• Title/Summary/Keyword: Exponential Function

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Analysis of Cementation Effect on Small Strain Shear Modulus of Sand (사질토의 미소변형 전단탄성계수에 대한 고결영향 분석)

  • Lee, Moon-Joo;Choo, Hyunwook;Choi, Sung-Kun;Lee, Woojin
    • KSCE Journal of Civil and Environmental Engineering Research
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    • v.29 no.2C
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    • pp.51-58
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    • 2009
  • In this study, the small strain shear moduli ($G_{max}$) of uncemented and gypsum-cemented sands are evaluated by performing a series of bender element tests on the specimens reconstituted in the calibration chamber. It is observed from the experimental results that $G_{max}$ of crushed-sands is about 35~50% smaller than that of natural sands. The increase in gypsum content is observed to result in an exponential increase of $G_{max}$ value. It is also shown that the relative density has more significant effect on $G_{max}$ of cemented sand, whereas the vertical effective stress has more significant influence on $G_{max}$ of uncemented one. A prediction equation for cemented sand is expressed as a function of gypsum content as well as void ratio and vertical effective stress.

Correlation Between Tensile Strength of Diaphragm and Resonance Frequency for Micro-Speaker (원형 마이크로스피커 진동판의 인장강도와 공명진동수 사이의 연관성)

  • Oh, Sei-Jin;Kim, Hae-Young
    • The Journal of the Acoustical Society of Korea
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    • v.28 no.4
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    • pp.299-307
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    • 2009
  • In this study, the acoustical properties of micro-speaker had been studied as a function of diaphragm patterns. The diaphragm was divided into two sections, such as edge and dome sides. The pattern change at each side affected the tensile strength of diaphragm. As a result, the resonance frequency was varied with the change. With increasing the number of pattern at the edge side, it was increased at the first, but it reversed to the exponential decrease of that. It increased due to the increase of tensile strength to be caused by using "U" type of drill and whirlwind pattern, and decreasing of drill angle at the edge side. However, it was decreased due to the decrease of tensile strength to be by increasing the number of radiation pattern and dome hight, and decreasing the dome radius at the dome side.

Service life evaluation of HPC with increasing surface chlorides from field data in different sea conditions

  • Jong-Suk Lee;Keun-Hyeok Yang;Yong-Sik Yoon;Jin-Won Nam;Seug-Jun Kwon
    • Advances in concrete construction
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    • v.16 no.3
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    • pp.155-167
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    • 2023
  • The penetrated chloride in concrete has different behavior with mix proportions and local exposure conditions, even in the same environments, so that it is very important to quantify surface chloride contents for durability design. As well known, the surface chloride content which is a key parameter like external loading in structural safety design increases with exposure period. In this study, concrete samples containing OPC (Ordinary Portland Cement), GGBFS (Ground Granulated Blast Furnace Slag), and FA (Fly Ash) had been exposed to submerged, tidal, and splash area for 5 years, then the surface chloride contents changing with exposure period were evaluated. The surface chloride contents were obtained from the chloride profile based on the Fick's 2nd Law, and the regression analysis for them was performed with exponential and square root function. After exposure period of 5 years in submerged and tidal area conditions, the surface chloride content of OPC concrete increased to 6.4 kg/m3 - 7.3 kg/m3, and the surface chloride content of GGBFS concrete was evaluated as 7.3 kg/m3 - 11.5 kg/m3. In the higher replacement ratio of GGBFS, the higher surface chloride contents were evaluated. The surface chloride content in FA concrete showed a range of 6.7 kg/m3 to 9.9 kg/m3, which was the intermediate level of OPC and GGBFS concrete. In the case of splash area, the surface chloride contents in all specimens were from 0.59 kg/m3 to 0.75 kg/m3, which was the lowest of all exposure conditions. Experimental constants available for durability design of chloride ingress were derived through regression analysis over exposure period. In the concrete with GGBFS replacement ratio of 50%, the increase rate of surface chloride contents decreased rapidly as the water to binder ratio increased.

Simulation of the Phase-Type Distribution Based on the Minimal Laplace Transform (최소 표현 라플라스 변환에 기초한 단계형 확률변수의 시뮬레이션에 관한 연구)

  • Sunkyo Kim
    • Journal of the Korea Society for Simulation
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    • v.33 no.1
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    • pp.19-26
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    • 2024
  • The phase-type, PH, distribution is defined as the time to absorption into a terminal state in a continuous-time Markov chain. As the PH distribution includes family of exponential distributions, it has been widely used in stochastic models. Since the PH distribution is represented and generated by an initial probability vector and a generator matrix which is called the Markovian representation, we need to find a vector and a matrix that are consistent with given set of moments if we want simulate a PH distribution. In this paper, we propose an approach to simulate a PH distribution based on distribution function which can be obtained directly from moments. For the simulation of PH distribution of order 2, closed-form formula and streamlined procedures are given based on the Jordan decomposition and the minimal Laplace transform which is computationally more efficient than the moment matching methods for the Markovian representation. Our approach can be used more effectively than the Markovian representation in generating higher order PH distribution in queueing network simulation.

An Optimum Design of Steel Frames by Second Order Elastic Analysis (2차 탄성해석법에 의한 강뼈대 구조물의 최적설계)

  • Park, Moon-Ho;Jang, Chun-Ho;Kim, Ki-Wook
    • Journal of the Korea institute for structural maintenance and inspection
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    • v.10 no.2
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    • pp.123-133
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    • 2006
  • The main objective of this study is to develop an optimization algorithm of framed structures with rigid and various semi-rigid connections using the multilevel dynamic programming and the sequential unconstrained minimization techniques (SUMT). The second-order elastic analysis is performed for steel framed structures. The second order elastic analysis is developed based on nonlinear beam-column theory considering the bowing effect. The following semi-rigid connections are considered; double web angle, top-seat angle and top-seat angle with web angle. We considered the three connection models, such as modified exponential, polynomial and three parameter model. The total weight of the structural steel is used as the objective function in the optimization process. The dimensions of steel cross section are selected as the design variables. The design constraints consist of strength requirements for axial, shear and flexural resistance and serviceability requirements.

Target Size of $(Na^++K^+)$-ATPase and $Na^+,\;K^+)$Pump of Human Erythrocytes (사람 적혈구막의 $(Na^++K^+)-ATPase/Na^+,\;K^+\;Pump$의 Target Size)

  • Hah, Jong-Sik;Jung, Chan Y.
    • The Korean Journal of Physiology
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    • v.19 no.1
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    • pp.15-23
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    • 1985
  • Previous biochemical studies indicate that $(Na^++K^+)-ATPase$ is composed of two subunits, ${\alpha}$ and ${\beta}$, in a form of ${\alpha}_2{\beta}_2$ with a molecular weight of approximately 300,000 daltons. There is also suggestive evidence that the $Na^+$, $K^+$ pump in human erythrocytes occurs in a complex with some glycolytic enzymes. We assessed here in situ assembly size of the $(Na^++K^+)-ATPase$ of human erythrocytes by applying classical target theory to radiation inactivation data of the ouabain-sensitive sodium flux and ATP hydrolysis of intact cells and ghosts. Cells(in the presence of cryoprotective agent) and ghosts were irradiated at $-45^{\circ}C$ to $-50^{\circ}C$ with an increasing dose of a 1.5 MeV electron beam, and after thawing, the pump and/or enzyme activities were assayed. Each activity measured was decreased as a simple exponential function of radiation dose, from which a radiation sensitive volume (target size) was calculated. When intact cells were used, the target size of both $(Na^++K^+)-ATPase$ and $Na^+$, $K^+$ pump was found to be approximately 600,000 daltons. This target size of the ATPase was reduced to approximately 325,000 daltons if the cells were pretreated with strophanthidin. When ghosts were used, the target size of the ATPase was again approximately 325,000 daltons. Our target size measurement suggests that, in intact cells, the $(Na^++K^+)-ATPase/Na^+,K^+$ pump exists either as a dimer of $(\alpha\beta)_2$ which is a functional unit or as a monomer of $(\alpha\beta)_2$ but in tight complex with other enzyme or enzymes. The results also suggest that this dimeric or heterocomplex association is dissociated during ghost preparation and strophanthidin treatment.

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Comparison of Disk Tension Infiltrometer and van Genuchten-Mualem Model on Estimation of Unsaturated Hydraulic Conductivity (장력 침투계(Disk Tension Infiltrometer)와 van Genuchten-Mualem 모형 적용에 따른 불포화수리 전도도의 비교 해석)

  • Hur, Seung-Oh;Jung, Kang-Ho;Park, Chan-Won;Ha, Sang-Keun;Kim, Geong-Gyu
    • Korean Journal of Soil Science and Fertilizer
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    • v.39 no.5
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    • pp.259-267
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    • 2006
  • Hydraulic conductivity is the rate of water flux on hydraulic gradient. The van Genuchten Mualem (VGM) model is frequently used for describing unsaturated state of soils, that is composed with the function of soil water potential and soil water content and requests various parameters. This study is to get the value of VGM parameters used Rosetta computer program based on neural network analysis method and to calculate VGM parameters. VGM parameters included Ko(effective saturated hydraulic conductivity), ${\theta}r$(residual soil water content), ${\theta}s$(saturated soil water content), L, n and m. The unsaturated hydraulic conductivity at 10 kPa was calculated by using Rosetta program. Unsaturated hydraulic conductivities of 17 soil series at 1, 3, 5, 7 kPa were also obtained by applying saturated hydraulic conductivity by disk tension infiltrometer based on Gardner and Wooding's equation. Water flow at the water potential of 3 kPa was very low except Namgye, Hagog, Baegsan, Sangju, Seogcheon, Yesan soil series. Unsaturated hydraulic conductivity at 1 kPa showed the highest value for Samgag soil series and was in order of Yesan, Hwabong, Hagog and Baegsan soil series. Those of Gacheon, Seocheon and Ugog soil series were very low. When the value by VGM was compared with the value by disc tension infiltrometer, there was a tendency with exponential function to soils without gravel but there was no tendency to soils including gravel. Conclusively, it would be limited that VGM model for unsaturated hydraulic conductivity analysis applies to Korean agricultural land including gravel and having steep slope, shallow soil depth.

Study on Local Bus Service after Bus Route Reform in Busan (버스노선개편 이후 부산 시내버스 운행실태에 관한 고찰)

  • Song, Ki-Wook;Jung, Hun-Young;Lee, Joon-Seung
    • Journal of Korean Society of Transportation
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    • v.26 no.3
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    • pp.41-51
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    • 2008
  • As the local bus service diagram after the bus route reform is studied by variable analysis based on traffic card data and income adjustment data, the characteristic of the local bus system is revealed in Busan Metropolitan city. The relationship between traveling length and traveling time is influenced by traveling velocity. In order to keep a headway within 10 minutes, bus service number per minute should be over 0.1013 vehicles. The traveling time of afternoon is generally longer than that of forenoon. Compared with the bus used by a lot people, the deviation of that used by a few people is larger in the all cases of length, headway, time and velocity. According to the analysis of the relationship among card trip number, average income and transfer rate, the relationship between card trip number and average income is expressed as linear function in the general bus and as exponential function in the high-grade & rapid bus. The 1% increase of transfer rate is equal to 6.3 trip/vehicle/day decrease and 4.9 trip/vehicle/day decrease in two bus types respectively. The four effective variables are defined by the discriminant analysis between the profitable routes and the unprofitable; According to discriminant size, bus service number per km, bus via suburb, subway meeting number, bus via university. In order to increase the income when the minibus will be included among public transit transfer system in 2008, it should be necessary to settle the bus network and revitalize the public transit better. In order to decrease the cost, it should be necessary to reorganize the hierarchy between the local bus and the minibus better.

The Production Objectives and Optimal Standard of Density Control Using Stand Density Management Diagram for Pinus densiflora Forests in Korea (임분밀도관리도를 이용한 소나무림의 적정 임분밀도 관리 기준 및 수확목표)

  • Park, Joon-hyung;Jung, Su-Young;Yoo, Byung-oh;Lee, Kwang-Soo;Park, Yong-bae;Kim, Hyung-Ho
    • Journal of Korean Society of Forest Science
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    • v.106 no.4
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    • pp.457-464
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    • 2017
  • This study has utilized the stand density management diagram to devise an efficient management standard for the stand density for Pinus densiflora that secures the health of the stands and predicted the harvest goals. The appropriate stand control level was estimated by modeling the relationship of the relative yield index (Ry) to the ratio of slender trees within the stand through an exponential function; the coefficient of determination ($R^2$) was found to be 0.424 according to the estimation. The ratio of slender trees within the stand showed a tendency of rapid increase at a certain relative yield index; with this relational function, the appropriate Ry value of 0.84 was obtained. By estimating the curve of the Ry value 0.84, which was the appropriate stand density management level, as well as the height of dominant trees in the central region of Korea, the production objective for each site index was set. Assuming that the final age by the site indices ranged from 10 to 16 for the P. densiflora in central region of Korea, the number of production was estimated to be between 426 to 1,311 trees per ha. It was predicted that the production of medium-diameter logs larger than 30 cm in diameter is possible for the target DBH at a site index of more than 16; small-diameter logs larger than 20 cm in diameter for site indices 12 and 14 enabled, and small-diameter logs of less than 20 cm for site index 10.

Effects of the irrigation Rate on Wetted Patterns in Sandy Loam Soil Under Trickle irrigation Condition (점적관개에서 관개율이 Sandy Loam토양의 습윤양상에 미치는 영향)

  • 김철수;이근후
    • Magazine of the Korean Society of Agricultural Engineers
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    • v.31 no.2
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    • pp.104-115
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    • 1989
  • In an effort to clarify the wetted patterns of sandy loam soil under trickle irrigation conditions, the distance of wetted zone, infiltration capacity and soil wetted patterns, etc. were measured by gypsum block as soil moisture sensor located every 5 cm vertically and horizontaly in the soil bin under the such conditions as a). irrigation rates set to 2, 4, 6, 8 liters per hour b). total amount of water applied fixed to 14.62 liters per soil bin c) the hearing force of soil measured by plate penetrometer ranging from 1.04 to 1.22kg/cm$_2$ The results can be summarized as follows ; 1. The wetted distance in horizontal direction(H), the wetted distance in vertical direction(D), the horizontal infiltration capacity (iH) and the vertical infiltration capacity(in)could by explained as a function of time t. 2. The horizontal wetted distance (H) is explained by an exponetial function H= a$.$ t where b was found ranging from 021 to 026 under surface trickle irrigation, which was considered a lotlower than the classical value of 0.5 and these measurements were indifferent to the increasing irrigation rates. 3. As for the surface trickle irrigation where horizontal infiltration capacity(iH) is explained as iH = A $.$ t h, the coefficient A increases with respect to irrigation rates within the limits of 0.89~1.34. 4. In terms of surface trickle irrigation of the ratio of Dm Which is maximum vertical wetted distance to Hm, which is maximum horizontal wetted distance, found to be within range of 1.0 to 1.21. It was also noted that the value of Dm decreses when irrigation rates increases while the value of Hm changes the opposite direction. 5. The optimum location of sensors from emitter for surface trickle irrigation should he inside of hemisphere whose lateral radius is 28~30cm long and vertical radius is 10~12cm long. The distance between emitters should be within 60cm long. 6. In the study of vertical wetted distance( D) where D= a $.$ tb, the exponential coefficient b ranged from 0.61 to 0.75 in surface trickle irrigation, and from 0A9 to 0.68 for subsurface trickle irrigation. These measurements showed an increasing tendency to with respect to irrigation rates. 7. In case of vertical infiltration capacity( in), where iD= A $.$ t 1-h, the coefficient A for surface trickle irrigation found to be within range of 0.16 to 0.19 and did not show any relationships with varying degree of irrigation rates. However, the coefficient was varying from 0.09 to 0.22 and showed a tendency to increase vis-a-vis irrigation rates for subsurface trickle irrigation, in contrast. 8. In the observation of subsurface trickle irrigation, it was found that Dm/Hm ratio was within 1.52 to 1.91 and showed a decreasing tendency with respect to increasing rates of irrigation. 9. The location of sensors for subsurface trickle irrigation follows same pattern as above, with vertical distance from emitter being 10~17cm long and horizontal 22~25cm long. The location of emitter should be 50 cm. 10.The relationship between VS which is the volume of wetted soil and Q which is the total amount of water when soil is reached field capacity could be explained as VS= 2.914Q0.91and the irrigation rates showed no impacts on the above relationship.

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