• Title/Summary/Keyword: Exponential Function

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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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Effect of $M_{2}CO_{3}$(M=Li, Na) Addition on the Humidity Sensitivity of $V_{2}O_{5}$-doped $TiO_2$ ($V_{2}O_{5}$를 dopant로 한 $TiO_2$의 감습에 미치는 $M_{2}CO_{3}$(M=Li, Na)의 영향)

  • 강이국;송창열;신용덕
    • Proceedings of the Korean Institute of Electrical and Electronic Material Engineers Conference
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    • 1995.11a
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    • pp.343-346
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    • 1995
  • In this paper, the effect of alkaline oxides on the humidity sensitivity of $V_2O_{5}$(2mol%)-doped $TiO_2$(98mol%) was investigated as functions of $Li_{2}Co_{3}$, $Na_{2}Co_{3}$. III-1. Measurement of Density. When the mole% of $Li_2$O is varied 0,1,2,5mol%, the more the mole% of additives is increased, the more difference of bulk and apparent density is largely narrowed. The difference of two densities of sample containing 2mol% $Na_2O$ was large all the moat. The sample containing 1mol% $Na_2O$ was small most. III-2. Observation of porosity. The porosity and total intrusion volume according to various amounts of $Li_2O$ was reduced and those of sample containing 2mol% $Na_2O$ as 31.13%, 0.1155mL/g was the highest and 1mol% $Na_2O$ was lowed most and 5, 10mol% $Na_2O$ was more high compare with sample without alkaline oxides. III-3. Characteristic of humidity sensitivity. 1. Impedance of samples containing $Li_2O$ was high compare with sample without alkaline oxides, so we thought it showed Poor sensitivity because it have no impedance changing rapidly as function of relative humidity. 2. When the humidity was increasing from 30RH% to 90RH%, the impedance of sample containing 2mol% $Na_2O$ at 120HZ changed exponential rapidly from 6${\times}$$10^{7}$$\Omega$) to 1.25${\times}$$10^4$$\Omega$. At under 50RH% and over 50RH%, the humidity sensitivity of samples containing 2mol% $Na_2O$ was best especially in the range of the low humidity. III-4. Characteristic of TG curves. When algal me oxide $M_{2}CO_{3}$(M=Li, Na) were added into $V_{2}O_{5}$-doped $TiO_2$, the stability of humidity sensitivity of samples containing amounts of $Li_2O$ was unstable. The samples containing 1mol% $Na_2O$ was unstable.

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Underlying Values of Real-time Traffic Information on Variable Message Sign Using Contingent Valuation Method(CVM) (조건부가치추정법을 이용한 VMS교통정보의 기본가치 추정연구)

  • Lee, Gyeong-A;Kim, Jun-Gi;O, Seong-Ho;Lee, Yeong-In
    • Journal of Korean Society of Transportation
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    • v.29 no.3
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    • pp.61-72
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    • 2011
  • In the benefits of ITS, there are intangible gains from real-time traffic information as well as classical gains such as travel time saving. These intangible gains are difficult to be estimated by existing transportation investment appraisal commonly used in SOC investment. The major reason is not because of the absence of methodology but because of the absence of generalized values of particular benefits from real time traffic information. This research explores the value of real-time traffic information on VMS that is the most representative of ITS services, by using CVM with Double Bounded Dichotomous Choice Question. Willingness-To-Pay (WTP) functions of drivers are built with survival functions using various types of probability distribution functions such as Exponential, Log-logistic, and Weibull functions. The results reveal that Log-logistic distribution is the most appropriate distribution model to estimate WTP, and the estimated coefficients are stable through LR (Likelihood Ratio) test. For the further study, it is recommended to perform statistical tests of temporal and spatial transferability that is not examined in this research due to the lack of data.

Filtering Rate Model of Farming Oyster, Crassostrea gigas with effect of Water Temperature and Size (수온과 크기의 영향을 고려한 양식굴, Crassostrea gigas의 여수율 모형)

  • KIM Yong-Sool
    • Korean Journal of Fisheries and Aquatic Sciences
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    • v.28 no.5
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    • pp.589-598
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    • 1995
  • Filtering rates of Crassostrea gigas were experimentally investigated with reference to effects of water temperature and size. Absorptiometric determinations of filtering rates with oysters being fed diatom Chaetoceros calcirtans were carried out in a closed system. Optical density of 675nm in path length 100mm cell used as the indication of food particles absorption was appeared directly In proportion with the concentration of diatom pigment $chlorophyll-\alpha$. In the closed system where $C_0$ is $OD_{675}$ at initial time 0, $C_t$, at time t, and Z is the decreasing coefficient of OD as meaning of instantaneous removal speed, then $C_t=C_0{\cdot} e^{-2t}$, $Z=In(C_t/C_0)/t$. On the assumption that the filtering rate is constant, then removal rate per unit time (d) is $d=-e^{-z}$. If t is used to time unit of hour (hr), the filtering rate (FR) in I/hr is given by $FR=V{\cdot}d=V(1-e^{-z})$, where V is the water volume (I) of the experimental vessel. Filtering rate increased as exponential function with increasing temperature while not over critical limit. The critical temperature for filtering rate was assumed to be between $28^{\circ}C$ and $29^{\circ}C$. And the weight exponent for filtering rate is 0.223. The model formula derived from the results as FR, $Ihr^{-1}$ = $Exp(0.208{\cdot}T-4.324){\cdot} (DW)^{0.223}$ (T<29 $^{\circ}C)$ where T is water temperature $(^{\circ}C

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Model Tests on the Characteristics of Lateral Behavior of Steel Pipe Pile in Homogeneous and Nonhomogeneous Soil Conditions (균질 지반과 비균질 지반에서 강관 모형말뚝의 수평거동 특성에 관한 모형실험)

  • 김병탁;김영수
    • Geotechnical Engineering
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    • v.14 no.6
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    • pp.153-166
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    • 1998
  • This paper shows the results of a series of model tests on the behavior of steel pipe pile which is subjected to lateral and inclined loads in homogeneous and non-homogeneous Nak-dong River sands. Non-homogeneous soil consisted of two layers, upper and lower layer. The purpose of the present paper is to investigate the effect of ratio of lower layer height to embedded pile length, ratio of soil modules of upper layer to lower layer and inclined load on the behavior of single pile. These effects can be quantified only by the results of model tests. As a result. in non-homogeneous sand soil, it is shown that the lateral behavior depends upon the ratio of soil modules of upper layer to lower layer more than other factors. And it was found that the relationship between the deflection ratio of non-homogeneous sand to homogeneous sand and the ratio of lower layer height to embedded pile length can be fitted to exponential function of H/L by model tests results. For the inclined load applied, it is shown that the bending moment-depth relationship is not similar to the case of laterally loaded pile and the depth of maximum bending moment at relative density of 90% increases about 70% more than the pile only loaded laterally.

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Adsorption Thermodynamics of Polyamidoamide Epichlorohydrin Polymer in an Aqueous Fibrous Suspension (섬유 현탁액내 PAE 고분자 흡착의 열역학적 고찰)

  • Sung-Hoon Yoon;Kwang-Suk Joo;Tae-Won Lee;Kun-Han Kim;Byung-Bin Park
    • Journal of the Korean Chemical Society
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    • v.47 no.3
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    • pp.220-228
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    • 2003
  • This study was to examine the thermodynamic features of polyelecrolytic adsorption of polyamidoamine-epichlorohydrin(PAE) in a papermaking wet-end. The PAE adsorption experiments were conducted in a stirred jar containing an aqueous fibrous suspension and evaluated in terms of Langmuir and Freundlich parameters. The electrokinetic property of a stock was examined by measuring the zeta potential of each colloidal suspension. The polyelectrolytic PCD titration was employed to determine the adsorbed amounts of PAE polymer. The zeta potential of a stock, being varied significantly depending upon the addition of PAE polymer, showed initially a sharp increase and later an exponential decay as a function of time . The PAE adsorption exhibited a pseudo-Langmuir adsorption behavior at$20^{\circ}C$ , whereas its Freundlich power(v) increased in a proportional way at an elevated temperature. The train numbers calculated on the basis of adsorption thermodynamics were 7 to 8. The length of the extended loop of PAE was calculated as 215 nm at $20^{\circ}C$ and increased at a rate of 9% at every $10^{\circ}C$ rise in temperature. The PAE adsorption was proven to be an exothermic physisorption with the estimated adsorption enthalpy of -27 to -29 kJ/mol.

Application of Objective Mapping to Surface Currents Observed by HF Radar off the Keum River Estuary (금강하구 연안에서 고주파 레이더로 관측된 표층해류에 대한 객관적 유속산출 적용)

  • Hwang, Jin-A;Lee, Sang-Ho;Choi, Byung-Joo;Kim, Chang-Soo
    • The Sea:JOURNAL OF THE KOREAN SOCIETY OF OCEANOGRAPHY
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    • v.16 no.1
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    • pp.14-26
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    • 2011
  • Surface currents were observed by high-frequency (HF) radars off the Keum River estuary from December 2008 to February 2009. The dataset of observed surface currents had data gaps due to the interference of electromagnetic waves and the deteriorating weather conditions. To fill the data gaps an optimal interpolation procedure was developed. The characteristics of spatial correlation in the surface currents off the Keum River estuary were investigated and the spatial data gaps were filled using the optimal interpolation. Then, the temporal and spatial distribution of the interpolated surface currents and the patterns of interpolation error were examined. The correlation coefficients between the surface currents in the coastal region were higher than 0.7 because tidal currents dominate the surface circulation. The sample data covariance matrix (C), spatially averaged covariance matrix with localization ($C^G_{sm}$) and covariance matrix fitted by an exponential function ($C_{ft}$) were used to interpolate the original dataset. The optimal interpolation filled the data gaps and suppressed the spurious data with spikes in the time series of surface current speed so that the variance of the interpolated time series was smaller than that of the original data. When the spatial data coverage was larger (smaller) than 70% of the region, the interpolation error produced by $C^G_{sm}$ ($C_{ft}$) was smaller compared with that by C.

Dynamic Model Considering the Biases in SP Panel data (SP 패널데이터의 Bias를 고려한 동적모델)

  • 남궁문;성수련;최기주;이백진
    • Journal of Korean Society of Transportation
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    • v.18 no.6
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    • pp.63-75
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    • 2000
  • Stated Preference (SP) data has been regarded as more useful than Revealed Preference (RP) data, because researchers can investigate the respondents\` Preference and attitude for a traffic condition or a new traffic system by using the SP data. However, the SP data has two bias: the first one is the bias inherent in SP data and the latter one is the attrition bias in SP panel data. If the biases do not corrected, the choice model using SP data may predict a erroneous future demand. In this Paper, six route choice models are constructed to deal with the SP biases, and. these six models are classified into cross-sectional models (model I∼IH) and dynamic models (model IV∼VI) From the six models. some remarkable results are obtained. The cross-sectional model that incorporate RP choice results of responders with SP cross-sectional model can correct the biases inherent in SP data, and also the dynamic models can consider the temporal variations of the effectiveness of state dependence in SP responses by assuming a simple exponential function of the state dependence. WESML method that use the estimated attrition probability is also adopted to correct the attrition bias in SP Panel data. The results can be contributed to the dynamic modeling of SP Panel data and also useful to predict more exact demand.

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Model Tests on the Lateral Behavior of Steel Pipe Piles(I) in the Nak -dong River Sand (강관말뚝의 수평거동에 대한 모형실험 연구(I) -대구지역 낙동강 모래에 대하여)

  • 김영수;허노영
    • Geotechnical Engineering
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    • v.13 no.5
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    • pp.59-74
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    • 1997
  • This paper shows the results of a series of model bests on the behavior of single steel pipe pile which is subjected to lateral load in Nak-dong river sand. The purpose of the present paper is to estimate the effect of Non -homogeneous soil, constraint condition of pile head, lateral load velocity, relative density of soil, embedded pile length, and flexural stiffness of pile on the behavior of single pile which is embedded in Nak-dong river strand. These effects can be quantined only by the results of model tests. The nonlinear responses of lateral loadieflection relationships are fitted to 2nd polynomial equations by model tests results. Also, the lateral load of a deflection, yield and ultimate lateral load max. bending moment, and yield bending moment can be expressed as exponential function in terms of relative density and deflection ratio. By comparing Brom's results with model results on the lateral ultimate load, it is found that short and long pile show the contrary results with each other. The contrary results are due to the smaller assumed soil reaction than the soil reaction of the Nakiong river sand at deep point. By comparing lateral behavior on the homogeneous soil with non-homogeneous soil, it is shown that lateral loadieflection relationship is very dependent on the upper relative density. This phenomenon is shown remarkably as the difference between upper and lower relative density increases.

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Analytical Consideration of Surface Dose and Kerma for Megavoltage Photon Beams in Clinical Radiation Therapy

  • Birgani, Mohammad Javad Tahmasebi;Behrooz, Mohammad Ali;Razmjoo, Sasan;Zabihzadeh, Mansour;Fatahiasl, Jafar;Maskni, Reza;Abdalvand, Neda;Asgarian, Zeynab;Shamsi, Azin
    • Asian Pacific Journal of Cancer Prevention
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    • v.17 no.1
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    • pp.153-157
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    • 2016
  • Background: In radiation therapy, estimation of surface doses is clinically important. This study aimed to obtain an analytical relationship to determine the skin surface dose, kerma and the depth of maximum dose, with energies of 6 and 18 megavoltage (MV). Materials and Methods: To obtain the dose on the surface of skin, using the relationship between dose and kerma and solving differential equations governing the two quantities, a general relationship of dose changes relative to the depth was obtained. By dosimetry all the standard square fields of $5cm{\times}5cm$ to $40cm{\times}40cm$, an equation similar to response to differential equations of the dose and kerma were fitted on the measurements for any field size and energy. Applying two conditions: a) equality of the area under dose distribution and kerma changes in versus depth in 6 and 18 MV, b) equality of the kerma and dose at $x=d_{max}$ and using these results, coefficients of the obtained analytical relationship were determined. By putting the depth of zero in the relation, amount of PDD and kerma on the surface of the skin, could be obtained. Results: Using the MATLAB software, an exponential binomial function with R-Square >0.9953 was determined for any field size and depth in two energy modes 6 and 18MV, the surface PDD and kerma was obtained and both of them increase due to the increase of the field, but they reduce due to increased energy and from the obtained relation, depth of maximum dose can be determined. Conclusions: Using this analytical formula, one can find the skin surface dose, kerma and thickness of the buildup region.