• 한국공간구조학회논문집
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• 제19권4호
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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.

• 한국환경과학회지
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• 제16권8호
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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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• 제3권2호
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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.

• 대한기계학회논문집B
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• 제20권7호
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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.

• 대한화학회지
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• 제40권6호
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• pp.409-414
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• 1996

선형 비평형 열역학의 최소 엔트로피 생성원리를 사용하여 정상 평면충격파 형상에 대한 Navier-Stokes 유체방정식의 적용한계를 연구하였다. 해석적 결과를 얻기 위하여 평형상태에 가까운 하류 위치에서 방정식을 선형화 하였다. 하류 극한의 경계조건을 충족하는 Navier-Stokes 방정식의 해를 충격파 진행속도의 마하수 M=1 근처에서 급수전개하였을 때, 일차항까지는 열역학의 요구조건과 부합하였다.

• 대한수학회지
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• 제44권4호
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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.

• 대한수학회보
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• 제60권5호
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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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• 제11권4호
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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.

• 대한조선학회논문집
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• 제55권4호
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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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• 제56권2호
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• pp.222-228
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• 2018

석유화학산업의 대표적인 물질로 쓰이는 벤젠은 각종 화학 제품의 기초 물질이다. 그러나 일반적으로 벤젠은 석유화학 산업에서 순수 물질로 존재하지 못하고 알코올류와 벤젠 혼합물로 존재하게 된다. 또한 알코올을 한 성분으로 하는 혼합물은 공비 혼합물이 생성되기 때문에 분리 정제를 위해서는 상평형 데이터가 필수적이다. 본 연구에서는 알코올을 대표하는 1-프로판올을 사용하여 1-프로판올/벤젠 계에 대하여 재순환 평형장치를 이용하여 평형 온도/압력 효과에 따른 상평형 연구를 수행하였다. 측정된 기-액 평형 데이터는 UNIQUAC 식과 WILSON 식을 이용하여 상관관계 시키고 Gibbs/Duhem식을이용하여열역학적건전성을확인하였다. 상평형실험결과 RMSE (Root Mean Square Error)와 AAD (Average Absolute Deviation)는 두 모델식에서 0.05 이하의 값을 보여 실험값과 계산 값이 잘 일치함을 알 수 있었다. 또한 Gibbs/Duhem식을 이용하여 열역학적 건전성을 판별한 결과 잔류항 값이 ${\pm}0.2$ 이내에 분포하는 것을 통해 데이터에 대한 건전성을 확인할 수 있었다.