• Title/Summary/Keyword: exponential distribution

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

  • Park, Deok-Won
    • The Journal of the Petrological Society of Korea
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    • v.26 no.3
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    • pp.297-309
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    • 2017
  • Jurassic granite from Geochang was analysed with respect to the characteristics of the rock cleavage. The comprehensive evaluation for rock cleavages was performed through the combination of the 16 parameters derived from the enlarged photomicrographs of the thin section and the spacing-cumulative frequency diagrams. The results of analysis for the representative values of these spacing parameters with respect to the rock cleavage are summarized as follows. First, the above parameters can be classified into group I (spacing frequency (N), total spacing ($1m{\geq}$), constant (a), exponent (${\lambda}$), slope of exponential straight line (${\theta}$), length of line (oa') and trigonometric ratios ($sin{\theta}$, $tan{\theta}$) and group II (mean spacing (Sm), difference value between mean spacing and median spacing (Sm-Sme), density (${\rho}$), lengths of lines (oa and aa'), area of a right-angled triangle (${\Delta}oaa^{\prime}$) and trigonometric ratio($cos{\theta}$). The values of the 8 parameters belonging to group I show an order of H(hardway, H1+H2)

Simplified Method for Estimation of Mean Residual Life of Rubble-mound Breakwaters (경사제의 평균 잔류수명 추정을 위한 간편법)

  • Lee, Cheol-Eung
    • Journal of Korean Society of Coastal and Ocean Engineers
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    • v.34 no.2
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    • pp.37-45
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    • 2022
  • A simplified model using the lifetime distribution has been presented to estimate the Mean Residual Life (MRL) of rubble-mound breakwaters, which is not like a stochastic process model based on time-dependent history data to the cumulative damage progress of rubble-mound breakwaters. The parameters involved in the lifetime distribution can be easily estimated by using the upper and lower limits of lifetime and their likelihood that made a judgement by several experts taking account of the initial design lifetime, the past sequences of loads, and others. The simplified model presented in this paper has been applied to the rubble-mound breakwater with TTP armor layer. Wiener Process (WP)-based stochastic model also has been applied together with Monte-Carlo Simulation (MCS) technique to the breakwater of the same condition having time-dependent cumulative damage to TTP armor layer. From the comparison of lifetime distribution obtained from each models including Mean Time To Failure (MTTF), it has found that the lifetime distributions of rubble-mound breakwater can be very satisfactorily fitted by log-normal distribution for all types of cumulative damage progresses, such as exponential, linear, and logarithmic deterioration which are feasible in the real situations. Finally, the MRL of rubble-mound breakwaters estimated by the simplified model presented in this paper have been compared with those by WP stochastic process. It can be shown that results of the presented simplified model have been identical with those of WP stochastic process until any ages in the range of MTT F regardless of the deterioration types. However, a little of differences have been seen at the ages in the neighborhood of MTTF, specially, for the linear and logarithmic deterioration of cumulative damages. For the accurate estimation of MRL of harbor structures, it may be desirable that the stochastic processes should be used to consider properly time-dependent uncertainties of damage deterioration. Nevertheless, the simplified model presented in this paper can be useful in the building of the MRL-based preventive maintenance planning for several kinds of harbor structures, because of which is not needed time-dependent history data about the damage deterioration of structures as mentioned above.

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

  • Park, Deok-Won
    • The Journal of the Petrological Society of Korea
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    • v.25 no.4
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    • pp.311-324
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    • 2016
  • The characteristics of the rock cleavage in Jurassic granite from Geochang were analysed. The evaluation for three quarrying planes and three rock cleavages was performed using the parameters such as (1) reduction ratio between the value of spacing and the value of length, (2) microcrack spacing frequency(N), (3) total spacing($1mm{\geq}$), (4) exponential constant(a), (5) magnitude of exponent(${\lambda}$), (6) mean spacing($S_{mean}$), (7) difference value($S_{mean}-S_{median}$) between mean spacing and median spacing($S_{median}$) and (8) density of spacing. Especially the close dependence between the above spacing parameters and the parameters from the spacing-cumulative frequency diagrams was derived. The discrimination factors representing three quarrying planes and three rock cleavages were acquired through these mutual contrast. The analysis results of the research are summarized as follows. First, the reduction ratios of frequency(N), mean value, median value, the above difference value($S_{mean}-S_{median}$) and density for three rock cleavages are in orders of G(grain, (G1 + G2)/2) < H(hardway, (H1 + H2)/2) < R(rift, (R1 + R2)/2), H < G $\ll$ R, H < G $\ll$ R, H < G < R and H < G $\ll$ R. The values of the above five parameters for three planes show the various orders of R'(rift plane) $\ll$ H'(hardway plane) < G'(grain plane), R' $\ll$ G' < H', R' < H' < G', R' < G' < H' and R' $\ll$ H' < G', respectively. Second, the values of (I) parameters(2, 3, 4 and 5) and (II) parameters(6, 7 and 8) are in orders of (I) H < G < R 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. Third, to review the overall characteristics of the arrangement among the six diagrams, these diagrams show an order of R2 < R1 < G2 < G1 < H2 < H1 from the related chart. In other words, above six diagrams can be summarized in order of rift(R1 + R2) < grain(G1 + G2) < hardway(H1 + H2). These results indicate a relative magnitude of rock cleavage related to microcrack spacing. Especially, two parameters for each diagram, the above difference value($S_{mean}-S_{median}$) and mean spacing, could provide advanced information for prediction the order of arrangement among the diagrams. Finally, the general chart for three planes and three rock cleavages were made. From the related chart, three exponential straight lines for three rock cleavages show an order of R(R1 + R2) < G(G1 + G2) < H(H1 + H2). On the contrary, three lines for three planes show an order of H'(R2 + G2) < G'(R1 + H2) < R'(G1 + H1). Consequently, correlation of the mutually reverse order between three planes and three rock cleavages can be drawn from the related chart.

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.