• Title/Summary/Keyword: Exponential distribution

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Evaluation for Rock Cleavage Using Distribution of Microcrack Spacings (II) (미세균열의 간격 분포를 이용한 결의 평가(II))

  • Park, Deok-Won
    • The Journal of the Petrological Society of Korea
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    • v.25 no.2
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    • pp.151-163
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    • 2016
  • The characteristics of the rock cleavage in Jurassic granite from Geochang were analysed. The evaluation for the three directions of rock cleavages was performed using the parameters such as (1) frequency of microcrack spacing(N), (2) total spacing(${\leq}1mm$), (3) mean spacing($S_{mean}$), (4) difference value($S_{mean}-S_{median}$) between mean spacing($S_{mean}$) and median spacing($S_{median}$), (5) density of spacing(${\rho}$), (6) difference value between two exponents for the whole range of the diagrams(${\lambda}_H-{\lambda}_L$), (7) mean value of exponent(${\lambda}_M$), (8) mean value of exponential constant($a_M$), (9) difference value between two exponents for the section under the initial points of intersection(${\lambda}t_H-{\lambda}t_L$), (10) mean value of exponent(${\lambda}t_M$) and (11) mean value of exponential constant($at_M$). The results of correlation analysis between the values of parameters for three rock cleavages and those for three planes are as follows. The values of (I) parameters(1, 2, 7 and 8) and (II) parameters(3, 4 and 5) are in orders of (I) H(hardway, (H1 + H2)/2) < G(grain, (G1 + G2)/2) < R(rift, (R1 + R2)/2) and (II) R < G < H. On the contrary, the values of the above two groups(I~II) of parameters for three planes show reverse orders. Besides, the values of parameter $6({\lambda}_H-{\lambda}_L)$, parameter $9({\lambda}t_H-{\lambda}t_L)$, parameter $10({\lambda}t_M)$ and parameter $11(at_M)$ for three planes are in orders of R(rift plane, (G1 + H2)/2) < H(hardway plane, (R2 + G2)/2) < G(grain plane, (R1 + H2)/2), H < G < R, H < R < G and R < H < G, respectively. The values of the above four parameters for three rock cleavages show the various orders of R < H < G, R < H < G, H < G < R and H < G < R, respectively. Meanwhile, the spacing values equivalent to the initial points of contact and intersection between the two directions of diagrams were derived. The above spacing values for three rock cleavages are in order of rift(R1 and R2) < grain(G1 and G2) < hardway(H1 and H2). The spacing values for three planes are in order of rift plane(G1 and H1) < hardway plane(R2 and G2) < grain plane(R1 and H2). In particular, the intersection angles for three rock cleavages and three planes are in order of rift and rift plane < hardway and hardway plane < grain and grain plane. Consequently, the two diagrams of rift(R1 and R2) and rift plane(G1 and H1) show higher frequency of the point of contact and intersection. These characteristics of change were derived through the general chart for three planes and three rock cleavages. Lastly, the correlation analysis through the values of parameters along with the distribution pattern is useful for discriminating three quarrying planes.

Determination of Pedo-Transfer Function Using the Relation Between Soil Particle Distribution, Organic Matter and Water Movement in Soil Originated from Limestone (석회암 유래 토양에서의 물의 이동특성과 토양 입자 및 유기물과의 관계에 따른 Pedo-Transfer Function의 결정)

  • Hur, Seung-Oh;Jung, Kang-Ho;Sonn, Yeon-Kyu;Ha, Sang-Keun;Kim, Jeong-Gyu
    • Korean Journal of Soil Science and Fertilizer
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    • v.42 no.2
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    • pp.132-138
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    • 2009
  • Soils originated from limestone, located at the southern part of Kangwon province and Jecheon, Danyang of Chungbuk province are mainly composed of fine texture, have different properties from soils originated from granite and granite gneiss, especially for water movement. This study was conducted for making PTF(Pedo-Transfer Function) for Kfs(field saturaton hydraulic conductivity) estimation, and for investigating the relation between soil particle distribution and the infiltration and percolation rate in soils originated from limestone. Soils used for the experiment were 6 soils of Gwarim, Mosan, Jangseong, Maji, Anmi and Pyongan series. Infiltration and percolation rate for the soil were measured by a disc tension infiltrometer and a Guelph permeameter, respectively. The particle size distribution and organic matter content of the soils were analyzed. Kfs was not related with sand, silt, clay, and organic mattrer (OM) content because of forest soils which contained high gravel, pebble, and cobble content, and O layer with high OM content. After Mosan soil series and O layer of Gwarim series were excluded for the data analysis, Kfs was explained as a linear function with sand and clay content and a exponential function with OM content. As a result, the PTF equation was obtained as Kfs=-4.20558+0.479706*(S)+0.023187*exp(1.829*OM) ($R^2=0.6558^{*}$).

A Bayesian Estimation of Price for Commercial Property: Using subjective priors and a kriging technique (상업용 토지 가격의 베이지안 추정: 주관적 사전지식과 크리깅 기법의 활용을 중심으로)

  • Lee, Chang Ro;Eum, Young Seob;Park, Key Ho
    • Journal of the Korean Geographical Society
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    • v.49 no.5
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    • pp.761-778
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    • 2014
  • There has been relatively little study to model price for commercial property because of its low transaction volume in the market. Despite of this thin market character, this paper tried to estimate prices for commercial lots as accurate as possible. We constructed a model whose components consist of mean structure(global trend), exponential covariance function and a pure error term, and applied it to actual sales price data of Seoul. We explicitly took account of spatial autocorrelation of land price by utilizing a kriging technique, a representative method of spatial interpolation, because the land price of commercial lots has feature of differential price forming pattern depending on submarkets they belong to. In addition, we chose to apply a bayesian kriging to overcome data scarcity by incorporating experts' knowledge into prior probability distribution. The chosen model's excellent performance was verified by the result from validation data. We confirmed that the excellence of the model is attributed to incorporating both autocorexperts' knowledge and spatial autocorrelation in the model construction. This paper is differentiated from previous studies in the sense that it applied the bayesian kriging technique to estimate price for commercial lots and explicitly combined experts' knowledge with data. It is expected that the result of this paper would provide a useful guide for the circumstances under which property price has to be estimated reliably based on sparse transaction data.

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The Effect of Histamine on the Disappearance Rate of $D_2O$ from the Arterial Blood of Rabbits (토끼 동맥혈로 부터의 $D_2O$ 소실률에 대한 히스타민의 영향)

  • Kim, Kyong-Tai;Shin, Dong-Hoon
    • The Korean Journal of Physiology
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    • v.1 no.1
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    • pp.23-32
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    • 1967
  • Disappearance rate of injected $D_2O$ from the arterial blood as well as the effect of histamine on the rate were studied in rabbits. The concentrations of $D_2O$ in the serial arterial samples obtained through a Polyethylene tubing inserted into the carotid artery were assayed by the freezing point elevation method of Reaser. At zero time 3 ml of isotonic $D_2O$ in normal saline was injected into the jugular vein and at the same time serial sampling of arterial blood started. The serial sampling interval was either 7.7 sec or 12.3 sec. In the histamine treated animals histamine diphosphate (0,5 mg of histamine base) was injected intravenously 30 minutes prior to the zero time. The following results were obtained. 1. $D_2O$ concentration in arterial plasma water, x, was empirically obtained by the sum of 2 exponential terms of time, $x=Ae^{-k1t}+Be^{-k2t},$ and its theoretical basis was sought. The first term of the right member of the equation was regarded to be attributable to the compartment P which possessed instantaneous exchange of water with plasma. The second term was postulated to represent the poorly exchangeable compartment. 2. The constant A of the equation was evaluated as 4,37% and 14.3% in the control and histamine treated groups, respectively. B was 1.19% in the control and 0.849% in histamine treated animals. 3. The disappearance rates determined were; $k_1=0.0519{\pm}0.0221\;sec^{-1}\;K_2=0.00454{\pm}0.00247\;sec^{-1}$ in the control group. $k_1=0.1137{\pm}0.0290\;sec^{-1}\;K_2=0.00499{\pm}0.00204\;sec^{-1}$ in the histamine group. 4. In the histamine treated animals the disappearance rate of the first term was larger than that of the control animals, suggesting an enlarged size of the rapidly exchangeable compartment with regard to the plasma water. On the other hand the constant B was decreased by histamine administration, suggesting a distribution of $D_2O$ in an enlarged volume. This view was also made clear by comparing the apparent asymptotes to which the concentration curves of $D_2O$ approached in respective groups. The asymptotes in the histamine treated group showed lower values.

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Multiscale Analysis on Expectation of Mechanical Behavior of Polymer Nanocomposites using Nanoparticulate Agglomeration Density Index (나노 입자의 군집밀도를 이용한 고분자 나노복합재의 기계적 거동 예측에 대한 멀티스케일 연구)

  • Baek, Kyungmin;Shin, Hyunseong;Han, Jin-Gyu;Cho, Maenghyo
    • Composites Research
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    • v.30 no.5
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    • pp.323-330
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    • 2017
  • In this study, multiscale analysis in which the information obtained from molecular dynamics simulation is applied to the continuum mechanics level is conducted to investigate the effects of clustering of silicon carbide nanoparticles reinforced into polypropylene matrix on mechanical behavior of nanocomposites. The elastic behavior of polymer nanocomposites is observed for various states of nanoparticulate agglomeration according to the model reflecting the degradation of interphase properties. In addition, factors which mainly affect the mechanical behavior of the nanocomposites are identified, and new index 'clustering density' is defined. The correlation between the clustering density and the elastic modulus of nanocomposites is understood. As the clustering density increases, the interfacial effect decreased and finally the improvement of mechanical properties is suppressed. By considering the random distribution of the nanoparticles, the range of elastic modulus of nanocomposites for same value of clustering density can be investigated. The correlation can be expressed in the form of exponential function, and the mechanical behavior of the polymer nanocomposites can be effectively predicted by using the nanoparticulate clustering density.

A Stiudy on the Deveplopment of Algorithm for the Representative Unit Hydrograph of a Watershed as a Closed Linear System. (폐선형계로 본 유역대표 단위유량도의 유도를 위한 알고리즘의 개발에 관한 연구)

  • 김재한;이원환
    • Water for future
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    • v.13 no.2
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    • pp.35-47
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    • 1980
  • An algorithm is developed to derive a representative I hr-unit hydrograph through an analysis of rainfall-runoff relations of a watershed as a closed system. For the base flow seperation of a flood hydrograph the multi-deflection method is proposed herein, which gace better results compared with those by the existing empirical methods. A modified $\Phi$index method is also proposed in this stidy to determine the time distribution rainfall excess of a rainstorm, which is essetially a modification of the commonly used $\Phi$index method of rainfall seperation. With the so-obtained rainfall excess hyetograph and the direct runoff hydrograph a trial and error computation of the ordinates of 1 hr-unit hydrograph was executed in such a manner that the synthesized flood hydrograph closely approximates the observed one, thus resulting a unit hydrograph of a piecewise exponential function type. To verify the validity of this study the 1 hr-unit hydrographs for the Imha and Dongchon in Nagdong River basin, and Yongdam in Geum River basin were derived by this algorithm, and the results were compared with those by the conventional synthetic unit hydrograph method and the Nakayasu method. Besides, the validity of this stiudy was also tested by comparing the observed hydrograph with the one computed by applying the unit hydrograph to a specific rainfall event. To generalize the result of this study a computer program, consisited of a main and three subprograns (for rainfall excess estimation, convolution summation, and sorting), is developed as a package, which is believed to be applicable to other watersheds for the similar purpose as those in this study.

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Development and Application of Diffusion Wave-based Distributed Runoff Model (확산파에 기초한 분포형 유출모형의 개발 및 적용)

  • Lee, Min-Ho;Yoo, Dong-Hoon
    • Journal of Korea Water Resources Association
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    • v.44 no.7
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    • pp.553-563
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    • 2011
  • According to the improvement of computer's performance, the development of Geographic Information System (GIS), and the activation of offering information, a distributed model for analyzing runoff has been studied a lot in recently years. The distribution model is a theoretical and physical model computing runoff as making target basin subdivided parted. In the distributed model developed by this study, the volume of runoff at the surface flow is calculated on the basis of the parameter determined by landcover data and a two-dimensional diffusion wave equation. Most of existing runoff models compute velocity and discharge of flow by applying Manning-Strickler's mean velocity equation and Manning's roughness coefficient. Manning's roughness coefficient is not matched with dimension and ambiguous at computation; Nevertheless, it is widely used in because of its convenience for use. In order to improve those problems, this study developed the runoff model by applying not only Manning-Strickler's equation but also Chezy's mean velocity equation. Furthermore, this study introduced a power law of exponential friction factor expressed by the function of roughness height. The distributed model developed in this study is applied to 6 events of fan-shape basin, oblong shape test basin and Anseongcheon basin as real field conditions. As a result the model is found to be excellent in comparison with the exiting runoff models using for practical engineering application.

Spatial-Temporal Interpolation of Rainfall Using Rain Gauge and Radar (강우계와 레이더를 이용한 강우의 시공간적인 활용)

  • Hong, Seung-Jin;Kim, Byung-Sik;Hahm, Chang-Hahk
    • Journal of Korean Society for Geospatial Information Science
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    • v.18 no.3
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    • pp.37-48
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    • 2010
  • The purpose of this paper is to evaluate how the rainfall field effect on a runoff simulation using grid radar rainfall data and ground gauge rainfall. The Gwangdeoksan radar and ground-gauge rainfall data were used to estimate a spatial rainfall field, and a hydrologic model was used to evaluate whether the rainfall fields created by each method reproduced a realistically valid spatial and temporal distribution. Pilot basin in this paper was the Naerin stream located in Inje-gun, Gangwondo, 250m grid scale digital elevation data, land cover maps, and soil maps were used to estimate geological parameters for the hydrologic model. For the rainfall input data, quantitative precipitation estimation(QPE), adjusted radar rainfall, and gauge rainfall was used, and then compared with the observed runoff by inputting it into a $Vflo^{TM}$ model. As a result of the simulation, the quantitative precipitation estimation and the ground rainfall were underestimated when compared to the observed runoff, while the adjusted radar rainfall showed a similar runoff simulation with the actual observed runoff. From these results, we suggested that when weather radars and ground rainfall data are combined, they have a greater hydrological usability as input data for a hydrological model than when just radar rainfall or ground rainfall is used separately.

Probabilistic estimation of fully coupled blasting pressure transmitted to rock mass II - Estimation of rise time - (암반에 전달된 밀장전 발파입력의 획률론적 예측 II - 최대압력 도달시간 예측을 중심으로 -)

  • Park, Bong-Ki;Lee, In-Mo;Kim, Sang-Gyun;Lee, Sang-Don;Cho, Kook-Hwan
    • Journal of Korean Tunnelling and Underground Space Association
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    • v.6 no.1
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    • pp.25-40
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    • 2004
  • The supersonic shock wave generated by fully coupled explosion will change into subsonic shock wave, plastic wave, and elastic wave consecutively as the wave propagates through rock mass. While the estimation of the blast-induced peak pressure was the main aim of the companion paper, this paper will concentrate on the estimation of the rise time of blast-induced pressure. The rise time can be expressed as a function of explosive density, isentropic exponent, detonation velocity, exponential coefficient of the peak pressure attenuation, dynamic yield stress, plastic wave velocity, elastic wave velocity, rock density, Hugoniot parameters, etc. Parametric analysis was performed to pinpoint the most influential parameter that affects the rise time and it was found that rock properties are more sensitive than explosive properties. The probabilistic distribution of the rise time is evaluated by the Rosenblueth'S point estimate method from the probabilistic distributions of explosive properties and rock properties. Numerical analysis was performed to figure out the effect of rock properties and explosive properties on the uncertainty of blast-induced vibration. Uncertainty analysis showed that uncertainty of rock properties constitutes the main portion of blast-induced vibration uncertainty rather than that of explosive properties. Numerical analysis also showed that the loading rate, which is the ratio of the peak blasting pressure to the rise time, is the main influential factor on blast-induced vibration. The loading rate is again more influenced by rock properties than by explosive properties.

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Robust 1D inversion of large towed geo-electric array datasets used for hydrogeological studies (수리지질학 연구에 이용되는 대규모 끄는 방식 전기비저항 배열 자료의 1 차원 강력한 역산)

  • Allen, David;Merrick, Noel
    • Geophysics and Geophysical Exploration
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    • v.10 no.1
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    • pp.50-59
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    • 2007
  • The advent of towed geo-electrical array surveying on water and land has resulted in datasets of magnitude approaching that of airborne electromagnetic surveying and most suited to 1D inversion. Robustness and complete automation is essential if processing and reliable interpretation of such data is to be viable. Sharp boundaries such as river beds and the top of saline aquifers must be resolved so use of smoothness constraints must be minimised. Suitable inversion algorithms must intelligently handle low signal-to-noise ratio data if conductive basement, that attenuates signal, is not to be misrepresented. A noise-level aware inversion algorithm that operates with one elastic thickness layer per electrode configuration has been coded. The noise-level aware inversion identifies if conductive basement has attenuated signal levels so that they are below noise level, and models conductive basement where appropriate. Layers in the initial models are distributed to span the effective depths of each of the geo-electric array quadrupoles. The algorithm works optimally on data collected using geo-electric arrays with an approximately exponential distribution of quadrupole effective depths. Inversion of data from arrays with linear electrodes, used to reduce contact resistance, and capacitive-line antennae is plausible. This paper demonstrates the effectiveness of the algorithm using theoretical examples and an example from a salt interception scheme on the Murray River, Australia.