• Title/Summary/Keyword: system of integral equations

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Theoretical Analysis of a $1.48{\mu}m$ Diode Laser Pumped $Er^{3+}$ Doped Fiber Amplifier ($1.48{\mu}m$ 레이저 다이오드로 여기된 $Er^{3+}$ 첨가 광섬유 광증폭기에 대한 이론적 분석)

  • 김회종
    • Korean Journal of Optics and Photonics
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    • v.4 no.1
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    • pp.101-107
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    • 1993
  • We carried out the useful theoretical calculation for the optimum design of a 1.48 ${\mu}m$ diode laser pumped E$r^{3+}$ doped fiber amplifier. The model we established is based on the rate equations of three level laser system and the overlap integral between fundamental mode L$P_{01}$ and E$r^{3+}$ doped area. We determined several fiber parameters (N.A., V value, fiber length, E$r^{3+}$ concentration, cutoff wavelength etc.) for the optimum design of a high optical gain. We found that our theoretical results are very useful to the design of E$r^{3+}$ doped fiber used in EDFA.

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Analysis of Linear Consolidation Problems by the Boundary Element Method (경계요소법에 의한 선형 압밀문제의 해석)

  • 서일교
    • Computational Structural Engineering
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    • v.8 no.4
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    • pp.129-136
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    • 1995
  • This paper presents a boundary element method for obtaining approximate solutions of 2-dimensional consolidation problems based on the Biot's linear theory. Laplace transform is applied to differential equation system in order to eliminate the time dependency. The boundary integral equations in transformed space are formulated and the fundamental solutions are shown in a closed form. In order to convert the transformed solutions to the ones in real space, the Hosono's numerical Laplace transform inversion method is applied. As a numerical example, a half-space consolidation problem subjected to a strip local load is selected and the applicability of the method is demonstrated through the comparison with the exact solutions.

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A Numerical Simulation of Three- Dimensional Nonlinear Free surface Flows (3차원 비선형 자유표면 유동의 수치해석)

  • Chang-Gu Kang;In-Young Gong
    • Journal of the Society of Naval Architects of Korea
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    • v.28 no.1
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    • pp.38-52
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    • 1991
  • In this paper, a semi-Lagrangian method is used to solve the nonlinear hydrodynamics of a three-dimensional body beneath the free surface in the time domain. The boundary value problem is solved by using the boundary integral method. The geometries of the body and the free surface are represented by the curved panels. The surfaces are discretized into the small surface elements using a bi-cubic B-spline algorithm. The boundary values of $\phi$ and $\frac{\partial{\phi}}{\partial{n}}$ are assumed to be bilinear on the subdivided surface. The singular part proportional to $\frac{1}{R}$ are subtracted off and are integrated analytically in the calculation of the induced potential by singularities. The far field flow away from the body is represented by a dipole at the origin of the coordinate system. The Runge-Kutta 4-th order algorithm is employed in the time stepping scheme. The three-dimensional form of the integral equation and the boundary conditions for the time derivative of the potential Is derived. By using these formulas, the free surface shape and the equations of motion are calculated simultaneously. The free surface shape and fille forces acting on a body oscillating sinusoidally with large amplitude are calculated and compared with published results. Nonlinear effects on a body near the free surface are investigated.

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On the Study of Nonlinear Normal Mode Vibration via Poincare Map and Integral of Motion (푸앙카레 사상과 운동적분를 이용한 비선형 정규모드 진동의 연구)

  • Rhee, Huinam
    • Journal of KSNVE
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    • v.9 no.1
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    • pp.196-205
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    • 1999
  • The existence. bifurcation. and the orbital stability of periodic motions, which is called nonlinear normal mode, in a nonlinear dual mass Hamiltonian system. which has 6th order homogeneous polynomial as a nonlinear term. are studied in this paper. By direct integration of the equations of motion. Poincare Map. which is a mapping of a phase trajectory onto 2 dimensional surface in 4 dimensional phase space. is obtained. And via the Birkhoff-Gustavson canonical transformation, the analytic expression of the invariant curves in the Poincare Map is derived for small value of energy. It is found that the nonlinear system. which is considered in this paper. has 2 or 4 nonlinear normal modes depending on the value of nonlinear parameter. The Poincare Map clearly shows that the bifurcation modes are stable while the mode from which they bifurcated out changes from stable to unstable.

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Estimation for Primary Tunnel Lining Loads

  • Kim, Hak-Joon
    • Proceedings of the Korean Geotechical Society Conference
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    • 1998.05a
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    • pp.153-204
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    • 1998
  • Prediction of lining loads due to tunnelling is one of the major issues to be addressed in the design of a tunnel. The objective of this study is to investigate rational and realistic design loads on tunnel linings. factors influencing the lining load are summarized and discussed. The instruments for measuring the lining loads are reviewed and discussed because field measurements are often necessary to verify the design methods. Tunnel construction in the City of Edmonton has been very active for storm and sanitary purposes. Since the early 1970's, the city has also been developing an underground Light Rail Transit system. The load measurements obtained from these tunnels are compared with the results from the existing design methods. However, none of the existing methods are totally satisfactory, Therefore, there is some room for improvement in the prediction of lining loads. The convergence-confinement method is reviewed and applied to a case history of a tunnel in Edmonton. The convergence curves are obtained from 2-D finite element analyses using three different material models and theoretical equations. The limitation of the convergence-confinement method is discussed by comparing these curves with the field measurements. Three-dimensional finite element analyses are performed to gain a better understanding of stress and displacement behaviour near the tunnel face. An improved design method is proposed based on the review of existing design methods and the performance of numerical analyses. A specific method or combination of two different methods is suggested for the estimation of lining loads for different conditions of tunnelling. A method to determine the stress reduction factor is described. Typical values of dimensionless load factors nD/H for tunnels in Edmonton are obtained from parametric analyses. Finally, the loads calculated using the proposed method are compared with field measurements collected from various tunnels in terms of soil types and construction methods to verify the method. The proposed method gives a reasonable approximation of the lining loads. The proposed method is recommended as an approximate guideline for the design of tunnels, but the results should be confirmed by field measurements due to the uncertainties of the ground and lining properties and the construction procedures, This is the reason that in-situ monitoring should be an integral part of the design procedure.

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Highly Linear Wideband LNA Design Using Inductive Shunt Feedback

  • Jeong, Nam Hwi;Cho, Choon Sik;Min, Seungwook
    • JSTS:Journal of Semiconductor Technology and Science
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    • v.14 no.1
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    • pp.100-108
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    • 2014
  • Low noise amplifier (LNA) is an integral component of RF receiver and frequently required to operate at wide frequency bands for various wireless system applications. For wideband operation, important performance metrics such as voltage gain, return loss, noise figure and linearity have been carefully investigated and characterized for the proposed LNA. An inductive shunt feedback configuration is successfully employed in the input stage of the proposed LNA which incorporates cascaded networks with a peaking inductor in the buffer stage. Design equations for obtaining low and high impedance-matching frequencies are easily derived, leading to a relatively simple method for circuit implementation. Careful theoretical analysis explains that input impedance can be described in the form of second-order frequency response, where poles and zeros are characterized and utilized for realizing the wideband response. Linearity is significantly improved because the inductor located between the gate and the drain decreases the third-order harmonics at the output. Fabricated in $0.18{\mu}m$ CMOS process, the chip area of this wideband LNA is $0.202mm^2$, including pads. Measurement results illustrate that the input return loss shows less than -7 dB, voltage gain greater than 8 dB, and a little high noise figure around 6-8 dB over 1.5 - 13 GHz. In addition, good linearity (IIP3) of 2.5 dBm is achieved at 8 GHz and 14 mA of current is consumed from a 1.8 V supply.

State-Space Equation Model for Motion Analysis of Floating Structures Using System-Identification Methods (부유식 구조체 운동 해석을 위한 시스템 식별 방법을 이용한 상태공간방정식 모델)

  • Jun-Sik Seong;Wonsuk Park
    • Journal of the Computational Structural Engineering Institute of Korea
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    • v.37 no.2
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    • pp.85-93
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    • 2024
  • In this paper, we propose a method for establishing a state-space equation model for the motion analysis of floating structures subjected to wave loads, by applying system-identification techniques. Traditionally, the motion of floating structures has been analyzed in the time domain by integrating the Cummins equation over time, which utilizes a convolution integral term to account for the effects of the retardation function. State-space equation models have been studied as a way to efficiently solve floating-motion equations in the time domain. The proposed approach outlines a procedure to derive the target transfer function for the load-displacement input/output relationship in the frequency domain and subsequently determine the state-space equation that closely approximates it. To obtain the state-space equation, the method employs the N4SID system-identification method and an optimization approach that treats the coefficients of the numerator and denominator polynomials as design variables. To illustrate the effectiveness of the proposed method, we applied it to the analysis of a single-degree-of-freedom model and the motion of a six-degree-of-freedom barge. Our findings demonstrate that the presented state-space equation model aligns well with the existing analysis results in both the frequency and time domains. Notably, the method ensures computational accuracy in the time-domain analysis while significantly reducing the calculation time.

Probability Distribution of Nonlinear Random Wave Heights Using Maximum Entropy Method (최대 엔트로피 방법을 이용한 비선형 불규칙 파고의 확률분포함수)

  • 안경모
    • Journal of Korean Society of Coastal and Ocean Engineers
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    • v.10 no.4
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    • pp.204-210
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    • 1998
  • This paper presents the development of the probability density function applicable for wave heights (peak-to-trough excursions) in finite water depth including shallow water depth. The probability distribution applicable to wave heights of a non-Gaussian random process is derived based on the concept of the maximum entropy method. When wave heights are limited by breaking wave heights (or water depth) and only first and second moments of wave heights are given, the probability density function developed is closed form and expressed in terms of wave parameters such as $H_m$(mean wave height), $H_{rms}$(root-mean-square wave height), $H_b$(breaking wave height). When higher than third moment of wave heights are given, it is necessary to solve the system of nonlinear integral equations numerically using Newton-Raphson method to obtain the parameters of probability density function which is maximizing the entropy function. The probability density function thusly derived agrees very well with the histogram of wave heights in finite water depth obtained during storm. The probability density function of wave heights developed using maximum entropy method appears to be useful in estimating extreme values and statistical properties of wave heights for the design of coastal structures.

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A Study on the Design of Ship′s Bow Form using Surface Panel Method (판요소법을 이용한 선수형상 설계에 관한 연구[1])

  • Jae-Hoon Yoo;Hyo-Chul Kim
    • Journal of the Society of Naval Architects of Korea
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    • v.33 no.3
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    • pp.35-47
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    • 1996
  • A surface panel method treating a boundary-value problem of the Dirichlet type is presented to design a three dimensional body with free surface corresponding to a prescribed pressure distribution. An integral equation is derived from Green's theorem, giving a relation between total potential of known strength and the unknown local flux. Upon discretization, a system of linear simultaneous equations is formed including free surface boundary condition and is solved for an assumed geometry. The pseudo local flux, present due to the incorrect positioning of the assumed geometry, plays a role f the geometry corrector, with which the new geometry is computed for the next iteration. Sample designs for submerged spheroids and Wigley hull and carried out to demonstrate the stable convergence, the effectiveness and the robustness of the method. For the calculation of the wave resistance, normal dipoles and Rankine sources are distributed on the body surface and Rankine sources on the free surface. The free surface boundary condition is linearized with respect to the oncoming flow. Four-points upwind finite difference scheme is used to compute the free surface boundary condition. A hyperboloidal panel is adopted to represent the hull surface, which can compensate the defects of the low-order panel method. The design of a 5500TEU container carrier is performed with respect to reduction of the wave resistance. To reduce the wave resistance, calculated pressure on the hull surface is modified to have the lower fluctuation, and is applied as a Dirichlet type dynamic boundary condition on the hull surface. The designed hull form is verified to have the lower wave resistance than the initial one not only by computation but by experiment.

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