• Title/Summary/Keyword: Laplace Expansion

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Beat Maps of King Song-Dok Bell (성덕대왕신종의 맥놀이 지도)

  • Kim, Seock-Hyun
    • Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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    • 2002.11b
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    • pp.498-504
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    • 2002
  • Vibration beat phenomenon is theoretically investigated on a slightly asymmetric cylindrical shell, which is a simplified model of Korean bell. Mode pairs of the slightly asymmetric shell are obtained by receptance analysis and impulse response of the shell is derived using modal expansion and Laplace transform. Based on the impulse response model, beat mapping method is proposed to explain the reason that the beat of a bell vibration shows periodic distribution on the circumference. Beat characteristics of King Song-Dok Bell are explained in detail using the beat map and the measured modal data.

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Bounds for Stationary Waiting Times in a Class of Queueing Networks using Stochastic Ordering (확률적 순서를 이용한 대기행렬 망에서 안정 대기시간의 범위)

  • Seo Dong-Won
    • Journal of the Korean Operations Research and Management Science Society
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    • v.29 no.4
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    • pp.1-10
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    • 2004
  • In this paper we study bounds for characteristics of stationary waiting times in (max, +)-linear systems with a Poisson arrival process. which are prevalent in manufacturing systems, kanban systems, cyclic and acyclic fork-and-join type systems, finite or infinite capacity tandem queues with various kinds of blocking, transportation systems, and telecommunication networks, and so on. Recently, some results on series expansion for characteristics, such as higher moments, Laplace transform, and tail probability, of transient and stationary waiting times in a class of (max, +)-linear systems via Taylor series expansions have been studied. In order to overcome the computational complexity in those results, we consider bounds for characteristics of stationary waiting times using valuable stochastic ordering results. Some numerical examples are also provided.

Transient interactions between submerged elastic shells and acoustic shock waves from a moving source (움직이는 소스와 구형쉘의 상호작용 해석)

  • 이민형;이범헌;이승엽
    • Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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    • 2001.05a
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    • pp.85-89
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    • 2001
  • The problem of the transient interaction of a plane acoustic shock wave which has an infinitely steep wave front with a cylindrical or spherical elastic shell has been studied analytically from early fifties based on the integral transform and series solution techniques. Huang adopted an inverse Laplace transform, and used a finite number of terms of the infinite series expansion of the equations for the shells. In the 1990s, the results have been used by many authors for validation of computer codes. The object of this paper is to discuss the interaction between a moving source and submerged spherical shells. Since the center of source is moving the first contact location between the waves and shell changes depending on the source velocity and distance. These are considered in the analysis. Furthermore, constant source strength and decreasing strength are considered in the analysis. Radial velocities at several locations on the structure are obtained and the results are discussed.

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Modal Analysis of One Dimensional Distributed Parameter Systems by Using the Digital Modeling Technique (디지털 모델링 기법에 의한 1차원 연속계의 모드 해석)

  • 홍성욱;조종환
    • Journal of KSNVE
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    • v.9 no.1
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    • pp.103-112
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    • 1999
  • A new modeling and analysis technique for one-dimensional distributed parameter systems is presented. First. discretized equations of motion in Laplace domain are derived by applying discretization methods for partial differential equations of a one-dimensional structure with respect to spatial coordinate. Secondly. the z and inverse z transformations are applied to the discretized equations of motion for obtaining a dynamic matrix for a uniform element. Four different discretization methods are tested with an example. Finally, taking infinite on the number of step for a uniform element leads to an exact dynamic matrix for the uniform element. A generalized modal analysis procedure for eigenvalue analysis and modal expansion is also presented. The resulting element dynamic matrix is tested with a numerical example. Another application example is provided to demonstrate the applicability of the proposed method.

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Frequency-Dependent Line Capacitance and Conductance Calculations of On-Chip Interconnects on Silicon Substrate Using Fourier cosine Series Approach

  • Ymeri, H.;Nauwelaers, B.;Vandenberghe, S.;Maex, K.;De Roest, D.;Stucchi, M.
    • JSTS:Journal of Semiconductor Technology and Science
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    • v.1 no.4
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    • pp.209-215
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    • 2001
  • In this paper a method for analysis and modelling of coplanar transmission interconnect lines that are placed on top of silicon-silicon oxide substrates is presented. The potential function is expressed by series expansions in terms of solutions of the Laplace equation for each homogeneous region of layered structure. The expansion coefficients of different series are related to each other and to potentials applied to the conductors via boundary conditions. In the plane of conductors, boundary conditions are satisfied at $N_d$ discrete points with $N_d$ being equal to the number of terms in the series expansions. The resulting system of inhomogeneous linear equations is solved by matrix inversion. No iterations are required. A discussion of the calculated line admittance parameters as functions of width of conductors, thickness of the layers, and frequency is given. The interconnect capacitance and conductance per unit length results are given and compared with those obtained using full wave solutions, and good agreement have been obtained in all the cases treated

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Non-stationary mixed problem of elasticity for a semi-strip

  • Reut, Viktor;Vaysfeld, Natalya;Zhuravlova, Zinaida
    • Coupled systems mechanics
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    • v.9 no.1
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    • pp.77-89
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    • 2020
  • This study is dedicated to the dynamic elasticity problem for a semi-strip. The semi-strip is loaded by the dynamic load at the center of its short edge. The conditions of fixing are given on the lateral sides of the semi-strip. The initial problem is reduced to one-dimensional problem with the help of Laplace's and Fourier's integral transforms. The one-dimensional boundary problem is formulated as the vector boundary problem in the transform's domain. Its solution is constructed as the superposition of the general solution for the homogeneous vector equation and the partial solution for the inhomogeneous vector equation. The matrix differential calculation is used for the deriving of the general solution. The partial solution is constructed with the help of Green's matrix-function, which is searched as the bilinear expansion. The case of steady-state oscillations is considered. The problem is reduced to the solving of the singular integral equation. The orthogonalization method is applied for the calculations. The stress state of the semi-strip is investigated for the different values of the frequency.

Numerical analysis of turbulent recirculating flow in swirling combustor by non-orthogonal coordinate transformation (비직교 좌표변환에 의한 선회연소기내 난류재순환유동의 수치해석)

  • 신종근;최영돈
    • Transactions of the Korean Society of Mechanical Engineers
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    • v.12 no.5
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    • pp.1158-1174
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    • 1988
  • A numerical technique is developed for the solution of fully developed turbulent recirculating flow in the passage of variable area using the non-orthogonal coordinate transformation. In the numerical analysis, primitive pressure-velocity finite difference equations were solved by SIMPLER algorithm with 2-equation turbulence model and algebraic stress model (ASM). QUICK scheme on the differencing of convective terms which is free from the inaccuracies of numerical diffusion has been applied to the variable grids and the results compared with those from HYBRID scheme. In order to test the effect of streamline curvatures on turbulent diffusion Lee and Choi streamline curvature correction model which has been obtained by modifying the Leschziner and Rodi's model is testes. The ASM was also employed and the results are compared to those from another turbulence model. The results show that difference of convective differencing schemes and turbulence models give significant differences in the prediction of velocity fields in the expansion region and outlet region of the combustor, however show little differences in the parallel flow region.

Body Fat Segmentation of Abdominal CT Image (복부전산화단층영상의 체지방 분할방법)

  • Choi, Seokyoon
    • Journal of the Korean Society of Radiology
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    • v.13 no.3
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    • pp.489-493
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    • 2019
  • Obesity is increasing in our country due to lack of lifestyle and physical activity. Semi-automatic program is used in existing fat calculation program using computed tomography. Although methods for solving related problems have been proposed, this study proposes an algorithm using morphology operation and We want to solve the problem with a new method that has a simple procedure and a relatively small amount of computation. As a result of repetition of erosion and expansion Automatic fat mass calculation can be done in the future by using the developed partitioning result. By providing an accurate segmentation tool, it will be helpful to doctors and reduce the expense and inspection cost of retesting. through morphology operation, it was found that the problem was solved from the image.Automatic fat mass calculation can be done in the future by using the developed partitioning result. By providing an accurate segmentation tool, it will be helpful to doctors and reduce the expense and inspection cost of retesting.

Arctic Climate Change for the Last Glacial Maximum Derived from PMIP2 Coupled Model Results (제2차 고기후 모델링 비교 프로그램 시뮬레이션 자료를 이용한 마지막 최대빙하기의 북극 기후변화 연구)

  • Kim, Seong-Joong;Woo, Eun-Jin
    • Journal of Climate Change Research
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    • v.1 no.1
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    • pp.31-50
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    • 2010
  • The Arctic climate change for the Last Glacial Maximum(LGM) occurred at 21,000 years ago (21ka) was investigated using simulation results of atmosphere-ocean coupled models from the second phase of the Paleoclimate Modelling Intercomparison Program(PMIP2). In the analysis, we used seven models, the NCAR CCSM of USA, ECHAM3-MPIOM of German Max-Planxk Institute, HadCM3M2 of UK Met Office, IPSL-CM4 of France Laplace Institute, CNRM-CM3 of France Meteorological Institute, MIROC3.2 of Japan CCSR at University of Tokyo, and FGOALS of China Institute of Atmospheric Physics. All the seven models reproduces the Arctic climate features found in the present climate at 0ka(pre-industrial time) in a reasonable degree in comparison to observations. During the LGM, the atmospheric $CO_2$ concentration and other greenhouse gases were reduced, the ice sheets were expanded over North America and northern Europe, the sea level was lowered by about 120m, and orbital parameters were slightly different. These boundary conditions were implemented to simulated LGM climate. With the implemented LGM conditions, the biggest temperature reduction by more than $24^{\circ}C$ is found over North America and northern Europe owing to ice albedo feedback and the change in lapse rate by high elevation. Besides, the expansion of ice sheets leads to the marked temperature reduction by more then $10^{\circ}C$ over the Arctic Ocean. The temperature reduction in northern winter is larger than in summer around the Arctic and the annual mean temperature is reduced by about $14^{\circ}C$. Compared to low mid-latitudes, the temperature reduction is much larger in high northern altitudes in the LGM. This results mirror the larger warming around the Artic in recent century. We could draw some information for the future under global warming from the knowledge of the LGM.