• Title, Summary, Keyword: equilibrium process

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ITERATIVE METHODS FOR GENERALIZED EQUILIBRIUM PROBLEMS AND NONEXPANSIVE MAPPINGS

  • Cho, Sun-Young;Kang, Shin-Min;Qin, Xiaolong
    • Communications of the Korean Mathematical Society
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    • v.26 no.1
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    • pp.51-65
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    • 2011
  • In this paper, a composite iterative process is introduced for a generalized equilibrium problem and a pair of nonexpansive mappings. It is proved that the sequence generated in the purposed composite iterative process converges strongly to a common element of the solution set of a generalized equilibrium problem and of the common xed point of a pair of nonexpansive mappings.

A Simulation Study on the Removal Process of the Heavy Metal Ion in Aqueous Solution by the Functionalized Silica Beads (기능화된 실리카 비드를 이용한 수용액상의 중금속 이온의 제거공정에 대한 모사 연구)

  • Woo, Yoon-Hwan;Choo, Chang-Upp
    • Clean Technology
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    • v.17 no.2
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    • pp.150-155
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    • 2011
  • The removal process of heavy metal ion in aqueous solution by the functionalized silica bead was simulated using the finite difference method. Equilibrium model and non-equilibrium model were proposed and the effects of dimensionless groups and various parameters were investigated. Freundlich isotherm was used in equilibrium model and 1st order adsorption rate expression was assumed in non-equilibrium model. The comparison results by the predictions of equilibrium and non-equilibrium models showed good agreement. The predictions of equilibrium model were compared with experimental results reported in literature and showed the marginal agreement.

Removal of Heavy metal Ions from Aqueous Solutions by Adsorption on Magadiite

  • 정순용;이정민
    • Bulletin of the Korean Chemical Society
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    • v.19 no.2
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    • pp.218-222
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    • 1998
  • Removal of Cd(Ⅱ), Zn(Ⅱ) and Cu(Ⅱ) from aqueous solutions using the adsorption process on magadiite has been investigated. It was found that the removal percentage of metal cations at equilibrium increases with increasing temperature, and follows the order of Cd(Ⅱ) > Cu(Ⅱ) > Zn(Ⅱ). Equilibrium modeling of adsorption showed that the adsorptions of Cd(Ⅱ), Cu(Ⅱ), and Zn(Ⅱ) were fitted to Langmuir isotherm. Kinetic modeling of the adsorption showed that first order reversible kinetic model fitted to experimental data. From kinetic model and equilibrium data, the overall rate constant (k) and the equilibrium constant (K) for the adsorption process were calculated. The overall rates of adsorption of metal ions follow the order of Cd(Ⅱ) > Cu(Ⅱ) > Zn(Ⅱ). From the results of thermodynamic analysis, standard Gibbs free energy (ΔG°), standard enthalpy (ΔH°), and standard entropy (ΔS°) of adsorption process were calculated.

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Alternating Offers Bargaining Game and Wardrop's User Equilibrium (Nash의 협상게임과 Wardrop의 사용자 균형)

  • Lim, Yong-Taek
    • Journal of Korean Society of Transportation
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    • v.23 no.4
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    • pp.37-45
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    • 2005
  • This paper presents a relationship between Nash bargaining game and Wardrop user equilibrium, which has been widely used in transportation modeling for route choice problem. Wardrop user equilibrium assumes that drivers in road network have perfect information on the traffic conditions and they choose their optimal paths without cooperation each other. In this regards, if the bargaining game process is introduced in route choice modeling, we may avoid the strong assumptions to some extent. For such purpose, this paper derives a theorem that Nash bargaining solution is equivalent to Wardrop user equilibrium as the barging process continues and prove it with some numerical examples. The model is formulated based on two-person bargaining game. and n-person game is remained for next work.

An Investigation on Local Thermodynamic Equilibrium Assumption of Natural Convection in a Porous Medium (다공성 물질 안에서의 자연대류 현상에 대한 열역학적 국소평형상태 가정의 고찰)

  • Kim, In-Seon;Nam, Jin-Hyun;Kim, Charn-Jung
    • Proceedings of the KSME Conference
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    • pp.112-117
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    • 2000
  • A numerical study on natural convection in a vertical square cavity filled with a porous medium is carried out with Brinkman-Forchheimer-extended Darcy flow model, and the validity of local thermodynamic equilibrium assumption is studied. The local thermodynamic equilibrium refers to the state in which a single temperature can be used to describe a heat transfer process in a multiphase system. With this assumption, the analysis is greatly simplified because only one equation is needed to describe the heat transfer process. But prior to using this assumption, it is necessary to know in what conditions the assumption can be used. The numerical results of this study reveal that large temperature difference between fluid phase and solid phase exists near wall region, paticularily when the convection becomes dominant over conduction. And the influence of flow parameters such as fluid Rayleigh number, fluid Prandtl number, dimensionless particle diameter and conductivity ratio are investigated.

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Numerical Study of Chemical Performance of 30 tonf -class LRE Nozzle of KARI

  • Kang, Ki-Ha;Lee, Dae-Sung;Cho, Deok-Rae;Choi, H.S.;Choi, J.Y.
    • Proceedings of the Korean Society of Propulsion Engineers Conference
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    • pp.448-451
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    • 2008
  • Three methods of nozzle flow analysis, frozen-equilibrium, shifting-equilibrium and non-equilibrium approaches, were used to rocket nozzle flow, those were coupled with the methods of computational fluid dynamics code. For a design of high temperature rocket nozzle, chemical equilibrium analysis which shares the same numerical characteristics with frozen flow analysis can be an efficient design tool for predicting maximum thermodynamic performance of the nozzle. Frozen fluid analysis presents the minimum performance of the nozzle because of no consideration for the energy recovery. On the other hand, the case of chemical-equilibrium analysis is able to forecast the maximum performance of the nozzle due to consideration for the energy recovery that is produced for the fast reaction velocity compared with velocity of moving fluid. In this study, using the chemical equilibrium flow analysis code that is combined the modified frozen-equilibrium and the chemical-equilibrium. In order to understand the thermochemical characteristic components and the accompanying energy recovery, shifting-equilibrium flow analysis was carried out for the 30 $ton_f$-class KARI liquid rocket engine nozzle together with frozen flow. The performance evaluation based on the 30 $ton_f$-class KARI LRE nozzle flow analyses will provide an understanding of the thermochemical process in the nozzle and performances of nozzle.

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A Study on the Methods for Finding Initial Equilibrium Position of a Lifting Block for the Safe Erection (블록의 탑재 안전성을 위한 초기 평형 자세 탐색 방법 연구)

  • Chun, Do-Hyun;Roh, Myung-Il;Ham, Seung-Ho;Lee, Hye-Won
    • Journal of the Society of Naval Architects of Korea
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    • v.55 no.4
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    • pp.297-305
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    • 2018
  • In a shipyard, block lifting is an important process in the production of ships and offshore structures. Block lifting is a sensitive process because lifting blocks have to be erected with exact positions and orientations. If we use a numerical method for the process, it is important to find tensions of wires and positions of equalizers to maintain the initial equilibrium position of the block. At this time, equations of motion of the block should be solved to calculate the initial equilibrium position of the block. Because the solving technique changes according to the number of equalizers, a suitable equation for the corresponding problem is required. In this study, three types of equations are proposed to find the initial equilibrium position of the block according to the number of equalizers. The Newton-Raphson's method is used to solve nonlinear simultaneous equations and the optimization method is used to determine the appropriate solution to the undetermined problem. To evaluate the applicability of the proposed methods, the dynamic simulations are performed using the tensions calculated from the proposed methods, and the results are discussed. The results show that the proposed methods can be effectively used to determine initial equilibrium position of the block for the block lifting.

Dyeing Behavior of Low Temperature Plasma Treated Wool

  • Kan C.W.
    • Fibers and Polymers
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    • v.7 no.3
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    • pp.262-269
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    • 2006
  • In this paper, the effects of low temperature plasma (LTP) treatment on the dyeing properties of the wool fiber were studied. The wool fibers were treated with oxygen plasma and three types of dye that commonly used for wool dyeing, namely: (i) acid dye, (ii) chrome dye and (iii) reactive dye, were used in the dyeing process. For acid dyeing, the dyeing rate of the LTP-treated wool fiber was greatly increased but the final dyeing exhaustion equilibrium did not show any significant change. For chrome dyeing, the dyeing rate of the LTP-treated wool fiber was also increased but the final dyeing exhaustion equilibrium was only increased to a small extent. In addition, the rate of afterchroming process was similar to the chrome dyeing process. For the reactive dyeing, the dyeing rate of the LTP-treated wool fiber was greatly increased and also the final dyeing exhaustion equilibrium was increased significantly. As a result, it could conclude that the LTP treatment could improve the dyeing behavior of wool fiber in different dyeing systems.

An Equilibrium Diffusion Model of Demand and Supply of New Product and Empirical Analysis (신기술 제품의 확산에 관한 수요$\cdot$공급의 균형확산모형과 실증분석)

  • Ha, Tae-Jeong
    • Journal of Technology Innovation
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    • v.13 no.1
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    • pp.113-139
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    • 2005
  • The purpose of this study is to analyse the diffusion process of personal computer (PC) in Korea during the 1990's. To achieve the goal, five research steps have been done such as the literature survey of diffusion theory, set-up of theoretic equilibrium model of supply and demand, derivation of an equilibrium path using Hamiltonian, and empirical analysis. The empirical analysis has been performed based on that equilibrium path. The results can be summarized as follows : First, technological attribute of diffusing product influences the diffusion speed of Product. It has been proven that the size of the network has a significant effect on the diffusion of PC in empirical study Second, supply factors have an important role in the diffusion process. According to the empirical analysis, decreasing cost of production as a result of technological advance promotes the speed of diffusion. This point seems to be manifest theoretically, but existing empirical models have not included supply factors explicitly, Third, it has been found out that expectation of decreasing cost would influence the speed of diffusion negatively as expected ex ante. Theoretically this result is supported by arbitrage condition of purchasing timing.

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Study on Equilibrium, Kinetic and Thermodynamic for Adsorption of Coomassi Brilliant Blue G Using Activated Carbon (입상 활성탄에 의한 Coomassi Brilliant Blue G의 흡착에 대한 평형, 동력학 및 열역학에 관한 연구)

  • Lee, Jong-Jib
    • Clean Technology
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    • v.20 no.3
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    • pp.290-297
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    • 2014
  • Batch adsorption studies were carried out for equilibrium, kinetics and thermodynamic parameters for adsorption of coomassi brilliant blue G (CBBG) using activated carbon with varying the operating variables like initial concentration, contact time and temperature. Equilibrium adsorption data were fitted into Langmuir, Freundlich and Dubinin-Radushkevich isotherms. From estimated separation factor of Langmuir and Freundlich, this process could be employed as effective treatment for removal of CBBG. Also from Dubinin-Radushkevich isotherm model, adsorption energy (E) indicated adsorption process is physical adsorption. From kinetic experiments, the adsorption reaction was found to confirm to the pseudo second order model with good correlation. Intraparticle diffusion was rate controlling step. Thermodynamic parameters like change of free energy, enthalpy, and entropy were also calculated to predict the nature of adsorption. The change of enthalpy (406.12 kJ/mol) indicated endothermic nature of the adsorption process. The change of entropy (1.66 kJ/mol K) showed increasing disorder in process. The change of free energy found that the spontaneity of process increased with increasing adsorption temperature.