• Title/Summary/Keyword: Energy-stable method

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AN ENERGY-STABLE AND SECOND-ORDER ACCURATE METHOD FOR SOLVING THE INCOMPRESSIBLE NAVIER-STOKES EQUATIONS

  • KIM, JEONGHO;JUNG, JINWOOK;PARK, YESOM;MIN, CHOHONG;LEE, BYUNGJOON
    • Journal of the Korean Society for Industrial and Applied Mathematics
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    • v.23 no.2
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    • pp.93-114
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    • 2019
  • In this article, we introduce a finite difference method for solving the Navier-Stokes equations in rectangular domains. The method is proved to be energy stable and shown to be second-order accurate in several benchmark problems. Due to the guaranteed stability and the second order accuracy, the method can be a reliable tool in real-time simulations and physics-based animations with very dynamic fluid motion. We first discuss a simple convection equation, on which many standard explicit methods fail to be energy stable. Our method is an implicit Runge-Kutta method that preserves the energy for inviscid fluid and does not increase the energy for viscous fluid. Integration-by-parts in space is essential to achieve the energy stability, and we could achieve the integration-by-parts in discrete level by using the Marker-And-Cell configuration and central finite differences. The method, which is implicit and second-order accurate, extends our previous method [1] that was explicit and first-order accurate. It satisfies the energy stability and assumes rectangular domains. We acknowledge that the assumption on domains is restrictive, but the method is one of the few methods that are fully stable and second-order accurate.

Model simplification using the energy dispersion method (에너지 분산 방법을 이용한 모델 간소화)

  • 권기호;최계근
    • 제어로봇시스템학회:학술대회논문집
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    • 1986.10a
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    • pp.65-67
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    • 1986
  • The model simplification method of the linear time invariant continuous system is proposed. Using the energy dispersion method the dynamic modes with dominent energy contribution are selected, and the poles of the denomenater are retained. And there is investigated how the dynamic modes affected the system characteristic. The parameters of the numerator are determined by time moment matching method. This method is that the algorithm is simple and also the simplified model found is always stable if the original system is stable, and through examples we assured that this method leads to good results in both transient and steady state responses.

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Stable Haptic Interaction with Reference Energy Following Scheme (에너지 추종방법을 이용한 안정적 햅틱 상호작용)

  • Ryu Jee-Hwan
    • Journal of Institute of Control, Robotics and Systems
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    • v.12 no.3
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    • pp.277-283
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    • 2006
  • A recently proposed method for stabilizing haptic interfaces and teleoperation systems was tested with a 'PHANToM' commercial haptic device. The 'Passivity Observer' (PO) and 'Passivity Control1er' (PC) stabilization method was applied to stabilize the system but also excited a high frequency mode in the device. To solve this problem, we propose a method to use a timevarying desired energy threshold instead of fixed zero energy threshold for the PO, and make the actual energy input follow the timevarying energy threshold. With the time-varying energy threshold, we make the PC control action smooth without sudden impulsive behavior by distributing the dissipation. The proposed new PO/PC approach is applied to PHANToM with high stiffness (K = 5000N/m), and stable and smooth contact is guaranteed. Resetting and active environment display problems also can be solved with the reference energy following idea.

Switching rules based on fuzzy energy regions for a switching control of underactuated robot systems

  • Ichida, Keisuke;Izumi, Kiyotaka;Watanabe, Keigo;Uchida, Nobuhiro
    • 제어로봇시스템학회:학술대회논문집
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    • 2005.06a
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    • pp.1949-1954
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    • 2005
  • One of control methods for underactuated manipulators is known as a switching control which selects a partially-stable controller using a prespecified switching rule. A switching computed torque control with a fuzzy energy region method was proposed. In this approach, some partly stable controllers are designed by the computed torque method, and a switching rule is based on fuzzy energy regions. Design parameters related to boundary curves of fuzzy energy regions are optimized offline by a genetic algorithm (GA). In this paper, we discuss on parameters obtained by GA. The effectiveness of the switching fuzzy energy method is demonstrated with some simulations.

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Computer Graphics : Theoretical Study of Antibacterial Quinolone Derivatives as DNA-Intercalator (Computer Graphies : Quinolone계 항균제의 DNA-Intercalator에 관한 이론적 연구)

  • 서명은
    • YAKHAK HOEJI
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    • v.39 no.1
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    • pp.78-84
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    • 1995
  • Based on Computer graphics molecular modeling method, quinolone derivatives as DNA-gyrase inhibitors formed stable DNA-intercalation complex with deoxycytidilyl-3',5'-deoxy guanosine[d($C_{p}G)_{2}$] dinucleotide. When d($C_{p}G)_{2}$ and d($A_{p}T)_{2}$, were compared in order to find out which DNA could form more stable DNA-Drug complex based on interaction energy($\Delta$E) and DNA-Drug complex energy, d($C_{p}G)_{2}$ resulted in lower energy than d($A_{p}T)_{2}$.

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Calculating of the Unrelaxed Surface Energy of Spinel Ferrites (스피넬 페라이트의 비이완 표면에너지 계산)

  • Shin, Hyung-Sup;Sohn, Jeongho
    • Korean Journal of Materials Research
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    • v.25 no.12
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    • pp.713-718
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    • 2015
  • A new method is proposed for the calculation of the unrelaxed surface energy of spinel ferrite. The surface energy calculation consists of (1) setting the central and computational domains in the semi-infinite real lattice, having a specific surface, and having an infinite real lattice; (2) calculation of the lattice energies produced by the associated portion of each ion in the relative domain; and (3) dividing the difference between the semi-infinite lattice energy and the infinite lattice energy on the exposed surface area in the central domain. The surface energy was found to converge with a slight expansion of the domain in the real lattice. This method is superior to any other so far reported due to its simple concept and reduced computing burden. The unrelaxed surface energies of the (100), (110), and (111) of $ZnFe_2O_4$ and $Fe_3O_4$ were evaluated by using in the semi-infinite real lattices containing only one surface. For the normal spinel $ZnFe_2O_4$, the(100), which consisted of tetrahedral coordinated $Zn^{2+}$ was electrostatically the most stable surface. But, for the inverses pinel $Fe_3O_4$, the(111), which consisted of tetrahedral coordinated $Fe^{3+}$ and octahedral coordinated $Fe^{2+}$ was electrostatically the most stable surface.

The Evaluation of the Fracture Criterion having an Effect on Crack Extension Simulation for a Thin Sheet (박판시험편의 균열성장 시물레이션에 미치는 파괴기준 평가)

  • 권오헌
    • Journal of the Korean Society of Safety
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    • v.15 no.4
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    • pp.15-19
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    • 2000
  • The exact estimation of the ductile crack growth in a thin sheet would be needed in part of the commercial transport aircraft industry fields. A 2-dimensional elastic plastic finite element analysis was carried out to simulate a stable crack extension in a thin sheet 2024 aluminium alloy. Two kinds of crack modeling were used to evaluate curves of the stable crack extension. And then CTOA(crack tip opening angle) and CTED(crack tip energy density) were calculated in order to determine whether they can be used as useful crack extension criterions in a thin sheet. Results indicate that stable crack extension behaviors were simulated well and CTED is more admirable even though CTOA also is reasonable as a criterion for a stable crack extension in a thin 2024 aluminium alloy sheet.

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Feedback stabilization of linear systems with delay in control by receding horizon (지연요소를 갖는 시스템의 안정화 방법)

  • 권욱현
    • 전기의세계
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    • v.28 no.5
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    • pp.44-48
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    • 1979
  • For ordinary systems the receding horizon method has beer proved by the author as a very useful and easy tool to find stable feedback controls. In this paper an open-loop optimal control which minimizes the control energy with a suitable upper limit and terminal control and state constraints is derived and then transformed to the closed-loop control. The stable feedback control law is obtained from the closed-loop control. The stable feedback control law is obtained from the closed-loop control by the receding horizon concept. It is shown by the Lyapunov method that the control law derived from the receding, horizon concept is asymtotically stable under the complete controllability condition. The stable feedback control which is similar to but more general than the receding horizon control is presented in this paper To the author's knowledge the control laws in this paper are easiest to stabilize systems with delay in control.

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Assessment of Optimal Constitution Rate of Windturbine and Photovoltaic Sources for Stable Operation of Microgird (마이크로그리드의 안정적 운영을 위한 풍력 및 태양광 발전원 최적 구성 비율 산정 방안 연구)

  • Lee, Su-Mi;Chun, Yeong-Han
    • The Transactions of The Korean Institute of Electrical Engineers
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    • v.59 no.2
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    • pp.272-276
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    • 2010
  • Renewable energy sources are considered to be environment-friendly alternatives those are increasingly introduced in the power systems. Microgrid is one of the systems in which renewable sources have a main role as a energy suppliers. Decision of constitution rates of renewable energy sources is very important for the economical and stable operation of microgird systems. In this paper, we present a method to assess an optimal constitution rate of renewable sources especially of windturbine and photovoltaic systems.

A CONSTRAINED CONVEX SPLITTING SCHEME FOR THE VECTOR-VALUED CAHN-HILLIARD EQUATION

  • LEE, HYUN GEUN;LEE, JUNE-YUB;SHIN, JAEMIN
    • Journal of the Korean Society for Industrial and Applied Mathematics
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    • v.23 no.1
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    • pp.1-18
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    • 2019
  • In contrast to the well-developed convex splitting schemes for gradient flows of two-component system, there were few efforts on applying the convex splitting idea to gradient flows of multi-component system, such as the vector-valued Cahn-Hilliard (vCH) equation. In the case of the vCH equation, one need to consider not only the convex splitting idea but also a specific method to manage the partition of unity constraint to design an unconditionally energy stable scheme. In this paper, we propose a constrained Convex Splitting (cCS) scheme for the vCH equation, which is based on a convex splitting of the energy functional for the vCH equation under the constraint. We show analytically that the cCS scheme is mass conserving and unconditionally uniquely solvable. And it satisfies the constraint at the next time level for any time step thus is unconditionally energy stable. Numerical experiments are presented demonstrating the accuracy, energy stability, and efficiency of the proposed cCS scheme.