• Journal of Korean Association for Spatial Structures
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• v.19 no.4
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• pp.69-76
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• 2019

A stadium roof that uses the pin-jointed spatial truss system has to be designed by taking into account the unstable phenomenon due to the geometrical non-linearity of the long span. This phenomenon is mainly studied in the single-free-node model (SFN) or double-free-node model (DFN). Unlike the simple SFN model, the more complex DFN model has a higher order of characteristic equations, making analysis of the system's stability complicated. However, various symmetric conditions can allow limited analysis of these problems. Thus, this research looks at the stability of the DFN model which is assumed to be symmetric in shape, and its load and equilibrium state. Its governing system is expressed by nonlinear differential equations to show the double Duffing effect. To investigate the dynamic behavior and characteristics, we normalize the system of the model in terms of space and time. The equilibrium points of the system unloaded or symmetrically loaded are calculated exactly. Furthermore, the stability of these points via the roots of the characteristic equation of a Jacobian matrix are classified.

• Journal of Environmental Science International
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• v.16 no.8
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• pp.907-912
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• 2007

Ion exchange resin was used to remove silica ion at ultralow concentration. The effects of temperature, type of ion exchange resin and single/mixed-resin systems on removal efficiency were estimated. As temperature increased, the slope of concentration profile became stiff, and the equilibrium concentration was higher. In the single resin system, the removal of silica was continued up to 400 min, but the silica concentration was recovered to initial concentration after 400 min due to the effect of dissolved $CO_2$. In the mixed-resin system it took about 600 min to reach equilibrium. Because of faster cation exchange reaction than anion exchange reaction, the effect of $CO_2$ could be removed. Based on the experimental results carried out in the mixed-resin system, the selectivity coefficients of silica ion for each ion exchange resin were calculated at some specific temperatures. The temperature dependency of the selectivity coefficient was expressed by the equation of Kraus-Raridon type.

• Journal of Biosystems Engineering
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• v.3 no.2
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• pp.62-68
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• 1978

Equilibrium moisture content of rough rice is an important factor because it has a close relationship to storage and drying problems. Determination of the EMC for 10 different varieties of rough rice were made in atmospheres of various constant humidities at three different constant temperatures. In addition , some physical properties were also measured for two different levels of moisture content of the samples. The results may be summarized as follows ; 1. Several physical properties of ten different varieties of rough were measured. Significant difference of the properties was appeared between the varieties in which the difference was pronounced in the dimensions of the varieties. Also, all the dimensions were increased as the moisture content of the rough rice was increased from 14 % to 16%. 2. Significant difference of the equilibrium moisture content was also appeared between some of the varieties in which the equilibrium moisture content of Josaengtongil and Minehikari was 24.26% while that of the others was in the range between 18 to 19% at the conditions of relative humidity of 84% and temperature of 47℃ , respectively. Similar pattern was also observed in other conditions. 3. The values of the constant of Henderson's equation were calculated from the data obtained but they are believed to be useful until more precise and complete data are obtained. There was a good agreement between the calculated and experimental results.

• Transactions of the Korean Society of Mechanical Engineers B
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• v.20 no.7
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• pp.2367-2374
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• 1996

A generalized Scheil equation for the solute redistribution in the absence of the back diffusion during the dendritic solidification of binary alloys is derived, in which coarsening of the secondary dendrite arms is taken into account. The obtained equation essentially includes the original Scheil equation as a subset. Calculated results for typical cases show that the coarsening affects the microsegregation significantly. The eutectic fraction predicted for coarsening is considerably smaller than that for fixed arm spacing. The most important feature of the present equation in comparison with the Scheil equation lies in the fact that there exists a lower limit of the initial composition below which the eutectic is not formed. Based on the generalized Scheil equation and the lever rule, a new regime map of the eutectic formation on the initial composition-equilibrium partition coefficient plane is proposed. The map consists of three regimes: the eutectic not formed, conditionally formed and unconditionally formed, bounded by the solubility and diffusion controlled limit lines.

• Journal of the Korean Chemical Society
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• v.40 no.6
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• pp.409-414
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• 1996

The limit of applicability of Navier-Stokes equation to stationary plane shock-waves is examined by using the principle of minimum entropy production of linear irreversible thermodynamics. In order to obtain analytic results, the equation is linearized near the equilibrium of downstream. Results show that the solution of Navier-Stokes equation which fits the boundary condition of far downstream flow is consistent with the thermodynamic requirement within the first order when the solution is expanded around the M=1, where M is the Mach number of upstream speed.

• Journal of the Korean Mathematical Society
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• v.44 no.4
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• pp.787-797
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• 2007

In this paper, the following fourth-order rational difference equation $$x_{n+1}=\frac{{x_n^b}+x_n-2x_{n-3}^b+a}{{x_n^bx_{n-2}+x_{n-3}^b+a}$$, n=0, 1, 2,..., where a, b ${\in}$ [0, ${\infty}$) and the initial values $X_{-3},\;X_{-2},\;X_{-1},\;X_0\;{\in}\;(0,\;{\infty})$, is considered and the rule of its trajectory structure is described clearly out. Mainly, the lengths of positive and negative semicycles of its nontrivial solutions are found to occur periodically with prime period 15. The rule is $1^+,\;1^-,\;1^+,\;4^-,\;3^+,\;1^-,\;2^+,\;2^-$ in a period, by which the positive equilibrium point of the equation is verified to be globally asymptotically stable.

• Bulletin of the Korean Mathematical Society
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• v.60 no.5
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• pp.1335-1364
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• 2023

The aim of this paper is to investigate the spectral instability of roll waves bifurcating from an equilibrium in the 2-dimensional generalized Swift-Hohenberg equation. We characterize unstable Bloch wave vectors to prove that the rolls are spectrally unstable in the whole parameter region where the rolls exist, while they are Eckhaus stable in 1 dimension [13]. As compared to [18], showing that the stability of the rolls in the 2-dimensional Swift-Hohenberg equation without a quadratic nonlinearity is determined by Eckhaus and zigzag curves, our result says that the quadratic nonlinearity of the equation is the cause of such instability of the rolls.

• Korea-Australia Rheology Journal
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• v.11 no.4
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• pp.287-291
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• 1999

The tube model theory of entangled polymer presumes that the polymer chain holds its equilibrium contour length under certain conditions of flow; at times longer than a certain characteristic time, ${\tau}_k$, in the stress relaxation process following any flow history; in steady flow of rates smaller than ${{\tau}_k}^{-1}$; etc. Rheological phenomena associated with this presumption are discussed.

• 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.

• Korean Chemical Engineering Research
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• v.56 no.2
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• pp.222-228
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• 2018

Benzene is one of the most widely used basic materials in the petrochemical industry. Generally, benzene exists as a mixture with alcohols rather than as a pure substance. Further, the alcohols-added mixtures usually exhibit an azeotropic composition. In this context, knowledge of the phase equilibrium behavior of the mixture is essential for its separation and purification. In this study, the vapor-liquid equilibrium data were measured in favor of a recirculating VLE apparatus under constant pressure for the 1 - propanol / benzene system. The measured vapor - liquid equilibrium data were also correlated by using the UNIQUAC and WILSON models and the thermodynamic consistency test based on the Gibbs/Duhem equation was followed. The results of the phase equilibrium experiment revealed RMSEs (Root Mean Square Error) and AADs (Average Absolute Deviation) of less than 0.05 for both models, indicating a good agreement between the experimental value and the calculated value. The results of the thermodynamic consistency test also confirmed through the residual term within ${\pm}0.2$.