• Title/Summary/Keyword: Nonlinear equations

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A study on the optimization of network resource allocation scheme based on access probabilities (접근확률 기반의 네트워크 자원할당방식의 최적화에 관한 연구)

  • Kim Do-Kyu
    • Journal of the Korea Institute of Information and Communication Engineering
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    • v.10 no.8
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    • pp.1393-1400
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    • 2006
  • This paper optimizes the access probabilities (APs) in a network resource allocation scheme based on access probabilities in order that the waiting time and the blocking probability are minimized under the given constraints, and obtains its performance. In order to optimize APs, an infinite number of balance equations is reduced to a finite number of balance equations by applying Neuts matrix geometric method. And the nonlinear programming problem is converted into a linear programming problem. As a numerical example, the performance measures of waiting time and blocking probability for optimal access probabilities and the maximum utilization under the given constraints are obtained. And it is shown that the scheme with optimal APs gives more performance build-up than the strategy without optimization.

A Mathematical Model for the Behavior of Nitrogen and Phosphorus During the Aerobic Digestion (호기성 소화과정 중 질소 및 인의 거동에 대한 수학적 모형)

  • Choung, Youn Kyoo;Ko, Kwang Baik;Park, Joon Hong
    • KSCE Journal of Civil and Environmental Engineering Research
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    • v.14 no.3
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    • pp.635-644
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    • 1994
  • A mathematical model was developed to predict the concentrations of various nutrients in supernatants during aerobic digestion which is suitable to be employed in small wastewater treatment plants with such advantages as low capital cost and stable process. Significant reactions were determined with observing the behavior of nitrgen and phosphorus, and the model equations were built up in the form of simultaneous differential equations considering Mass Balance. Laboratory batch experiments were carried out at $20^{\circ}C$ and pH $7.5{\pm}0.5$ on the aerobic digestion of waste activated sludge at different solid levels. Nonlinear regression analysis was performed to estimate various reaction rate constants. The developed model can predict the behavior of Biomass N, dissolved organic N, $NH_4{^-}$-N, $NO_x{^-}$-N, and Biomass P, dissolved organic P, $PO_4{^-}$-P in aerobic digestion process. In this study, the results of simulation showed that dissolved nutrients had more effects on supernatants than nutrients in biomass, and phosphorus was more effective on supernatants than nitrogen.

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Effect of Friction on the Hysteresis of the Thrust Forces Acting on Auto Leveling Devices in Vehicle Head Lamps (헤드 램프 빛의 각도 자동 조절 장치에 작용하는 추력의 히스테리시스에 대한 마찰의 영향)

  • Baek, Hong;Kim, Jae-Hoon;Nam, Jin-Sik;Park, Sang-Shin
    • Tribology and Lubricants
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    • v.35 no.6
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    • pp.369-375
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    • 2019
  • This paper presents a new method on how to calculate the thrust forces acting on an auto-leveling device in headlamps for passenger vehicles. The leveling device is used to lower the angle of lights when a load in the trunk of the vehicle lifts it. In the process of the headlamp design, it is imperative to predict the external forces so that the designers can decide whether to proceed or not. The device is composed of three pivot joints with no reaction moment, a plate that holds the lamp, and a leveling motor that changes rotation to linear motion. In this study, force balance, moment balance, and geometric compatibility are applied to the leveling device system so that a nonlinear system of equations can be derived; the multi-dimensional Newton-Raphson algorithm is then used to solve these. A sensitivity analysis is carried out to verify which design variables affect the system the most: the mass of the lamp and the height between the pivot and leveling device affect the thrust forces the most. Then, considering the friction forces between the moving parts, the hysteresis of the forces are derived. An experimental apparatus, designed and developed in this study, is used to verify the exactness of the derived equations. The results from experiments coincide well with the calculated results. The friction hysteresis, in particular, proves this upon analysis.

Performance Analysis of Heat Sink for LED Downlight Using Lumped Parameter Model (집중변수모델을 이용한 LED조명등 방열기구의 성능분석)

  • Kim, Euikwang;Jo, Youngchul;Yi, Seungshin;An, Younghoon
    • Journal of Energy Engineering
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    • v.26 no.2
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    • pp.64-72
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    • 2017
  • The performance analysis of the 70 W class LED lighting system suitable for the Middle East environment was performed using the lumped parameter model. The LED light is composed of a heating substrate, a heat pipe, and a heat sink. We divided the LED lights into four objects and applied energy equilibrium to each of them to establish four lumped nonlinear differential equations. The solution of the simultaneous equations was obtained by the Runge-Kutta method. Convective heat transfer coefficients of the lumped model were obtained by multidimensional CFD analysis. As a result of comparison with experiment, it was found that the heating substrate had an error of $1.5^{\circ}C$ and the upper heat sink had an error of $1.8^{\circ}C$ and the relative error was about 0.6 %. Using this model, temperature distribution analysis was performed for normal operating conditions with an ambient temperature of $55^{\circ}C$, with sunlight only, with abnormal operating conditions with sunlight, and without an upper heat sink.

Linear decentralized learning control for the robot moving on the horizontal plane

  • Lee, Soo-Cheol
    • Proceedings of the Korean Operations and Management Science Society Conference
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    • 1995.04a
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    • pp.869-879
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    • 1995
  • The new field of learning control develops controllers that learn to improve their performance at executing a given task, based on experience performing this task. The simplest forms of learning control are based on the same concept as integral control, but operating in the domain of the repetitions of the task. In the previous paper, I had studied the use of such controllers in a decentralized system, such as a robot with the controller for each link acting independently. The basic result of the paper is to show that stability of the learning controllers for all subsystems when the coupling between subsystems is turned off, assures stability of the decentralized learning in the coupled system, provided that the sample time in the digital learning controller is sufficiently short. In this paper, we present two examples. The first illustrates the effect of coupling between subsystems in the system dynamics, and the second studies the application of decentralized learning control to robot problems. The latter example illustrates the application of decentralized learning control to nonlinear systems, and also studies the effect of the coupling between subsystems introduced in the input matrix by the discretization of the system equations. The conclusion is that for sufficiently small learning gain, and sufficiently small sample time, the simple learning control law based on integral control applied to each robot axis will produce zero tracking error in spite o the dynamic coupling in the robot equations. Of course, the results of this paper have much more general application than just to the robotics tracking problem. Convergence in decentralized systems is seen to depend only on the input and output matrices, provided the sample time is suffiently small.

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Design of MMIC Variable Gain LNA Using Behavioral Model for Wireless LAM Applications (거동모델을 이용한 무선랜용 MMIC 가변이득 저잡음 증폭기 설계)

  • Park, Hun;Yoon, Kyung-Sik;Hwang, In-Gab
    • The Journal of Korean Institute of Communications and Information Sciences
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    • v.29 no.6A
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    • pp.697-704
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    • 2004
  • This paper describes the design and fabrication of an MMIC variable gain LNA for 5GHz wireless LAN applications, using 0.5${\mu}{\textrm}{m}$ gate length GaAs MESFET transistors. The advantages of high gain and low noise performance of E-MESFETS and excellent linear performance of D-MESFETS are combined as a cascode topology in this design. Behavioral model equations are derived from the MESFET nonlinear current voltage characteristics by using Turlington's asymptote method in a cascode configuration. Using the behavioral model equations, a 4${\times}$50${\mu}{\textrm}{m}$ E-MESFET as a common source amplifier and a 2${\times}$50${\mu}{\textrm}{m}$ D-MESFET as a common gate amplifier are determined for the cascode amplifier. The fabricated variable gain LNA shows a noise figure of 2.4dB, variable gain range of more than 17dB, IIP3 of -4.8dBm at 4.9GHz, and power consumption of 12.8mW.

Numerical Simulation of Two-Dimensional Shipping Water by Using a Simplified Model (단순화 모델에 의한 2차원 갑판침입수의 수치 시뮬레이션)

  • Kim, Yong J.;Kim, In C.
    • Journal of the Society of Naval Architects of Korea
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    • v.33 no.2
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    • pp.1-12
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    • 1996
  • Hydrodynamic characteristics of shipping water on deck are investigated by using a simplified two-dimensional model. Formulation of the shipping water on deck leads to a nonlinear hyperbolic system of equations based on the shallow-water wave theory. Time-domain solution of these equations are obtained numerically using a finite difference method which adopts predictor-corrector method for time-marching and 2nd upwind differencing method for convection term calculation. To confirm the validity of the present numerical method, we calculated some shallow-water wave problems accompanying a bore and compared the obtained results with the analytic solutions. We found good agreements between them. Though the calculation results of shipping water on deck, we show that the shipping water flows into the deck as a rarefying wave arid grows into a bore after colliding with a deck structure. Also we examined the effects of acceleration and slope of deck and found that they have significant influences on the flow of shipping water.

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Empirical Equations for Checking Validity of Access Hole Parameters for WUF-W Connections (WUF-W 접합부의 액세스 홀 형상변수 타당성 평가를 위한 경험식 제안)

  • Han, Sang Whan;Yoon, Yong;Kim, Y. Debbie
    • Journal of Korean Society of Steel Construction
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    • v.29 no.4
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    • pp.303-310
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    • 2017
  • The welded unreinforced flange-welded web(WUF-W) connection is an all-welded moment connection, which is qualified for special moment frame(SMF) connections. However, previous studies reported that some WUF-W connections did not meet the drift requirement specified for SMF connections and such unexpected connection performance was resulted from weld access hole geometry. The objective of this study is to determine the permissible ranges of major access hole parameters such as access hole slope and the length of flat portion that lead to the satisfactory performance of WUF-W connections using Nonlinear finite element analyses are conducted. This study also proposes simple empirical equations to check the validity of access hole parameters to be selected in design process.

A Relative Nodal Displacement Method for Element Nonlinear Analysis (상대 절점 변위를 이용한 비선형 유한 요소 해석법)

  • Kim Wan Goo;Bae Dae sung
    • Transactions of the Korean Society of Mechanical Engineers A
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    • v.29 no.4 s.235
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    • pp.534-539
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    • 2005
  • Nodal displacements are referred to the initial configuration in the total Lagrangian formulation and to the last converged configuration in the updated Lagrangian furmulation. This research proposes a relative nodal displacement method to represent the position and orientation for a node in truss structures. Since the proposed method measures the relative nodal displacements relative to its adjacent nodal reference frame, they are still small for a truss structure undergoing large deformations for the small size elements. As a consequence, element formulations developed under the small deformation assumption are still valid for structures undergoing large deformations, which significantly simplifies the equations of equilibrium. A structural system is represented by a graph to systematically develop the governing equations of equilibrium for general systems. A node and an element are represented by a node and an edge in graph representation, respectively. Closed loops are opened to form a spanning tree by cutting edges. Two computational sequences are defined in the graph representation. One is the forward path sequence that is used to recover the Cartesian nodal displacements from relative nodal displacement sand traverses a graph from the base node towards the terminal nodes. The other is the backward path sequence that is used to recover the nodal forces in the relative coordinate system from the known nodal forces in the absolute coordinate system and traverses from the terminal nodes towards the base node. One open loop and one closed loop structure undergoing large deformations are analyzed to demonstrate the efficiency and validity of the proposed method.

Meshless Local Petrov-Galerkin (MLPG) method for dynamic analysis of non-symmetric nanocomposite cylindrical shell

  • Ferezghi, Yaser Sadeghi;Sohrabi, Mohamadreza;Nezhad, Seyed Mojtaba Mosavi
    • Structural Engineering and Mechanics
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    • v.74 no.5
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    • pp.679-698
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    • 2020
  • In this paper, the meshless local Petrov-Galerkin (MLPG) method is developed for dynamic analysis of non-symmetric nanocomposite cylindrical shell equations of elastic wave motion with nonlinear grading patterns under shock loading. The mechanical properties of the nanocomposite cylinder are obtained based on a micro-mechanical model. In this study, four kinds of grading patterns are assumed for carbon nanotube mechanical properties. The displacements can be approximated using shape function so, the multiquadrics (MQ) Radial Basis Functions (RBF) are used as the shape function. In order to discretize the derived equations in time domains, the Newmark time approximation scheme with suitable time step is used. To demonstrate the accuracy of the present method for dynamic analysis, at the first a problem verifies with analytical solution and then the present method compares with the finite element method (FEM), finally, the present method verifies by using the element free Galerkin (EFG) method. The comparison shows the high capacity and accuracy of the present method in the dynamic analysis of cylindrical shells. The capability of the present method to dynamic analysis of non-symmetric nanocomposite cylindrical shell is demonstrated by dynamic analysis of the cylinder with different kinds of grading patterns and angle of nanocomposite reinforcements. The present method shows high accuracy, efficiency and capability to dynamic analysis of non-symmetric nanocomposite cylindrical shell, which it furnishes a ground for a more flexible design.