. For the best traffic control optimization, linear and non-linear equations in the transition state are dealing with the perturbation of the linear car-following. In the conclusions, we construct a realizable system for the central automatic traffic control with a computer. Furthermore, fixed periodic switching system by manual with the automatic traffic control system is recommended for emergency perturbation.

• 소음진동
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• 제6권4호
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• pp.469-474
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• 1996

Dynamic stability of an axially oscillating cantilever beam is investigated in this paper. The equations of motion are derived and transformed into non-dimensional ones. The equations include harmonically oscillating parameters which originate from the motion-induced stiffness variation. Using the equations, the multiple scale perturbation method is employed to obtain a stability diagram. The stability diagram shows that relatively large unstable regions exist around the frequencies of the first bending natural frequency, twice the first bending natural frequency, and twice the second bending natural frequency. The validity of the diagram is proved by direct numerical simulations of the dynamic system.

• 한국원자력학회:학술대회논문집
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• 한국원자력학회 1998년도 춘계학술발표회논문집(2)
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• pp.160-165
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• 1998

Under the heavy irradiation, when the production and the recombination of interstitials and vacancies are included, the diffusion equations become nonlinear. An effort has been made to arrange an appropriated transformation of these nonlinear differential equations to soluble Poisson's equations, so that analytical solutions for simultaneously calculating the concentrations of interstitials and vacancies in the angular dependent Cottrell's potential of the edge dislocation have been derived from the well-known Green's theorem and perturbation theory.

• Nuclear Engineering and Technology
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• 제31권2호
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• pp.151-156
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• 1999

Under the heavy irradiation of crystalline materials when the production and the recombination of interstitials and vacancies are included, the diffusion equations become nonlinear. An effort has been made to arrange an appropriate transformation of these nonlinear differential equations to more solvable Poisson's equations, finally analytical solutions for simultaneously calculating the concentrations of interstitials and vacancies in the angular dependent Cottrell's potential of the edge dislocation have been derived from the well-known Green's theorem and perturbation theory.

• Journal of applied mathematics & informatics
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• 제31권1_2호
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• pp.131-145
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• 2013

In this paper, we present an initial value technique for solving singularly perturbed differential difference equations with a boundary layer at one end point. Taylor's series is used to tackle the terms containing shift provided the shift is of small order of singular perturbation parameter and obtained a singularly perturbed boundary value problem. This singularly perturbed boundary value problem is replaced by a pair of initial value problems. Classical fourth order Runge-Kutta method is used to solve these initial value problems. The effect of small shift on the boundary layer solution in both the cases, i.e., the boundary layer on the left side as well as the right side is discussed by considering numerical experiments. Several numerical examples are solved to demonstate the applicability of the method.

• 한국대기환경학회지
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• 제16권5호
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• pp.539-544
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• 2000

A simple analytic model is proposed here to analyze the concentration deficit field caused by a large area of vegetated area. With non-dimensional deposition velocity chosen as small parameter, the regular perturbation method is exploited to derive the mass balance equation and the dynamic equations for the concentration deficit field, Analytic solutions to those equations are obtained in a closed form for several cases of interest, assuming that the concentration field is stationary and the plume can be nicely approximated as Gaussian for a point source. The results suggest that quite a negligible fraction (less than 1%) of the gaseous air pollutants emitted into the air is removed by the vegetated area of which width is 4 km in wind-wise direction, the typical dimension of the Restricted Development Zones around the metropolitan regions in South Korea.

• 한국수자원학회논문집
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• 제34권6호
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• pp.651-657
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• 2001

본 논문에서는 단파의 파군이 계단형 지형을 통과할 때 발생하는 2차 장파를 이론적으로 연구하였다. 먼저, 수심 변화에 의한 단파의 회절을 해석하였으며, 다변수 섭동법을 이용하여 2차 장파의 지배방정식을 유도하였다. 2차 장파 방정식을 해석하여 서로 다른 속도로 진행하는 자유장파와 구속장파가 발생함을 보였다.

• 대한기계학회논문집A
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• 제24권5호
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• pp.1093-1102
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• 2000

Dynamic behaviors are analyzed for an automatic ball balancer with double races which is a device to reduce eccentricity of rotors. Equations of motion are derived by using the polar coordinate sys tem instead of the rectangular coordinate system which is used in other previous researches. To analyze the stability around equilibrium positions, the perturbation method is used. On the other hand, the time responses are computed from the nonlinear equations of motion by using a time integration method.

• 한국지진공학회:학술대회논문집
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• 한국지진공학회 2001년도 추계 학술발표회 논문집 Proceedings of EESK Conference-Fall 2001
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• pp.243-250
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• 2001

Industrial machines are sometimes exposed to the danger of earthquake. In the design of a mechanical system, this factor should be accounted for from the viewpoint of reliability. A method to analyze a complex nonlinear structure system under random excitation is proposed. First, the actual random excitation, such as earthquake, is approximated to the corresponding Gaussian process far the statistical analysis. The modal equations of overall system are expanded sequentially. Then, the perturbed equations are synthesized into the overall system and solved in probabilistic way. Several statistical properties of a random process that are of interest in random vibration applications are reviewed in accordance with nonlinear stochastic problem. The obtained statistical properties of the nonlinear random vibration are evaluated in each substructure. Comparing with the results of the numerical simulation proved the efficiency of the proposed method.