• 제목/요약/키워드: Parabolic Equations

검색결과 255건 처리시간 0.022초

pH 와 온도(溫度)에 따른 토양(土壤)의 규산(硅酸) 흡(吸) · 탈착(脫着)에 대(對)한 역학적(力學的) 연구(硏究) (Kinetics of Silica Sorption and Desorption in Soil as affected by pH and Temperature)

  • 이상은
    • 한국토양비료학회지
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    • 제25권4호
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    • pp.342-356
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    • 1992
  • 규산(硅酸)의 흡(吸) 탈착기구(脫着機構)를 밝히기 위하여 pH 3수준(水準)(pH 5, 6.5, 8)과 온도(溫度) 3수준(水準)을 두고 stirred-flow 방법(方法)을 이용(利用)한 kinetic study를 실내실험(室內實驗)으로 수행(遂行)하였다. 실험(實驗) 결과(結果)는 아래와 같다. 1. 규산(硅酸)의 흡(吸) 탈착량(脫着量)은 실험기간내(實驗期間內)에 최대치(最大値)에 도달(到達)하지 않고 계속(繼續) 증가(增加)하였다. 2. 규산(硅酸)의 흡(吸) 탈착량(脫着量)은 pH증가(增加)와 온도(溫度) 증가(增加)에 따라 크게 증가(增加)하였으며 pH의 영향(影響)은 온도(溫度)의 영향(影響)에 비(比)하여 컸다. 3. 규산(硅酸)의 등온(等溫) 흡착(吸着)은 C type 형태(形態)인 것으로 나타났으며 Freundlich 등온(等溫) 흡착식(吸着式)을 따르는 것으로 나타났다. 4. 탈착(脫着) 과정후(過程後)의 pH 변화(變化)는 낮은 pH처리(處理) 조건(條件)(pH 5, 6.5)에서는 증가(增加)하는 반면(反面) 높은 pH 조건(條件)에서는 감소(減少)하였다. 위의 결과(結果)들을 종합(綜合)하여 볼때 규산(硅酸)의 토양흡착(土壤吸着) 기구(機構)는 다분자층(多分子層) 흡착(吸着)으로서 흡착(吸着)된 규산(硅酸)이 새로운 흡착(吸着)자리를 제공(提供)하나 흡착(吸着)에너지는 흡착량(吸着量)이 배가(培加)될수록 지수적(指數的)으로 감소(減少)되며, 한편 pH 조건(條件)에 따라 흡착(吸着) ligand 형태(形態)가 변(變)하는 것으로 보였다. 5. 규산(硅酸) 흡(吸) 탈착(脫着)의 역학(力學)은 first-order와 parabolic diffusion 역학(力學) 등식(等式)에 잘 부합(附合)되나 이들을 이용(利用)한 흡착기구(吸着機構)에 대(對)한 설명(說明)은 본(本) 실험(實驗)에서 어려웠다. 6. First-order와 parabolic diffusion 역학(力學) 등식(等式)에 사용(使用)되는 fraction term(Fa와 Fd)은 반응속도(反應速度)에 미치는 온도(溫度)의 영향(影響)의 평가(評價)시 나쁜 영향(影響)을 끼치므로 이에 대(對)한 연구(硏究)가 필요(必要)한 것으로 보였다.

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새로운 혼합알고리즘을 이용한 CPFS 내에서의 일어나는 동적 열전달의 수식화 및 해석 (Modeling and analysis of dynamic heat transfer in the cable penetration fire stop system by using a new hybrid algorithm)

  • 윤인섭;윤종필;권성필
    • 한국가스학회지
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    • 제7권4호
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    • pp.44-52
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    • 2003
  • 본 논문은 원자력발전소 방화벽에 설치된 케이블관통부 충전시스템(CPFS: Cable penetration fire stop) 안에서 일어나는 동적 열전달 현상을 수식화하고, 새로운 혼합알고리즘을 이용해서 수치적으로 계산하여, 3차원 그래픽으로 나타내는 작업에 관한 연구이다. CPFS 내에서의 열전도 현상을 주어진 초기조건과 경계조건하에서 포물선 편미분방정식(Parabolic PDE)으로 수식화하였다. 계산을 단순화하기 위하여 전체 열 흐름을 z-축직선상에서의 일어나는 열전도 성분과 x-y-좌표 평면상에서 일어나는 열전도 성분으로 나누었다. z-축과 평행한 직선상에서 일어나는 열전도를 나타내는 PDE는 연속과완화법(SOR: Sequential over-relaxation)을 이용하여 유한불연속 점들에 대한 연립상미분방정식(ODE)으로 만들어서 풀었고, x-y-좌표 평면상에서 일어나는 열전도에 관한 PDE는 Galerkin 유한요소법(FEM: Finite element method)을 적용하여 ODE로 전환해서 풀었다. 여기서 시간과 공간의 함수인 온도는 각 직선상의 점들과 각 평면상의 요소절점들에 대해서 일정한 시간간격으로 초기온도와 경계온도를 업데이트하여 번갈아 가며 계산한다. 이러한 일련의 계산결과를 바탕으로 CPFS시스템 내에서의 온도분포의 동적인 변화를 계산해 낼 수 있었다. 결론적으로 관통하는 케이블이 CPFS시스템의 온도분포에 매우 중요한 역할을 한다는 것을 알 수 있었다. 시뮬레이션 결과는 CPFS내의 온도분포를 쉽게 이해할 수 있도록 3차원 그래픽으로 나타냈으며, 관통하는 케이블이 방화시스템의 온도분포에 매우 중요한 영향을 끼친다는 것을 알 수 있었다. 마지막으로 계산결과를 실험결과와 직접 비교함으로써, 개발된 모델과 계산 알고리즘의 정당성을 보였다.

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KZK 모델을 이용한 파라메트릭 어레이 음향 신호 처리 (Audio Signal Processing using Parametric Array with KZK Model)

  • 이종현;;이재일;김원호;배진호
    • 한국인터넷방송통신학회논문지
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    • 제9권5호
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    • pp.139-146
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    • 2009
  • 본 논문에서는 파라메트릭 어레이를 이용한 음향신호에 대한 수치 모델링 기법 및 분석 결과를 제시한다. 사용된 음성 파라메트릭 배열의 분석 수치모델은 KZK(Khokhlov-Zabolotskaya-Kuznetsov)로서 KZK수치모델은 시간영역의 차분방정식 알고리즘을 사용하며 파라메트릭배열의 정확한 응답특성이 분석이 가능하다. 시간영역기반의 KZK모델은 음원의 크기와 전송주파수의 영향을 받으며, 가청신호응답은 출력레벨과 빔폭의 크기를 포함한다. 음성신호에 대하여 파라메트릭 배열을 효율적으로 적용시키기 위해서는 고려해야할 요소는 표본화 주파수, 트랜스듀서의 반경 및 변조방식 파라미터 등이 있다. 본 논문에서는 다양한 요소 중 표본화 주파수에 따른 응답신호의 왜곡 분석 및 실험 결과를 시뮬레이션을 통해 제시하였다.

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A refined quasi-3D hybrid-type higher order shear deformation theory for bending and Free vibration analysis of advanced composites beams

  • Meradjah, Mustapha;Bouakkaz, Khaled;Zaoui, Fatima Zohra;Tounsi, Abdelouahed
    • Wind and Structures
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    • 제27권4호
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    • pp.269-282
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    • 2018
  • In this paper, a new displacement field based on quasi-3D hybrid-type higher order shear deformation theory is developed to analyze the static and dynamic response of exponential (E), power-law (P) and sigmoïd (S) functionally graded beams. Novelty of this theory is that involve just three unknowns with including stretching effect, as opposed to four or even greater numbers in other shear and normal deformation theories. It also accounts for a parabolic distribution of the transverse shear stresses across the thickness, and satisfies the zero traction boundary conditions at beams surfaces without introducing a shear correction factor. The beam governing equations and boundary conditions are determined by employing the Hamilton's principle. Navier-type analytical solutions of bending and free vibration analysis are provided for simply supported beams subjected to uniform distribution loads. The effect of the sigmoid, exponent and power-law volume fraction, the thickness stretching and the material length scale parameter on the deflection, stresses and natural frequencies are discussed in tabular and graphical forms. The obtained results are compared with previously published results to verify the performance of this theory. It was clearly shown that this theory is not only accurate and efficient but almost comparable to other higher order shear deformation theories that contain more number of unknowns.

정상교합의 치열궁형태에 관한 연구 (A STUDY OF DENIAL ARCH FORM IN NORMAL OCCLUSION)

  • 조주환;이기수
    • 대한치과교정학회지
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    • 제14권2호
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    • pp.249-261
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    • 1984
  • This study was to investigate the fitness of the dental arch line to the parabola, and to estimate correlation between the parabola and some ratios of the dental arch measurements. The sample was consisted of the 64 plaster casts showing normal occlusion which was taken from males and females of Korea, aging from 15 to 18 years. The photos of occlusal surface of the plaster casts were taken, and 38 landmarks on the film were selected. The 3 dental arch lines on each dental arch were imaged. One is the dental arch line passing the points of the most buccal surfaces of the teeth, another is that passing the buccal cusp tips of the posterior teeth and the incisal edges, and the other is that passing the midpoints of the teeth. The landmarks on the film were digitized, and measurements and statistics were performed by the IBM computer. The results were as follows; 1. The fitness of the dental arch to the parabola was very good. The fitness of thor upper dental arch was above $91\%$, and that of the lower dental arch was $93\%$. 2. The dental arch line passing the points of the most buccal surfaces of teeth was best fit to the parabola, the buccal cusp tip arch line and the midpoint arch line in order. 3. Correlation between the ratio of oblique molar dental height to molar width and the parabola was very high. 4. The ratio of oblique molar dental height to molar width was devided into 4 groups by the quartiles, and mean parabolic equations and curves were calculated and drawn.

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On Implementation of the Finite Difference Lattice Boltzmann Method with Internal Degree of Freedom to Edgetone

  • Kang, Ho-Keun;Kim, Eun-Ra
    • Journal of Mechanical Science and Technology
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    • 제19권11호
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    • pp.2032-2039
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    • 2005
  • The lattice Boltzman method (LBM) and the finite difference-based lattice Boltzmann method (FDLBM) are quite recent approaches for simulating fluid flow, which have been proven as valid and efficient tools in a variety of complex flow problems. They are considered attractive alternatives to conventional finite-difference schemes because they recover the Navier-Stokes equations and are computationally more stable, and easily parallelizable. However, most models of the LBM or FDLBM are for incompressible fluids because of the simplicity of the structure of the model. Although some models for compressible thermal fluids have been introduced, these models are for monatomic gases, and suffer from the instability in calculations. A lattice BGK model based on a finite difference scheme with an internal degree of freedom is employed and it is shown that a diatomic gas such as air is successfully simulated. In this research we present a 2-dimensional edge tone to predict the frequency characteristics of discrete oscillations of a jet-edge feedback cycle by the FDLBM in which any specific heat ratio $\gamma$ can be chosen freely. The jet is chosen long enough in order to guarantee the parabolic velocity profile of a jet at the outlet, and the edge is of an angle of $\alpha$=23$^{o}$. At a stand-off distance w, the edge is inserted along the centerline of the jet, and a sinuous instability wave with real frequency is assumed to be created in the vicinity of the nozzle exit and to propagate towards the downstream. We have succeeded in capturing very small pressure fluctuations resulting from periodic oscillation of the jet around the edge.

A Parametric Study on Ethanol Production from Xylose by Pichia stipitis

  • Lee Tae-Young;Kim Myoung-Dong;Kim Kyu-Yong;Park Kyungmoon;Ryu Yeon-Woo;Seo Jin-Ho
    • Biotechnology and Bioprocess Engineering:BBE
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    • 제5권1호
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    • pp.27-31
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    • 2000
  • Characteristics of ethanol production by a xylose-fermenting yeast, Pichia stipitis Y-7124, were studied. The sugar consumption rate and specific growth rate were higher in the glucose-containing medium than in the xylose-containing medium. Specific activities of xylose reductase and xylitol dehydrogenase were higher in the medium with xylose than glucose, suggesting their induction by xylose. Maximum specific growth rate and ethanol yield were achieved at 30 g xylose/L concentration without formation of by-products such as xylitol and acetic acid whereas a maximum ethanol concentration was obtained at 130 g/L xylose. Adding a respiratory inhibitor, rotenone, increased a maximum ethanol concentration by $10\%$ compared with the control experiment. In order to evaluate the pattern of ethanol inhibition on specific growth rate, a kinetic model based on Luong's equations was applied. The relationship between ethanol concentration and specific growth rate was hyperbolic for glucose and parabolic for xylose. A maximum ethanol concentration at which cells did not grow was 33.6 g/L for glucose and 44.7 g/L for xylose.

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Analytical investigation of bending response of FGM plate using a new quasi 3D shear deformation theory: Effect of the micromechanical models

  • Bouiadjra, Rabbab Bachir;Mahmoudi, Abdelkader;Benyoucef, Samir;Tounsi, Abdelouahed;Bernard, Fabrice
    • Structural Engineering and Mechanics
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    • 제66권3호
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    • pp.317-328
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    • 2018
  • In this paper, a new refined quasi-three-dimensional (3D) shear deformation theory for the bending analysis of functionally graded plate is presented. The number of unknown functions involved in this theory is only four against five or more in the case of the other shear and normal deformation theories. Due to its quasi-3D nature, the stretching effect is taken into account in the formulation of governing equations. In addition, the effect of different micromechanical models on the bending response of these plates is studied. Various micromechanical models are used to evaluate the mechanical characteristics of the FG plates whose properties vary continuously across the thickness according to a simple power law. The present theory accounts for both shear deformation and thickness stretching effects by a parabolic variation of displacements across the thickness, and the zero traction boundary conditions on the top and bottom surfaces of the plate without using shear correction factors. The problem is solved for a plate simply supported on its edges and the Navier solution is used. The results of the present method are compared with others from the literature where a good agreement has been found. A detailed parametric study is presented to show the effect of different micromechanical models on the flexural response of a simply supported FG plates.

A nonlocal zeroth-order shear deformation theory for free vibration of functionally graded nanoscale plates resting on elastic foundation

  • Bounouara, Fatima;Benrahou, Kouider Halim;Belkorissat, Ismahene;Tounsi, Abdelouahed
    • Steel and Composite Structures
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    • 제20권2호
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    • pp.227-249
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    • 2016
  • The objective of this work is to present a zeroth-order shear deformation theory for free vibration analysis of functionally graded (FG) nanoscale plates resting on elastic foundation. The model takes into consideration the influences of small scale and the parabolic variation of the transverse shear strains across the thickness of the nanoscale plate and thus, it avoids the employ use of shear correction factors. Also, in this present theory, the effect of transverse shear deformation is included in the axial displacements by using the shear forces instead of rotational displacements as in available high order plate theories. The material properties are supposed to be graded only in the thickness direction and the effective properties for the FG nanoscale plate are calculated by considering Mori-Tanaka homogenization scheme. The equations of motion are obtained using the nonlocal differential constitutive expressions of Eringen in conjunction with the zeroth-order shear deformation theory via Hamilton's principle. Numerical results for vibration of FG nanoscale plates resting on elastic foundations are presented and compared with the existing solutions. The influences of small scale, shear deformation, gradient index, Winkler modulus parameter and Pasternak shear modulus parameter on the vibration responses of the FG nanoscale plates are investigated.

Low-dimensional modelling of n-type doped silicene and its carrier transport properties for nanoelectronic applications

  • Chuan, M.W.;Lau, J.Y.;Wong, K.L.;Hamzah, A.;Alias, N.E.;Lim, C.S.;Tan, M.L.P
    • Advances in nano research
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    • 제10권5호
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    • pp.415-422
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    • 2021
  • Silicene, a 2D allotrope of silicon, is predicted to be a potential material for future transistor that might be compatible with present silicon fabrication technology. Similar to graphene, silicene exhibits the honeycomb lattice structure. Consequently, silicene is a semimetallic material, preventing its application as a field-effect transistor. Therefore, this work proposes the uniform doping bandgap engineering technique to obtain the n-type silicene nanosheet. By applying nearest neighbour tight-binding approach and parabolic band assumption, the analytical modelling equations for band structure, density of states, electrons and holes concentrations, intrinsic electrons velocity, and ideal ballistic current transport characteristics are computed. All simulations are done by using MATLAB. The results show that a bandgap of 0.66 eV has been induced in uniformly doped silicene with phosphorus (PSi3NW) in the zigzag direction. Moreover, the relationships between intrinsic velocity to different temperatures and carrier concentration are further studied in this paper. The results show that the ballistic carrier velocity of PSi3NW is independent on temperature within the degenerate regime. In addition, an ideal room temperature subthreshold swing of 60 mV/dec is extracted from ballistic current-voltage transfer characteristics. In conclusion, the PSi3NW is a potential nanomaterial for future electronics applications, particularly in the digital switching applications.