• Title/Summary/Keyword: exponential function

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The Change of Pillar Strength due to Joint Dip Angles, Total Trace Length and Width-to-Height ratio of a Pillar (절리면의 방향, 절리선 길이 및 광주 형상비가 광주 강도에 미치는 영향 분석)

  • Choi, Ji-won;Lee, Yong-Ki;Song, Jae-Joon
    • Tunnel and Underground Space
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    • v.30 no.3
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    • pp.226-241
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    • 2020
  • The stability of underground mine cavity is closely related with pillar strength. The vulnerability of pillars can be judged and reinforced if the pillar strength is known. The pillar strength is affected by characteristics of discontinuities and shape of a pillar. The change of pillar strength due to a discontinuity passing through the center of a pillar, width-to-height ratio of a pillar and small joints existing within a pillar was analyzed using PFC 3D. The result showed that the pillar strength is influenced by dip angle of a discontinuity and it increases as width-to-height ratio of a pillar increases. The pillar strength decreases as the number of contained joints increases. The relationship between total trace length observable from the pillar surface and the pillar strength was regressed with exponential function. The correlation coefficient of the regression was high enough so that pillar strength can be predicted using total trace length if a joint set exists in a pillar. Lastly, the method to estimate the strength of a pillar that includes two joint sets was proposed if the joint dip angles are 60°, 30°. The method also need total trace lengths of two joint sets.

Reaction Rate Analysis of Combustion for Indonesian Coal Char Applied by External/Internal Diffusion (외부 및 내부 확산을 적용한 인도네시아 석탄촤의 연소 반응율 분석)

  • Hwang, Chan-Won;Kim, Ryang-Gyoon;Ryu, Kwang-Il;Wu, Ze-Lin;Jeon, Chung-Hwan
    • Korean Chemical Engineering Research
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    • v.52 no.1
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    • pp.133-140
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    • 2014
  • The experiment was designed to compare the char combustion kinetics of pulverized Indonesia coals commonly utilized in Korea power plants. The reaction rate of coal char has been formulated using the external and internal effectiveness factors to describe the diffusion effect quantitatively. The Random Pore Model (RPM) was used for applying internal specific surface area as a function of carbon conversion ratio. Reaction rate was obtained from reaction time using the Wire Heating Reactor (WHR) which can heat and measure the char particle temperature at the same time. BET and TGA were used to obtain physical properties such as internal specific surface area and structural parameter. Three kinds of Indonesia Sub-bituminous coals "BARAMULTI, ENERGYMAN, AGM" were used in order to derive the activation energy and pre-exponential factor. The results of this study showed that the effect of internal diffusion than that of external diffusion is the dominant as comparison of kinetics was reflected in external and internal effectiveness factors. For three kinds of coal char, finally, activation energy of intrinsic kinetics indicates 110~118 kJ/mol.

A comparative study of borehole size and tool effect on dispersion curves (시추공경과 공내검층기가 분산곡선에 미치는 영향에 대한 비교 연구)

  • Zhao, Weijun;Kim, Jong-Man;Kim, Yeong-Hwa
    • Geophysics and Geophysical Exploration
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    • v.12 no.1
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    • pp.154-162
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    • 2009
  • Sonic wave dispersion characteristics are one of the most important targets of study, particularly in estimating shear wave velocity from borehole sonic logging. We have tested dispersion characteristics using monopole and dipole sources. Theoretical dispersion curves were computed for tool-absent and tool-included models having the same physical properties but different diameters (including ${\Phi}520mm$, ${\Phi}150mm$, and ${\Phi}76mm$). Comparisons were made between boreholes of different sizes and between tool-absent and tool-included models. Between the tool-included and the tool-absent boreholes, a close similarity in dispersion curve shape was revealed for the monopole source, and a significant difference was shown for the dipole source. However, for the cut-off frequency, particularly in the engineering boreholes (${\Phi}76mm$ and ${\Phi}50mm$), a significant difference was observed for signals from the monopole source, but approximately the same cut-off frequencies were found with the dipole source. This indicates the need of careful choice of source frequency in monopole-source sonic logging, particularly in an engineering borehole. The results of numerical experiments show that cut-off frequency is exponentially proportional to the inverse of borehole radius, irrespective of the mode type and the presence of a tool, and that the cut-off frequencies for each borehole environment could be expressed as an exponential function, rather than the inversely proportional relationship between the cut-off frequency and the borehole radius that was previously generally recognised. From the direct comparison of dispersion curves, the effects on the dispersion characteristics of borehole size and the presence of the tool can be revealed more clearly than in previous studies, which presented the dispersion curve and/or characteristics for each borehole environment separately.

Study on Variability of WTP Estimates by the Estimation Methods using Dichotomous Choice Contingent Valuation Data (양분선택형 조건부가치측정(CV) 자료의 추정방법에 따른 지불의사금액의 변동성 연구)

  • Shin, Youngchul
    • Environmental and Resource Economics Review
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    • v.25 no.1
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    • pp.1-25
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    • 2016
  • This study investigated the variability of WTP estimates(i.e. mean or median) with ad hoc assumptions of specific parametric probability distributions(i.e. normal, logistic, lognormal, and exponential distribution) to estimate WTP function using dichotomous choice CV data on mortality risk reduction. From the perspective of policy decision, the variability of these WTP estimates are intolerable in comparison with those of Turnbull nonparametric estimation method which is free from ad hoc distribution assumptions. The Turnbull nonparametric estimation can avoid a kind of misspecification bias due to ad hoc assumption of specific parametric distributions. Furthermore, the WTP estimates by Turnbull nonparametric estimation are robust because the similar estimates are elicited from a dichotomous choice or double dichotomous choice CV data, and the statistically significant WTP estimates can be obtained even though it is not possible by parametric estimation methods. If there are considerable variability among those WTP estimates by parametric estimation methods in condition with no criteria of model adequacy, the mean WTPs from Turnbull nonparametric estimation can be the robust estimates without ad hoc assumptions, which can avoid controversial issues in the perspective of policy decisions.

Soil Water Storage and Antecedent Precipitation Index at Gwangneung Humid-Forested Hillslope (광릉 산지사면에서의 선행강우지수와 토양저류량 비교연구)

  • Gwak, Yong-Seok;Kim, Su-Jin;Lee, Eun-Hyung;Hamm, Se-Yeong;Kim, Sang-Hyun
    • Korean Journal of Agricultural and Forest Meteorology
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    • v.18 no.1
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    • pp.30-41
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    • 2016
  • The temporal variation of soil water storage is important in hydrological modeling. In order to evaluate an antecedent wetness state, the antecedent precipitation index (API) has been used. The aim of this article is to compare observed soil water storage with APIs calculated by widely used four equations, to configure the relationship between soil water storage and API by a regression model for one-year(2009), and to predict the soil water storage for the next two years(2010~2011). The soil water storage was evaluated from the observed soil moisture dataset in soil depths of 10, 30, 60cm at 21 locations by TDR measurement system for 3 years. As a result, API with the exponential function among the four equations can describe the variation of the observed soil water storage. Monthly optimized parameters of the API's equations seemed to be roughly related with the (potential) evapotranspiration (PET). Using revised monthly optimized parameters of APIs considering the seasonal pattern of PET, we characterize the relationship between API and the observed soil water storage for one year, which looks better than those of other researches.

The recombination velocity at III-V compound heterojunctions with applications to Al/$_x$/Ga/$_1-x$/As-GaAs/$_1-y$/Sb/$_y$/ solar cells

  • 김정순
    • 전기의세계
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    • v.28 no.4
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    • pp.53-63
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    • 1979
  • Interface recombination velocity in $Al_{x}$G $a_{1-x}$ As-GaAs and $Al_{0.85}$, G $a_{0.15}$ As-GaA $s_{1-y}$S $b_{y}$ heterojunction systems is studied as a function of lattice mismatch. The results are applied to the design of highly efficient III-V heterojunction solar cells. A horizontal liquid-phase epitaxial growth system was used to prepare p-p-p and p-p-n $Al_{x}$G $a_{1-x}$ As-GaA $s_{1-y}$S $b_{y}$-A $l_{x}$G $a_{1-x}$ As double heterojunction test samples with specified values of x and y. Samples were grown at each composition, with different GaAs and GaAs Sb layer thicknesses. A method was developed to obtain the lattice mismatch and lattice constants in mixed single crystals grown on (100) and (111)B oriented GaAs substrates. In the AlGaAs system, elastic lattice deformation with effective Poisson ratios .mu.$_{eff}$ (100=0.312 and .mu.$_{eff}$ (111B) =0.190 was observed. The lattice constant $a_{0}$ (A $l_{x}$G $a_{1-x}$ As)=5.6532+0.0084x.angs. was obtained at 300K which is in good Agreement with Vegard's law. In the GaAsSb system, although elastic lattice deformation was observed in (111) B-oriented crystals, misfit dislocations reduced the Poisson ratio to zero in (100)-oriented samples. When $a_{0}$ (GaSb)=6.0959 .angs. was assumed at 300K, both (100) and (111)B oriented GaAsSb layers deviated only slightly from Vegard's law. Both (100) and (111)B zero-mismatch $Al_{0.85}$ G $a_{0.15}$As-GaA $s_{1-y}$S $b_{y}$ layers were grown from melts with a weight ratio of $W_{sb}$ / $W_{Ga}$ =0.13 and a growth temperature of 840 to 820 .deg.C. The corresponding Sb compositions were y=0.015 and 0.024 on (100) and (111)B orientations, respectively. This occurs because of a fortuitous in the Sb distribution coefficient with orientation. Interface recombination velocity was estimated from the dependence of the effective minority carrier lifetime on double-heterojunction spacing, using either optical phase-shift or electroluminescence timedecay techniques. The recombination velocity at a (100) interface was reduced from (2 to 3)*10$^{4}$ for y=0 to (6 to 7)*10$^{3}$ cm/sec for lattice-matched $Al_{0.85}$G $a_{0.15}$As-GaA $s_{0.985}$S $b_{0.015}$ Although this reduction is slightly less than that expected from the exponential relationship between interface recombination velocity and lattice mismatch as found in the AlGaAs-GaAs system, solar cells constructed from such a combination of materials should have an excellent spectral response to photons with energies over the full range from 1.4 to 2.6 eV. Similar measurements on a (111) B oriented lattice-matched heterojunction produced some-what larger interface recombination velocities.ities.ities.s.

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Relationship of box counting of fractured rock mass with Hoek-Brown parameters using particle flow simulation

  • Ning, Jianguo;Liu, Xuesheng;Tan, Yunliang;Wang, Jun;Tian, Chenglin
    • Geomechanics and Engineering
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    • v.9 no.5
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    • pp.619-629
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    • 2015
  • Influenced by various mining activities, fractures in rock masses have different densities, set numbers and lengths, which induce different mechanical properties and failure modes of rock masses. Therefore, precisely expressing the failure criterion of the fractured rock influenced by coal mining is significant for the support design, safety assessment and disaster prevention of underground mining engineering subjected to multiple mining activities. By adopting PFC2D particle flow simulation software, this study investigated the propagation and fractal evolution laws of the micro cracks occurring in two typical kinds of rocks under uniaxial compressive condition. Furthermore, it calculated compressive strengths of the rocks with different confining pressures and box-counting dimensions. Moreover, the quantitative relation between the box-counting dimension of the rocks and the empirical parameters m and s in Hoek-Brown strength criterion was established. Results showed that with the increase of the strain, the box-counting dimension of the rocks first increased slowly at the beginning and then exhibited an exponential increase approximately. In the case of small strains of same value, the box-counting dimensions of hard rocks were smaller than those of weak rocks, while the former increased rapidly and were larger than the latter under large strain. The results also presented that there was a negative correlation between the parameters m and s in Hoek-Brown strength criterion and the box-counting dimension of the rocks suffering from variable mining activities. In other words, as the box-counting dimensions increased, the parameters m and s decreased linearly, and their relationship could be described using first order polynomial function.

A Study on the Analysis of Time-Regional Distribution of PRecipitation Frequency and Rainfall INternsity in Korea. (강수빈도 및 강우강도의 시공적 분포분석에 관한 연구)

  • 이재준;손광익
    • Water for future
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    • v.14 no.4
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    • pp.53-72
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    • 1981
  • In this study, South Korea is divided into 5 zones and is studied about the analysis of time-regional distribution of previpitation frequency and rainfall intensity in Korea. In the previpitation frequency analysis, the basic data groups of 39 stations were selected. The diagram of previpitation frequency was drawn, and the time-regional distribution of precipitation frequency was analized. In the rainfall intensity analysis, the basic data groups of 36 stations were selected. The probable rainfall, I-D-F curve, and regression equation between 24hr. and 10min.-18hr. areal depth were obtained. The results of this study are following; 1) The precipitation class of max. recurrence probability in every season except summer was commonly (1) 1-5mm, (2) 0.1-1mm, (3) 5-10mm in order. 2) The zone of max. recurrence frequency owing to the precipitation class was zone II in precipitation frequency of below 20mm, zone IV in precipitation frequency of 30-40mm, zone I in precipitation frequency of above 70mm for a year. 3) The recurrence probability of precipitation in Korea can be represented to the equation of exponential function; $$W(x)=e^{\alpha+\beta}$$ 4) The first and third zones were expected heavy rain for the short and long duration. 5) The I.D.F. curves were drawn, and established that the time interval for the least deviation of I.D.F curve is 10~40min., 40min. -4hr., 4~24hr. 6) The regression equations of areal mean depth between 24hr. and 10min.-18hr. for each zone were obtained. 7)The probable rainfall of 36 points were calculated.

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Comparison of Groundwater Recharge between HELP Model and SWAT Model (HELP 모형과 SWAT 모형의 지하수 함양량 비교)

  • Lee, Do-Hun;Kim, Nam-Won;Chung, Il-Moon
    • Journal of Korea Water Resources Association
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    • v.43 no.4
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    • pp.383-391
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    • 2010
  • The groundwater recharge was assessed by using both SWAT and HELP models in Bocheong-cheon watershed. The SWAT model is a comprehensive surface and subsurface model, but it lacks the physical basis for simulating a soil water percolation process. The HELP model which has a drawback in simulating subsurface lateral flow and groundwater flow component can simulate soil water percolation process by considering the unsaturated flow effect of soil layers. The SWAT model has been successfully applied for estimating groundwater recharge in a number of watersheds in Korea, while the application of HELP model has been very limited. The subsurface lateral flow parameter was proposed in order to consider the subsurface lateral flow effect in HELP model and the groundwater recharge was simulated by the modified exponential decay weighting function in HELP model. The simulation results indicate that the recharge of HELP model significantly depends on the values of lateral flow parameter. The recharge errors between SWAT and HELP are the smallest when the lateral flow parameter is about 0.6 and the recharge rates between two models are shown to be reasonably comparable for daily, monthly, and yearly time scales. The HELP model is useful for estimating groundwater recharge at watershed scale because the model structure and input parameters of HELP model are simpler than that of SWAT model. The accuracy of assessing the groundwater recharge might be improved by the concurrent application of SWAT model and HELP model.

Fracture Toughness Prediction of RPV Steels Using Crack Arrest Load of Load-Displacement Curve in Charpy V - Notch Impact Test (샤피 V - 노치 충격 하중-변위 곡선의 균열정지하중을 이용한 원자로압력용기강의 파괴인성 예측)

  • Park, Jeong-Yong;Kim, Ju-Hak;Lee, Yun-Gyu;Hong, Jun-Hwa
    • Korean Journal of Materials Research
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    • v.10 no.4
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    • pp.305-311
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    • 2000
  • Applicability of crack arrest load measured from the Charpy V-notch impact test has been investigated to predict the fracture toughness of nuclear reactor pressure vessel (RPV) steels (ASME SA508 Cl.3). The temperature dependence of the crack arrest load was well described by the type of exponential function characterized by an index temperature at which the crack arrest load is 2kN. The specific index temperature, which also well correlated with $T_{NDT}\;and\;T_{41J}$ is expected to be representative index temperature characterizing the crack arrest fracture toughness of RPV steels. Also, the crack arrest load correlated well with the stable crack length measured from the fracture surface. From the measurements of the crack arrest load and the stable crack length, the lower bound fracture toughness, $K_{Ia}$ of RPV steels could be predicted with sufficient accuracy.

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