• 한국수자원학회논문집
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• 제33권2호
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• pp.195-205
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• 2000

도달시간 산정에 있어 고려되어야 할 요소에는 유역형상과 흐름상태, 유출특성 등이 있다. 한편 Singh(1976)은 지표면흐름을 Kinematic Wave 이론으로 해석하였으며 유역형상을 평면형상과 수렴형상, 발산형상으로 분류하여 유역형상에 따른 도달시간 산정식을 제시하였다. 본 논문에서는 Singh이 제시한 평면형상에서의 도달시간 산정식에 기초하여 불투수 지표면 유출에서의 도달시간 산정을 다루었다. 이를 위한 이론식 유도는 흐름을 개수로 흐름(층류, 완난류, 전난류)으로 파악하여 수행하였고 각 개수로 흐름상태에 대한 이론식을 제시하였다. 또한 강우강도를 주요 인자로 고려하여 재현기간별 강우강도를 포함한 근사식 즉 복합형 도달시간 산정식을 개발하였다.

• Structural Engineering and Mechanics
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• 제37권4호
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• pp.401-413
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• 2011

The aerodynamic stability of orthotropic tensioned membrane structures with rectangular plane is theoretically studied under the uniform ideal potential flow. The aerodynamic force acting on the membrane surface is determined by the potential flow theory in fluid mechanics and the thin airfoil theory in aerodynamics. Then, based on the large amplitude theory and the D'Alembert's principle, the interaction governing equation of wind-structure is established. Under the circumstances of single mode response, the Bubnov-Galerkin approximate method is applied to transform the complicated interaction equation into a system of second order nonlinear differential equation with constant coefficients. Through judging the stability of the system characteristic equation, the critical divergence instability wind velocity is determined. Finally, from different parametric analysis, we can conclude that it has positive significance to consider the characteristics of orthotropic and large amplitude for preventing the instability destruction of structures.

• 대한기계학회논문집B
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• 제22권1호
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• pp.1-11
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• 1998

For the analysis of phonon heat transfer within short time and spatial scales, conventional macroscopic heat conduction equations with jump boundary conditions are tried and the results are compared to those of equation of phonon radiative transport(EPRT), which is one of microscopic transport equation. In transient state the macroscopic temperatures show far different behavior from EPRT. In steady state the hyperbolic temperatures with temperature jump at the wall from time relaxation model agrees well with EPRT temperatures. Since EPRT is also an approximate form of microscopic transport equation and there are no experimental results to verify the proposed model in this study, we can not conclude whether the approaching method from this study is valid or not. To the authors' knowledge, there are no experimental results available which can be used to test the validity of these models. Such an experiment, while difficult to conduct, would be invaluable.

• 대한수학회지
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• 제42권6호
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• pp.1121-1136
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• 2005

Nonstandard finite difference schemes are considered for a generalization of the Cahn-Hilliard equation with Neumann boundary conditions and the Kuramoto-Sivashinsky equation with periodic boundary conditions, which are of the type $$U_t\;+\;\frac{{\partial}^2}{{\partial}x^2} g(u,\;U_x,\;U_{xx})\;=\;\frac{{\partial}^{\alpha}}{{\partial}x^{\alpha}}f(u,\;u_x),\;{\alpha}\;=\;0,\;1,\;2$$. Stability and error estimate of approximate solutions for the corresponding schemes are obtained using the extended Lax-Richtmyer equivalence theorem. Three examples are provided to apply the nonstandard finite difference schemes.

• 대한수학회논문집
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• 제18권3호
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• pp.569-580
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• 2003

The Lotka-McKendrick equation which describes the evolution of a single population under the phenomenological conditions is developed from the well-known Malthus’model. In this paper, we introduce the Lotka-McKendrick equation for the description of the dynamics of a population. We apply a discontinuous Galerkin finite element method in age-time domain to approximate the solution of the system. We provide some numerical results. It is experimentally shown that, when the mortality function is bounded, the scheme converges at the rate of $h^2$ in the case of piecewise linear polynomial space. It is also shown that the scheme converges at the rate of $h^{3/2}$ when the mortality function is unbounded.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제13권4호
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• pp.293-305
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• 2009

In this article, we study a reduced-order modelling for distributed feedback control problem of the Burgers equations. Brief review of the centroidal Voronoi tessellation (CVT) are provided. A weighted (nonuniform density) CVT is introduced and low-order approximate solution and compensator-based control design of Burgers equation is discussed. Through weighted CVT (or CVT-nonuniform) method, obtained low-order basis is applied to low-order functional gains to design a low-order controller, and by using the low-order basis order of control modelling was reduced. Numerical experiments show that a solution of reduced-order controlled Burgers equation performs well in comparison with a solution of full order controlled Burgers equation.

• 대한수학회보
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• 제51권1호
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• pp.77-82
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• 2014

We prove that if ${\mid}a_1{\mid}$ is large and ${\mid}a_0{\mid}$ is small enough, then every approximate zero of power series equation ${\sum}^{\infty}_{n=0}a_nx^n$=0 can be approximated by a true zero within a good error bound. Further, we obtain Hyers-Ulam stability of zeros of the polynomial equation of degree n, $a_nz^n$ + $a_{n-1}z^{n-1}$ + ${\cdots}$ + $a_1z$ + $a_0$ = 0 for a given integer n > 1.

• 대한수학회지
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• 제54권1호
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• pp.193-213
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• 2017

We investigate an efficient approximation of solution to stochastic Burgers equation driven by an additive space-time noise. We discuss existence and uniqueness of a solution through the Orstein-Uhlenbeck (OU) process. To approximate the OU process, we introduce the Karhunen-$Lo{\grave{e}}ve$ expansion, and sparse grid stochastic collocation method. About spatial discretization of Burgers equation, two separate finite element approximations are presented: the conventional Galerkin method and Galerkin-conservation method. Numerical experiments are provided to demonstrate the efficacy of schemes mentioned above.

• 제어로봇시스템학회논문지
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• 제19권7호
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• pp.577-582
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• 2013

In this paper Legendre wavelets are used to approximate the solutions of linear time-invariant system. The Legendre wavelet and its integral operational matrix are presented and an efficient algorithm to solve the Sylvester matrix equation is proposed. The algorithm is based on the decomposition of the Sylvester matrix equation and the preorder traversal algorithm. Using the special structure of the Legendre wavelet's integral operational matrix, the full order Sylvester matrix equation can be solved in terms of the solutions of pure algebraic matrix equations, which reduce the computation time remarkably. Finally a numerical example is illustrated to demonstrate the validity of the proposed algorithm.

• 대한전자공학회논문지
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• 제11권2호
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• pp.27-32
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• 1974

전방향성을 가지는 다소선으로 만들어진 Biconical Antenna의 특성 임피던스식을 해석적으로 구하고, 이식에 의하여 소선수의 변화가 특성 임피던스에 미치는 영향을 고찰하였다. 이 식은 매우 복잡한 형태를하고, 있으나 정각이 40°보다 작다고 하였을 때 얻어지는 근사식은 매우 간단해지며 이것이 바로 Shelkunoff의 식과 일치함을 볼 수 있었다. 그러나 상기 엄밀식과 근사식에 의한 특성 임피던스의 전자계산치를 비교 분석한 결과 항각이 70° 이하인 범위에서는 양자의 차가 별로 크지 않았으므로 정각이 70°보다 작은 범위에서는 상기의 근사식을 적용할 수 있는 것으로 생각한다.