• Title/Summary/Keyword: Non-linear Equation

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A Three-Dimensional Galerkin-FEM Model with Density Variation (밀도 변화를 포함하는 3차원 연직함수 전개모형)

  • 이호진;정경태;소재귀;강관수;정종율
    • Journal of Korean Society of Coastal and Ocean Engineers
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    • v.8 no.2
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    • pp.123-136
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    • 1996
  • A three-dimensional Galerkin-FEM model which can handle the temporal and spatial variation of density is presented. The hydrostatic approximation is used and density effects are included by means of conservation equation of heat and the equation of state. The finite difference grids are used in the horizontal plane and a set of linear-shape functions is used for the vertical expansion. The similarity transform is introduced to solve resultant matrix equations. The proposed model was first applied to the density-driven circulation in an idealized basin in the presence of the heat exchange between the air and the sea. The advection terms in the momentum equation were ignored, while the convection terms were retained in the heat equation. Coefficients of the vertical eddy viscosity and diffusivity were fixed to be constant. Calculation in a non-rotating idealized basin shows that the difference in heat capacity with depth gives rise to the horizontal gradient of temperature. Consequently, there is a steady new in the upper layer in the direction of increasing depth with compensatory counter flow .in the lower layer. With Coriolis force, geostrophic flow was predominant due to the balance between the pressure gradient and the Coriolis force. As a test in region of irregular topography, the model is applied to the Yellow Sea. Although the resultant flow was very complex, the character of the flow Showed to be geostrophic on the whole.

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Mathematical Description of Soil Loss by Runoff at Inclined Upland of Maize Cultivation (옥수수 재배 경사지 밭에서 물 유출에 따른 토양유실 예측 공식)

  • Hur, Seung-Oh;Jung, Kang-Ho;Ha, Sang-Keon;Kwak, Han-Kang;Kim, Jeong-Gyu
    • Korean Journal of Soil Science and Fertilizer
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    • v.38 no.2
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    • pp.66-71
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    • 2005
  • Soil loss into stream and river by runoff shall be considered for non-point source pollution management as national land conservation. The purpose of this study was to develop the mathematical equation to predict soil loss from inclined uplands of maize cultivation due to the runoff by rainfall which mainly converges on July and August. Soil loss was concentrated on May because of low canopy over an entire field in 2002 and on June and July because of heavy rainfall in 2003. By regression analysis the relation between runoff and soil loss can be represented by a linear equation of y =1.5291x - 3.4933, where y is runoff ($Mg\;ha^{-1}$) and x is soil loss ($kg\;ha^{-1}$). The determination coefficient of this equation was 0.839 (P<0.001). Therefore, the mathematical equation derived from the practical experiment at the inclined upland can be applicable to predict soil loss accompanied by runoff due to periodic rainfall converging on short periods within a couple of months.

A Study on The Velocity Distribution in Closed Conduit by Using The Entropy Concept (엔트로피 개념을 이용한 관수로내의 유속분포에 관한 연구)

  • Choo, Tai Ho;Ok, Chi Youl;Kim, Jin Won;Maeng, Seung Jin
    • KSCE Journal of Civil and Environmental Engineering Research
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    • v.29 no.4B
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    • pp.357-363
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    • 2009
  • When yields the mean velocity of the closed conduit which is used generally, it is available to use Darcy Weisbach Friction Loss Head equation. But, it is inconvenient very because Friction Loss coefficient f is the function of Reynolds Number and Relative roughness (${\varepsilon}$/d). So, it is demanded more convenient equation to estimate. In order to prove the reliability and an accuracy of Chiu's velocity equation from the research which sees hereupon, proved agreement very well about measured velocity measurement data by using Laser velocimeter which is a non-insertion velocity measuring equipment from the closed conduit (Laser Doppler Velocimeter: LDV) and an insertion velocity measuring equipment and the Pitot tube which is a supersonic flow meter (Transit-Time Flowmeters). By proving theoretical linear-relation between maximum velocity and mean velocity in laboratory flume without increase and decrease of discharge, the equilibrium state of velocity in the closed conduit which reachs to equilibrium state corresponding to entropy parameter M value has a trend maintaining consistently this state. If entropy M value which is representing one section is determinated, mean velocity can be gotten only by measuring the velocity in the point appearing the maximum velocity. So, it has been proved to estimate simply discharge and it indicates that this method can be a theoretical way, which is the most important in the future, when designing, managing and operating the closed conduit.

Development of a Simulation Program to Predict the Performance of the Multi-grade Lubricant before Blending Base Oil with Additives (기유와 첨가제 혼합 전 다등급 윤활유의 성능 예측 시뮬레이션 프로그램 개발)

  • Chun, Sang-Myung
    • Tribology and Lubricants
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    • v.28 no.2
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    • pp.47-55
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    • 2012
  • Generally, to product multi-grade oil like engine oil, a sort of mineral base oil is mixed with a fundamental additive package liquid and a polymer liquid as viscosity index improver in order to improve the lubricating property of base oil. That is, engine oil is the mixture of more than two fluids. Specially, a polymeric type liquid cannot be seen as the linear viscosity like Newtonian fluids. In this research, by using the governing equation describing non-Newtonian hydrodynamic lubrication related with the mixture of incompressible fluids based on the principle of continuum mechanics, it will be compared the bearing performance between the mixture of each liquid to be blended and multi-grade engine oil as a single fluid in a high speed hydrodynamic journal bearing. Further, it is to be found the way estimating the performance of the blended multi-grade engine lubricant in a journal bearing in advance before blending by using the physical properties of mineral base oil, fundamental additive liquid and polymer liquid of viscosity index improver. So, it can be reduced the number of trial and error to get the wanted lubricant by selecting the proper volume fraction of each liquid to satisfy the expected performance and estimating in advance the performance of various multi-grade oils before blending. Therefore, it can be shorten the developing time and saved the developing cost.

A Study on the Structural Reliability (구조물(構造物)의 신뢰성(信賴性)에 관한 소고(小考) -원형단면의 인장재를 중심으로-)

  • Son, Seung Yo
    • KSCE Journal of Civil and Environmental Engineering Research
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    • v.5 no.2
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    • pp.51-57
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    • 1985
  • In the design of civil engineering structures, the designers are invariably faced to the uncertainties and the randomness of the design parameters such as material properties and loads. Even when the structures are built, the actual geometries of the structures are also subject to their random variations from their nominal design values. Thus, the reliability of a structure in terms of these uncertainties and variations becomes a matter of great concern to the structural designers. This study employs the First Order Second Moment Method to evluate numerically the reliability of a simple tension member and discusses the influence on the final failure probability of that structure due to: 1) use of equivalent normal distribution in place of non-normal distribution, 2) linearization of non linear limit state equation. A discussion is also made on the necessity of fundamental studies on the distrubution characteristics of the strength of locally produced construction materials and those of the loads frequently encountered in the structural design.

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Characterization of Rice lodging by Factor analysis (요인분석을 이용한 벼 도복 특성 분석)

  • Seo, Young-Jin;Huh, Min-Soon;Kim, Chang-Bae;Lee, Dong-Hoon;Choi, Jung;Kim, Chan-Yong
    • Korean Journal of Soil Science and Fertilizer
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    • v.34 no.3
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    • pp.173-177
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    • 2001
  • This study was conducted to investigate a potential utilitization of multivariate statistical analysis(Factor analysis, Discrimination analysis) on interpretation of rice plant lodging reason. Rice plants were sampled in paddy around Taegu city at from 25 to 29 of September in 2000. Mineral nutrient content(phosphate, potassium) of rice plant were significantly higher at 99% level, Silicate content were lower at 95% level in lodged samples than in normal. Plant characteristics associate with lodging(Culm length, second and third internode length, bight of center gravity) were significantly longer in lodged rice plant than in non lodged. Result of Factor analysis were that first principle component were culm length, second(N2) and third internode length(N3), second principle component were Ca content, first internode length(N1) and N3/culm length, third principle component were center gravity length(G) and G/culm length, fourth were nitrogen, phosphate, and potassium content, fifth were N2/culm length, N2+N3/culm length, Sixth was silicate content of rice plant. Linear discriminant equation distinguished lodged rice plants with non lodged rice plants very well. Prediction value was 100%, most explainable variable were phosphate content, culm length and third length.

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Comparative Analysis of Subsurface Estimation Ability and Applicability Based on Various Geostatistical Model (다양한 지구통계기법의 지하매질 예측능 및 적용성 비교연구)

  • Ahn, Jeongwoo;Jeong, Jina;Park, Eungyu
    • Journal of Soil and Groundwater Environment
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    • v.19 no.4
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    • pp.31-44
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    • 2014
  • In the present study, a few of recently developed geostatistical models are comparatively studied. The models are two-point statistics based sequential indicator simulation (SISIM) and generalized coupled Markov chain (GCMC), multi-point statistics single normal equation simulation (SNESIM), and object based model of FLUVSIM (fluvial simulation) that predicts structures of target object from the provided geometric information. Out of the models, SNESIM and FLUVSIM require additional information other than conditioning data such as training map and geometry, respectively, which generally claim demanding additional resources. For the comparative studies, three-dimensional fluvial reservoir model is developed considering the genetic information and the samples, as input data for the models, are acquired by mimicking realistic sampling (i.e. random sampling). For SNESIM and FLUVSIM, additional training map and the geometry data are synthesized based on the same information used for the objective model. For the comparisons of the predictabilities of the models, two different measures are employed. In the first measure, the ensemble probability maps of the models are developed from multiple realizations, which are compared in depth to the objective model. In the second measure, the developed realizations are converted to hydrogeologic properties and the groundwater flow simulation results are compared to that of the objective model. From the comparisons, it is found that the predictability of GCMC outperforms the other models in terms of the first measure. On the other hand, in terms of the second measure, the both predictabilities of GCMC and SNESIM are outstanding out of the considered models. The excellences of GCMC model in the comparisons may attribute to the incorporations of directional non-stationarity and the non-linear prediction structure. From the results, it is concluded that the various geostatistical models need to be comprehensively considered and comparatively analyzed for appropriate characterizations.

Effect of De-hulling on Ileal Amino Acids Digestibility of Soybean Meals Fed to Growing Pigs

  • Kang, Y.F.;Li, D.F.;Xing, J.J.;Mckinnon, P.J.;Sun, D.Y.
    • Asian-Australasian Journal of Animal Sciences
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    • v.16 no.6
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    • pp.928-939
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    • 2003
  • A study was carried out to determine the effect of de-hulling on apparent and true ileal amino acids digestibility of soybean meals for growing pigs. Twenty barrows (Duroc${\times}$Large white${\times}$Longer white) were fitted with a simple T-cannula at the distal ilium. Digestibility of 20 experimental diets was determined, nine of them were de-hulled soybean meal diets, and nine of them were regular soybean meal diets and two low protein casein diets for determination of endogenous amino acid correction for true digestibility determination. A TEX>$5<{\times}5<$ Latin Squares Design was adopted in this trail. The results showed that de-hulling increased apparent ileal digestibility of isoleucine, threonine, aspartic, tyrosine and indispensable and dispensable amino acid (p<0.05) in soybean meals. Furthermore, dehulling is also increased apparent digestibility of arginine, leucine, lysine, phenylalanine, alanine, glutamic acid, serine and gross amino acids (p<0.01). However, there were no significant differences found for histidine, methionine, tryptophan, cystine and glycine (p>0.05). Similar responses were found for true ileal digestibility. In three dehulled and non-dehulled pairs soybean meals from the same respective sources, de-hulling increased apparent digestibility of lysine, methionine, threonine and cystine 1.42%, 2.06%, 2.18% and 1.40% respectively. True digestibility of lysine, methionine, threonine and cystine was increased 1.65%, 1.94%, 2.30% and 1.82% respectively. A prediction equation for true ileal amino acid digestibility (including lysine and arginine) was established by multivariate linear regression. The independent variables included relevant amino acid, organic matter, crude protein, ether extract and nitrogen free extract. The coefficient R2 values of lysine and agrinine were 0.596 and 0.531 respectively. According to the crude protein content, a prediction equation for lysine and arginine content in soybean meal was also established by single linear regression. The coefficient $R^2$ values of lysine and agrinine were 0.636 and 0.636 respectively.

Age and Growth of the Jedo Venus Clam, Protothaca jedoensis on the West Coast of Korea (한국 서해산 살조개 Protothaca jedoensis의 연령과 성장)

  • Kim, Ji-Hyun;Kim, Jong-Sheek;Kim, Yong-Ho;Chung, Ee-Yung;Ryu, Dong-Ki
    • The Korean Journal of Malacology
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    • v.19 no.2
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    • pp.125-132
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    • 2003
  • Age and growth of the the Jedo venus clam, Protothaca jedoensis were investigated using samples from the subtidal zone of Boryeong, Chungcheongnam- do, Korea from January to December, 1999. The relationship between shell height and ring radius in each group was expressed as a regression line. Therefore, it could be recognized that there is a correspondence in the formation of each ring. Based on the monthly variation of the marginal index of the shell, it was suggested that the annual ring mark formation occurred during the period of February to March once a year. The relationship between shell height (SH) and total weight (TW) was represented by the non-linear equation: TW = 0.0007 SH$^{2.8919}$, and also in the relationship between shell length (SL) and shell height (SH), shell height (SH) and shell width (SW) were represented by the linear equations: SL=1.1067SH+1.778, SW=0.6758SH-0.9824. Growth curves for shell height and total weight fitted to the von Bertalanffy equation were expressed as: SH$_t$ = 81.546(1-e$^{-0.176(t+0.381)}$), TW$_t$ = 227.65(1-e$^{-0.176(t+0.381)})^{2.8919}$.

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Development of FURA Code and Application for Load Follow Operation (FURA 코드 개발과 부하 추종 운전에 대한 적용)

  • Park, Young-Seob;Lee, Byong-Whi
    • Nuclear Engineering and Technology
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    • v.20 no.2
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    • pp.88-104
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    • 1988
  • The FUel Rod Analysis(FURA) code is developed using two-dimensional finite element methods for axisymmetric and plane stress analysis of fuel rod. It predicts the thermal and mechanical behavior of fuel rod during normal and load follow operations. To evaluate the exact temperature distribution and the inner gas pressure, the radial deformation of pellet and clad, the fission gas release are considered over the full-length of fuel rod. The thermal element equation is derived using Galerkin's techniques. The displacement element equation is derived using the principle of virtual works. The mechanical analysis can accommodate various components of strain: elastic, plastic, creep and thermal strain as well as strain due to swelling, relocation and densification. The 4-node quadratic isoparametric elements are adopted, and the geometric model is confined to a half-pellet-height region with the assumption that pellet-pellet interaction is symmetrical. The pellet cracking and crack healing, pellet-cladding interaction are modelled. The Newton-Raphson iteration with an implicit algorithm is applied to perform the analysis of non-linear material behavior accurately and stably. The pellet and cladding model has been compared with both analytical solutions and experimental results. The observed and predicted results are in good agreement. The general behavior of fuel rod is calculated by axisymmetric system and the cladding behavior against radial crack is used by plane stress system. The sensitivity of strain aging of PWR fuel cladding tube due to load following is evaluated in terms of linear power, load cycle frequency and amplitude.

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