• Title/Summary/Keyword: higher order solution

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TWO-DIMENSIONAL STAGNATION FLOW TOWARD A PLANE WALL COATED WITH MAGNETIC FLUID OF UNIFORM THICKNESS (균일 두께의 자성유체 피막이 있는 평면 벽을 향하는 2차원 정체 유동)

  • Ko, Hyung-Jong;Kim, Kyoung-Hoon;Kim, Se-Woong
    • Journal of computational fluids engineering
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    • v.12 no.4
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    • pp.20-27
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    • 2007
  • Two-dimensional stagnation flow toward a plane wall coated with magnetic fluid of uniform thickness is investigated. The flow field is represented as a similarity solution of the Navier-Stokes equation for this incompressible laminar flow. The resulting third order ordinary differential equation is solved numerically by using the shooting method and by determining two shooting parameters so as to satisfy the boundary and interface conditions. Features of the flow including streamline patterns are investigated for the varying values of density ratio, viscosity ratio, and Reynolds number. An adverse flow with double eddy pair in magnetic fluid region is found to emerge as the Reynolds number becomes higher than a threshold value. The results for the interface velocity, interface and wall shear stress, and boundary layer and displacement thickness are also presented.

Shape Reconstruction from Unorganized Cloud of Points using Adaptive Domain Decomposition Method (적응적 영역분할법을 이용한 임의의 점군으로부터의 형상 재구성)

  • Yoo Dong-Jin
    • Journal of the Korean Society for Precision Engineering
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    • v.23 no.8 s.185
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    • pp.89-99
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    • 2006
  • In this paper a new shape reconstruction method that allows us to construct surface models from very large sets of points is presented. In this method the global domain of interest is divided into smaller domains where the problem can be solved locally. These local solutions of subdivided domains are blended together according to weighting coefficients to obtain a global solution using partition of unity function. The suggested approach gives us considerable flexibility in the choice of local shape functions which depend on the local shape complexity and desired accuracy. At each domain, a quadratic polynomial function is created that fits the points in the domain. If the approximation is not accurate enough, other higher order functions including cubic polynomial function and RBF(Radial Basis Function) are used. This adaptive selection of local shape functions offers robust and efficient solution to a great variety of shape reconstruction problems.

A semi-analytical solution to spherical cavity expansion in unsaturated soils

  • Tang, Jianhua;Wang, Hui;Li, Jingpei
    • Geomechanics and Engineering
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    • v.25 no.4
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    • pp.283-294
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    • 2021
  • This paper presents a rigorous solution for spherical cavity expansion in unsaturated soils under constant suction condition. The hydraulic behavior that describes the saturation-suction relationship is modeled by a void ratio-dependent soil-water characteristic curve, which allows the hydraulic behavior to fully couple with the mechanical behavior that is described by an extended critical state soil model for unsaturated soil through the specific volume. Considering the boundary condition and introducing an auxiliary coordinate, the problem is formulated to a system of first-order differential equations with three principal stress components and suction as basic unknowns, which is solved as an initial value problem. Parameter analyses are conducted to investigate the effects of suction and the overconsolidation ratio on the overall expansion responses, including the pressure-expansion response, the distribution of the stress components around the cavity, and the stress path of the soil during cavity expansion. The results reveal that the expansion pressures and the distribution of the stress components in unsaturated soils are generally higher than those in saturated soils due to the existence of suction.

HIGHER ORDER GALERKIN FINITE ELEMENT METHOD FOR THE GENERALIZED DIFFUSION PDE WITH DELAY

  • LUBO, GEMEDA TOLESSA;DURESSA, GEMECHIS FILE
    • Journal of applied mathematics & informatics
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    • v.40 no.3_4
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    • pp.603-618
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    • 2022
  • In this paper, a numerical solution of the generalized diffusion equation with a delay has been obtained by a numerical technique based on the Galerkin finite element method by applying the cubic B-spline basis functions. The time discretization process is carried out using the forward Euler method. The numerical scheme is required to preserve the delay-independent asymptotic stability with an additional restriction on time and spatial step sizes. Both the theoretical and computational rates of convergence of the numerical method have been examined and found to be in agreement. As it can be observed from the numerical results given in tables and graphs, the proposed method approximates the exact solution very well. The accuracy of the numerical scheme is confirmed by computing L2 and L error norms.

Quality characteristics of semi-dried persimmons soaked in different concentration of sugar solution (당액침지에 따른 반건시 가공품의 품질특성)

  • Kwon, Gi-Man;Kim, Jae-Won;Youn, Kwang-Sup
    • Food Science and Preservation
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    • v.22 no.3
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    • pp.314-321
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    • 2015
  • This study was conducted to investigate the quality and characteristics of semi-dried persimmons soaked in different concentrations of sugar solution and stored at $7^{\circ}C$ for 20 days. The L value and chroma value were significantly higher in S5 and S10 compared to the other concentrations of sugar solution. The ${\Delta}E$ and browning degree were increased according to the increase in concentration of sugar solution. Total sugar, reducing sugar, and sugar free contents were higher in the control (semi-dried persimmon) than those in S0, but they increased according to the increase in concentration of sugar solution. Polyphenol oxidase and peroxidase activities were decreased according to the increase in sugar solution concentration, which were highest in S0 among other semi-dried persimmons soaked in sugar solutions. Total ascorbic acid content was highest in S10 (12.29 mg/g), followed by S0 (2.54 mg/g), S5 (7.76 mg/g), S15 (6.05 mg/g), and S20 (5.05 mg/g). Total polyphenols, flavonoids and proanthocyanidins contents were the highest in S10 compared to other semi-dried persimmons soaked in sugar solutions. Furthermore, the same tendency was observed with DPPH radical scavenging ability. These results showed that 10% sugar solution could be applied to semi-dried persimmons in order to achieve high quality, nutritional value, and browning inhibition.

Effects of processing conditions of sea tangle (Laminaria spp.) alginate film on permeability of ester compounds (에스테르 화합물의 투과율에 영향을 미치는 다시마 Alginate 필름의 가공조건)

  • YOU Byeong-Jin;SHIM Jae-Man
    • Korean Journal of Fisheries and Aquatic Sciences
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    • v.33 no.2
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    • pp.143-147
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    • 2000
  • The effects of alginate extracting conditions from sea tangle and the effects of film preparation conditions on the physical properties of the alginate film were investigated by measuring ester compounds permeability. The higher concentration of sodium carbonate solution as extracting solvent made the higher ethyl acetate permeability of alginate film, but extracting time showed little efficacy of alginate film permeability. The higher concentration of sorbitol as a plasticizer showed higher ethyl acetate permeability of alginate film, Adding various plasticizers, the ethyl acetate permeability of algiante films was increased in order as follow : sorbitol, glycerol and polyethylene glycol. Ester compounds haying the lower molecular weight showed the higher permeability. And the higher temperature made the ethyl acetate permeability of algiante film to be high.

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Effects of Al Content on Microstructure and Hardness of Discontinuous Precipitates Formed by Isothermal Aging in Mg-Al Alloys (Mg-Al 합금에서 등온 시효로 생성된 불연속 석출물의 미세조직과 경도에 미치는 Al 함량의 영향)

  • Jun, Joong-Hwan
    • Journal of the Korean Society for Heat Treatment
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    • v.34 no.6
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    • pp.287-293
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    • 2021
  • This study was intended to investigate the influence of Al content on hardness and microstructural characteristics of discontinuous precipitates (DPs) formed by isothermal aging in Mg-8.7%Al and Mg-10%Al alloys. In order to obtain large amount of DPs in the microstructure, the alloy specimens were solution-treated at 688K for 24 h followed by water quenching, and then aged at 418K for 48h. The Mg-Al alloy with higher Al content was characterized by higher volume fraction of DPs at the same aging condition, lower interlamellar spacing of the DPs, thinner β phase layer and higher β phase content in the DPs. This is closely related to the higher velocity of discontinuous precipitation process resulting from the higher Al supersaturation in the α-(Mg) matrix. The Mg-10%Al alloy showed higher hardness of the DPs and greater difference in hardness between as-cast state and DPs than the Mg-8.7%Al alloy.

Stability of Ascorbic Acid in the Catechin Solution (Catechin용액 중에서 Ascorbic acid의 안정성)

  • Kim, Sang Oak
    • Journal of the Korean Society of Food Science and Nutrition
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    • v.12 no.3
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    • pp.284-288
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    • 1983
  • This experiment was carried out to investigate the stability of ascorbic acid (AsA) in the mixed solution of AsA and catechin according to the content changes of AsA and catechin under boiling, and for the respective concentration and pH. The loss of AsA was most for 10 minutes of boiling and accelerated by the mixture of catechin, but the loss was less in the high mixture rate than in the low the loss of catechin most for 10 minutes of boiling, also as the concentration of AsA becomes higher but that of cathchin lower, and as that of AsA lower but that of catechin higher, the loss of catechin becomes less moreover in the case of the low content ratio of catechin, the stability of AsA was better in order of the pH 4, pH 5, pH 6, namely as the pH increased, but in the case of the high better in order of the pH 6, pH 5, pH 4, that is as in decreased.

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Bending behaviour of FGM plates via a simple quasi-3D and 2D shear deformation theories

  • Youcef, Ali;Bourada, Mohamed;Draiche, Kada;Boucham, Belhadj;Bourada, Fouad;Addou, Farouk Yahia
    • Coupled systems mechanics
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    • v.9 no.3
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    • pp.237-264
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    • 2020
  • This article investigates the static behaviour of functionally graded (FG) plates sometimes declared as advanced composite plates by using a simple and accurate quasi-3D and 2D hyperbolic higher-order shear deformation theories. The properties of functionally graded materials (FGMs) are assumed to vary continuously through the thickness direction according to exponential law distribution (E-FGM). The kinematics of the present theories is modeled with an undetermined integral component and satisfies the free transverse shear stress conditions on the top and bottom surfaces of the plate; therefore, it does not require the shear correction factor. The fundamental governing differential equations and boundary conditions of exponentially graded plates are derived by employing the static version of principle of virtual work. Analytical solutions for bending of EG plates subjected to sinusoidal distributed load are obtained for simply supported boundary conditions using Navier'is solution procedure developed in the double Fourier trigonometric series. The results for the displacements and stresses of geometrically different EG plates are presented and compared with 3D exact solution and with other quasi-3D and 2D higher-order shear deformation theories to verify the accuracy of the present theory.

Enhancement of phosphate removal using copper impregnated activated carbon(GAC-Cu) (Cu(II)를 이용하여 표면개질된 활성탄의 인산염 제거효율 향상)

  • Shin, Jeongwoo;Kang, Seoyeon;An, Byungryul
    • Journal of Korean Society of Water and Wastewater
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    • v.35 no.6
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    • pp.455-463
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    • 2021
  • The adsorption process using GAC is one of the most secured methods to remove of phosphate from solution. This study was conducted by impregnating Cu(II) to GAC(GAC-Cu) to enhance phosphate adsorption for GAC. In the preparation of GAC-Cu, increasing the concentration of Cu(II) increased the phosphate uptake, confirming the effect of Cu(II) on phosphate uptake. A pH experiment was conducted at pH 4-8 to investigate the effect of the solution pH. Decrease of phosphate removal efficiency was found with increase of pH for both adsorbents, but the reduction rate of GAC-Cu slowed, indicating electrostatic interaction and coordinating bonding were simultaneously involved in phosphate removal. The adsorption was analyzed by Langmuir and Freundlich isotherm to determine the maximum phosphate uptake(qm) and adsorption mechanism. According to correlation of determination(R2), Freundlich isotherm model showed a better fit than Langmuir isotherm model. Based on the negative values of qm, Langmuir adsorption constant(b), and the value of 1/n, phosphate adsorption was shown to be unfavorable and favorable for GAC and GAC-Cu, respectively. The attempt of the linearization of each isotherm obtained very poor R2. Batch kinetic tests verified that ~30% and ~90 phosphate adsorptions were completed within 1h and 24 h, respectively. Pseudo second order(PSO) model showed more suitable than pseudo first order(PFO) because of higher R2. Regardless of type of kinetic model, GAC-Cu obtained higher constant of reaction(K) than GAC.