• 제목/요약/키워드: upper and lower solutions

검색결과 176건 처리시간 0.029초

Flow Characteristics in Spin-Up of a Three-Layer Fluid

  • Sviridov Evgeny;Hyun Jae Min
    • Journal of Mechanical Science and Technology
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    • 제20권2호
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    • pp.271-277
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    • 2006
  • A numerical study is made of the spin-up from rest of a three-layer fluid in a closed, vertically-mounted cylinder. The densities in the upper layer $\rho_1$, middle layer $\rho_2$ and lower layer $\rho_3\;are\;\rho_3\;>\;\rho_2\;>\;\rho_1$, and the kinematic viscosities are left arbitrary. The representative system Ekman number is small. Numerical solutions are obtained to the time-dependent axisymmetric Navier-Stokes equations, and the treatment of the interfaces is modeled by use of the Height of Liquid method. Complete three-component velocity fields, together with the evolution of the interface deformations, are depicted. At small times, when the kinematic viscosity in the upper layer is smaller than in the middle layer, the top interface rises (sinks) in the central axis (peripheral) region. When the kinematic viscosity in the lower layer is smaller than in the middle layer, the bottom interface rises (sinks) in the periphery (axis) region. Detailed shapes of interfaces are illustrated for several cases of exemplary viscosity ratios.

최소비용문제의 비정점 최적해에 대한 감도분석 (Sensitivity Analysis on the Non-tree Solution of the Minimum Cost Flow Problem)

  • 정호연;박순달
    • 한국경영과학회지
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    • 제20권1호
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    • pp.1-10
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    • 1995
  • The purpose of this paper is to develop a method of the sensitivity analysis that can be applied to a non-tree solution of the minimum cost flow problem. First, we introduce two types of sensitivity analysis. A sensitivity analysis of Type 1a is the well known method applicable to a tree solution. However this method can not be applied to a non-tree solution. So we propose a sensitivity analysis of Type 2 that keeps solutions of upper bounds at upper bounds, those of lower bounds at lower bounds, and those of intermediate values at intermediate values. For the cost coefficient we present a method that the sensitivity analysis of Type 2 is solved by finding the shortest path. Besides we also show that the results of Type 2 and Type 1 are the same in a spanning tree solution. For the right-hand side constant or the capacity, the sensitivity analysis of Type 2 is solved by a simple calculation using arcs with intermediate values.

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The Flash Points of the Butylacetate+2-Propanol System Measured By Air Blowing Tester

  • Ha, Dong Myeong;Lee, Sung Jin;Mok, Yun Soo;Choi, Jae Wook
    • International Journal of Safety
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    • 제2권1호
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    • pp.34-38
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    • 2003
  • The lower and upper flash points of the flammable binary system, butylacetate+2-propanol were measured by air blowing tester. The shape of the concentration-temperature region of flash depended on the components of the mixture in solution. The experimental data were compared with the values calculated by the reduced model under an ideal solution assumption and the flash point-prediction models based on Van Laar equation. Good qualitative agreement was obtained with these models. The prediction results of these models can thus be applied to incorporate inherently safer design for chemical process, such as the determination of the safe storage conditions for flammable solutions.

상하단이 자유롭게 수평동요하는 수중 조파판에 의해 생성된 수면파의 근사해석 (Linear Analysis of Water Surface Waves Generated by Submerged Wave Board Whose Upper and Lower Ends Oscillate Horizontally Freely)

  • 김효철;오정근;권종오;류재문
    • 대한조선학회논문집
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    • 제56권5호
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    • pp.418-426
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    • 2019
  • To derive a simplified analytic solution which can be utilized as a fundamental solution for the wave maker design, a segment of the wave board has been idealized as a submerged line segment in a two dimensional domain of a wave flume. The lower end of the line segment could be located at arbitrary depth of the wave flume and the upper end of the board could be also submerged to any depth from the free surface. The freely oscillating motion of the wave board is assumed to be defined by determining the condition of horizontal oscillation on both ends differently. The submerged wave board oscillating in horizontal direction could be specified by selecting the amplitude, frequency and the phase lag differently on lower and upper ends of the board. The simplified two dimensional wave generated by the wave board segment has been obtained by the first order perturbation method. It is found that the general solution of the freely oscillating wave board in two dimensional domain could be decomposed into the solution of flap motion with lower end hinge and swing motion with upper end hinge. The case study of the analytic solutions has been carried out to evaluate the effect on the wave height due to the difference of oscillation frequency, phase difference and variation of stroke between for the motion of both ends. It is found that the solution of the freely oscillating wave board could be utilized for the development of high performance wavemaker especially for irregular waves.

국가공간정보정책 추진체계의 바람직한 모형구축에 대한 연구 (A Study on The Construction of Desirable Model of the National Spatial Data Infrastructure Policy Promotion System)

  • 김태진
    • Spatial Information Research
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    • 제20권6호
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    • pp.91-98
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    • 2012
  • 국가공간정보 전략의 비전을 효율적으로 추진하기 위해서는 국가공간정보정책 추진체계를 합리적으로 정립하는 것이 중요하다. 특히, 국가공간정보정책 추진체계에 있어서 관련된 조직들 간의 협조 및 정책의 일관성은 매우 중요한 요소이다. 이러한 관점에서 본 연구의 목적은 바람직한 국가공간정보정책 추진체계 모형을 개발하고, 이를 통해 우리나라 국가공간정보 정책 추진체계의 문제점과 개선방안을 제시하는데 있다. 본 연구의 목적을 달성하기 위한 주요 연구방법은 문헌고찰과 내용분석이 사용되었다. 주요 분석결과는 다음과 같다. 첫째, 바람직한 국가공간정보정책 추진체계는 상위체계(기획수준)와 하위체계(집행수준)로 구성되어야 한다. 둘째, 국가공간정보정책 추진체계의 상위 체계와 하위체계는 수직적 및 수평적으로 연계되어야 한다. 셋째, 상위체계는 국가공간정보정책 추진위원회, 민간자문위원회, 그리고 분과위원회로 구성되어야 한다. 넷째, 국가공간정보사업의 집행을 위한 하위체계는 국가공간정보 최고관리자, 각 중앙 및 지방정부, 그리고 전문지원기관 등으로 구성되어야 한다.

Bending of a rectangular plate resting on a fractionalized Zener foundation

  • Zhang, Cheng-Cheng;Zhu, Hong-Hu;Shi, Bin;Mei, Guo-Xiong
    • Structural Engineering and Mechanics
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    • 제52권6호
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    • pp.1069-1084
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    • 2014
  • The long-term performance of plates resting on viscoelastic foundations is a major concern in the analysis of soil-structure interaction. As a powerful mathematical tool, fractional calculus may address these plate-on-foundation problems. In this paper, a fractionalized Zener model is proposed to study the time-dependent behavior of a uniformly loaded rectangular thin foundation plate. By use of the viscoelastic-elastic correspondence principle and the Laplace transforms, the analytical solutions were obtained in terms of the Mittag-Leffler function. Through the analysis of a numerical example, the calculated plate deflection, bending moment and foundation reaction were compared to those from ideal elastic and standard viscoelastic models. It is found that the upper and lower bound solutions of the plate response estimated by the proposed model can be determined using the elastic model. Based on a parametric study, the impacts of model parameters on the long-term performance of a foundation plate were systematically investigated. The results show that the two spring stiffnesses govern the upper and lower bound solutions of the plate response. By varying the values of the fractional differential order and the coefficient of viscosity, the time-dependent behavior of a foundation plate can be accurately captured. The fractional differential order seems to be dependent on the mechanical properties of the ground soil. A sandy foundation will have a small fractional differential order while in order to simulate the creeping of clay foundation, a larger fractional differential order value is needed. The fractionalized Zener model is capable of accounting for the primary and secondary consolidation processes of the foundation soil and can be used to predict the plate performance over many decades of time.

최소비용문제의 퇴화 정점 최적해에 대한 감도분석 (Sensitivity Analysis on the Degenerate Tree Solution of the Minimum Cost Flow Problem)

  • 정호연;박순달
    • 산업공학
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    • 제7권3호
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    • pp.193-199
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    • 1994
  • The purpose of this paper is to develop a method of the sensitivity analysis that can be applicable to a degenerate tree solution of the minimum cost flow problem. First, we introduce two types of sensitivity analysis. A sensitivity analysis of Type 1 is the well known method applicable to a spanning tree solution. However, this method have some difficulties in case of being applied to a degenerate tree solution. So we propose a sensitivity analysis of Type 2 that keeps solutions of upper bounds remaining at upper bounds, those of lower bounds at lower bounds, and those of intermediate values at intermediate values. For the cost coefficient, we present a method that the sensitivity analysis of Type 2 is solved by using the method of a sensitivity analysis of Type 1. Besides we also show that the results of sensitivity analysis of Type 2 are union set of those of Type 1 sensitivity analysis. For the right-hand side constant or the capacity, we present a simple method for the sensitivity analysis of Type 2 which uses arcs with intermediate values.

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BLOW-UP AND GLOBAL SOLUTIONS FOR SOME PARABOLIC SYSTEMS UNDER NONLINEAR BOUNDARY CONDITIONS

  • Guo, Limin;Liu, Lishan;Wu, Yonghong;Zou, Yumei
    • 대한수학회지
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    • 제56권4호
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    • pp.1017-1029
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    • 2019
  • In this paper, blows-up and global solutions for a class of nonlinear divergence form parabolic equations with the abstract form of $({\varrho}(u))_t$ and time dependent coefficients are considered. The conditions are established for the existence of a solution globally and also the conditions are established for the blow up of the solution at some finite time. Moreover, the lower bound and upper bound of the blow-up time are derived if blow-up occurs.

최소 종료시간 사격 스케줄을 위한 분지계획법 알고리즘 연구 (A Branch-and-Bound Algorithm to Minimize the Makespan in a Fire Scheduling Problem)

  • 차영호;방준영
    • 산업경영시스템학회지
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    • 제38권4호
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    • pp.132-141
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    • 2015
  • We focus on the fire scheduling problem (FSP), the problem of determining the sequence of targets to be fired at, for the objective of minimizing makespan to achieve tactical goals. In this paper, we assume that there are m available weapons to fire at n targets (> m) and the weapons are already allocated to targets. One weapon or multiple weapons can fire at one target and these fire operations should start simultaneously while the finish time of them may be different. We develop several dominance properties and a lower bound for the problem, and suggest a branch and bound algorithm implementing them. Also, In addition, heuristic algorithms that can be used for obtaining an initial upper bound in the B&B algorithm and for obtaining good solutions in a short time were developed. Computational experiments are performed on randomly generated test problems and results show that the suggested algorithm solves problems of a medium size in a reasonable amount of computation time. The proposed lower bound, the dominance properties, and the heuristics for upper bound are tested in B&B respectively, and the result showed that lower bound is effective to fathoming nodes and the dominance properties and heuristics also worked well. Also, it is showed that the CPU time required by this algorithm increases rapidly as the problem size increases. Therefore, the suggested B&B algorithm would be limited to solve large size problems. However, the employed heuristic algorithms can be effectively used in the B&B algorithm and can give good solutions for large problems within a few seconds.

Application of artificial neural networks to a double receding contact problem with a rigid stamp

  • Cakiroglu, Erdogan;Comez, Isa;Erdol, Ragip
    • Structural Engineering and Mechanics
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    • 제21권2호
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    • pp.205-220
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    • 2005
  • This paper presents the possibilities of adapting artificial neural networks (ANNs) to predict the dimensionless parameters related to the maximum contact pressures of an elasticity problem. The plane symmetric double receding contact problem for a rigid stamp and two elastic strips having different elastic constants and heights is considered. The external load is applied to the upper elastic strip by means of a rigid stamp and the lower elastic strip is bonded to a rigid support. The problem is solved under the assumptions that the contact between two elastic strips also between the rigid stamp and the upper elastic strip are frictionless, the effect of gravity force is neglected and only compressive normal tractions can be transmitted through the interfaces. A three layered ANN with backpropagation (BP) algorithm is utilized for prediction of the dimensionless parameters related to the maximum contact pressures. Training and testing patterns are formed by using the theory of elasticity with integral transformation technique. ANN predictions and theoretical solutions are compared and seen that ANN predictions are quite close to the theoretical solutions. It is demonstrated that ANNs is a suitable numerical tool and if properly used, can reduce time consumed.