• Title/Summary/Keyword: Dispersion equation

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Response of anisotropic porous layered media with uncertain soil parameters to shear body-and Love-waves

  • Sadouki, Amina;Harichane, Zamila;Elachachi, Sidi Mohammed;Erken, Ayfer
    • Earthquakes and Structures
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    • v.14 no.4
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    • pp.313-322
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    • 2018
  • The present study is dedicated to investigate the SH body-as well as Love-waves propagation effects in porous media with uncertain porosity and permeability. A unified formulation of the governing equations for one-dimensional (1-D) wave propagation in anisotropic porous layered media is presented deterministically. The uncertainties around the above two cited parameters are taken into account by random fields with the help of Monte Carlo Simulations (MCS). Random samples of the porosity and the permeability are generated according to the normal and lognormal distribution functions, respectively, with a mean value and a coefficient of variation for each one of the two parameters. After performing several thousands of samples, the mathematical expectation (mean) of the solution of the wave propagation equations in terms of amplification functions for SH waves and in terms of dispersion equation for Love-waves are obtained. The limits of the Love wave velocity in a porous soil layer overlaying a homogeneous half-space are obtained where it is found that random variations of porosity change the zeros of the wave equation. Also, the increase of uncertainties in the porosity (high coefficient of variation) decreases the mean amplification function amplitudes and shifts the fundamental frequencies. However, no effects are observed on both Love wave dispersion and amplification function for random variations of permeability. Lastly, the present approach is applied to a case study in the Adapazari town basin so that to estimate ground motion accelerations lacked in the fast-growing during the main shock of the damaging 1999 Kocaeli earthquake.

An Eulerian-Lagrangian Hybrid Numerical Method for the Longitudinal Dispersion Equation (Eulerian-Lagrangian 혼합모형에 의한 종확산 방정식의 수치해법)

  • 전경수;이길성
    • Water for future
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    • v.26 no.3
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    • pp.137-148
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    • 1993
  • A hybrid finite difference method for the longitudinal dispersion equation was developed. The method is based on combining the Holly-Preissmann scheme with the fifth-degree Hermite interpolating polynomial and the generalized Crank-Nicholson scheme. Longitudinal dispersion of an instantaneously-loaded pollutant source was simulated by the model and other characteristics-based numerical methods. Computational results were compared with the exact solution. The present method was free from wiggles regardless of the Courant number, and exactly reproduced the location of the peak concentration. Overall accuracy of the computation increased for smaller value of the weighting factor, $\theta$ of the model. Larger values of $\theta$ overestimated the peak concentration. Smaller Courant number gave better accuracy, in general, but the sensitivity was very low, especially when the value of $\theta$ was small. From comparisons with the hybrid method using the third-degree interpolating polynomial and with split-operator methods, the present method showed the best performance in reproducing the exact solution as the advection becomes more dominant.

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Comparison of the Results of Finite Difference Method in One-Dimensional Advection-Dispersion Equation (유한차분 모형에 의한 일차원 이송-확산방정식 계산결과의 비교)

  • 이희영;이재철
    • Water for future
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    • v.28 no.4
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    • pp.125-136
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    • 1995
  • ELM, a characteristic line based method, was applied to advection-dispersion equation, and the results obtained were compared with those of Eulerian schemes(Stone-Brian and QUICKEST). The calculation methods consisted of Lagrangian interpolation scheme and cubic spline interpolation scheme for the advection calculation, and the Crank-Nicholson scheme for the dispersion calculation. The results of numerical methods were as follows: (1) for Gaussian hill: ELM, using Lagrangian interpolation scheme, gave the most accurate computational result, ELM, using cubic spline interpolation scheme, and QUICKEST scheme gave numerical damping for Peclet number 50. Stone-Brian scheme gave phase shift introduced in the numerical solution for Peclet number 10 and 50. (2) for advanced front: All schemes gave accurate computational results for Peclet number 1 and 4. ELM, Lagrangian interpolation scheme, and Stone,Brian scheme gave dissipation error and ELM, using cubic spline interpolation scheme, and QUICKEST scheme gave numerical oscillation for Peclet number 50.

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A case study for the dispersion parameter modification of the Gaussian plume model using linear programming (Linear Programming을 이용한 가우시안 모형의 확산인자 수정에 관한 사례연구)

  • Jeong, Hyo-Joon;Kim, Eun-Han;Suh, Kyung-Suk;Hwang, Won-Tae;Han, Moon-Hee
    • Journal of Radiation Protection and Research
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    • v.28 no.4
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    • pp.311-319
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    • 2003
  • We developed a grid-based Gaussian plume model to evaluate tracer release data measured at Young Gwang nuclear site in 1996. Downwind distance was divided into every 10m from 0.1km to 20km, and crosswind distance was divided into every 10m centering released point from -5km to 5km. We determined dispersion factors, ${\sigma}_y\;and\;{\sigma}_z$ using Pasquill-Gifford method computed by atmospheric stability. Forecasting ability of the grid-based Gaussian plume model was better at the 3km away from the source than 8km. We confirmed that dispersion band must be modified if receptor is far away from the source, otherwise P-G method is not appropriate to compute diffusion distance and diffusion strength in case of growing distance. So, we developed an empirical equation using linear programming. An objective function was designed to minimize sum of the absolute value between observed and computed values. As a result of application of the modified dispersion equation, prediction ability was improved rather than P-G method.

An Esitimation of Lognitudinal Dispersion Coefficient in Natural Stram Using Hydraulic Model (수리모형을 이용한 자연하천에서 종확산계수 추정)

  • Yun, Se-Ui;Han, Geon-Yeon;Han, Jeong-Seok;Kim, Jeong-Su
    • Journal of Korea Water Resources Association
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    • v.33 no.4
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    • pp.407-417
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    • 2000
  • To estimate the longitudinal dispersion coefficient at the downstream of Jungrang-River, the undistorted 1/20 scale hydraulic model was used in this study. Experiments were conducted for dry season discharge, and Rhodamine B was used as a tracer. The relationship curve between concentration and conductivity of Rhodamine B was otained by laboratory test, and the conductivity which was measured in hydraulic model was converted to concentration using this curve. The longitudinal dispersion coefficient was calculated using the relationship between the peak concentration and the time to peak concentration. The results of this study were compared with the calculated values by the empirical equations for the longitudinal dispersion coefficient and with the field data. The results of comparison show that Parker's equation underestimates, and Liu'g equation and Iwasa and Aya's one overestimate, and McQuivey and Keefer's equations, Fischer's one, Magazine's one, and Seo and Cheong's one predict relatively well. The measured data sets were relatively close to the observed ones in natural river. The longitudinal dispersion coefficient at the downstream of Jungrang-River was estimated $10\textrm{m}^2/s$.

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Computational analysis of pollutant dispersion in urban street canyons with tree planting influenced by building roof shapes

  • Bouarbi, Lakhdar;Abed, Bouabdellah;Bouzit, Mohamed
    • Wind and Structures
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    • v.23 no.6
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    • pp.505-521
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    • 2016
  • The objective of this study is to investigate numerically the effect of building roof shaps on wind flow and pollutant dispersion in a street canyon with one row of trees of pore volume, $P_{vol}=96%$. A three-dimensional computational fluid dynamics (CFD) model is used to evaluate air flow and pollutant dispersion within an urban street canyon using Reynolds-averaged Navier-Stokes (RANS) equations and the Explicit Algebraic Reynolds Stress Models (EARSM) based on k-${\varepsilon}$ turbulence model to close the equation system. The numerical model is performed with ANSYS-CFX code. Vehicle emissions were simulated as double line sources along the street. The numerical model was validated by the wind tunnel experiment results. Having established this, the wind flow and pollutant dispersion in urban street canyons (with six roof shapes buildings) are simulated. The numerical simulation results agree reasonably with the wind tunnel data. The results obtained in this work, indicate that the flow in 3D domain is more complicated; this complexity is increased with the presence of trees and variability of the roof shapes. The results also indicated that the largest pollutant concentration level for two walls (leeward and windward wall) is observed with the upwind wedge-shaped roof. But the smallest pollutant concentration level is observed with the dome roof-shaped.

Comparison of the Vertical Velocity Distribution in the Natural Streamflow (자연하천의 연직방향 유속분포 비교(수공))

  • 박승기;김태철
    • Proceedings of the Korean Society of Agricultural Engineers Conference
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    • 2000.10a
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    • pp.346-351
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    • 2000
  • The study was carried out to investigate the characteristics of vertical velocity distribution measured by current meter at Kangkyung station in Keum river during the period of 1995 to 1997. It suggests the quadratic parabola equation to estimate the vertical velocity profile only from the measurement data of surface velocity. The equation was found to be statistically very stable and showed high significance to express the surface velocity and bottom velocity. The vertical velocity profile was determined by the relationships to the surface velocity, and a coefficient of the quadratic parabola equation. The vertical velocity profile can be applied to calculating the mean velocity and discharge, and to and to analyse the dispersion of pollutant materials in the streamflow.

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Evaluation of Microwave Dielectric Properties in $(Pb_{0.5}Ca_{0.5})(Fe_{0.5}Ta_{0.5})O_3$ Ceramics by the Dielectric Mixing Rule (유전체 혼합 법칙을 이용한 $(Pb_{0.5}Ca_{0.5})(Fe_{0.5}Ta_{0.5})O_3$세라믹스의 마이크로파 유전특성 평가)

  • 박흥수;윤기현;김응수
    • Journal of the Korean Ceramic Society
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    • v.37 no.3
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    • pp.240-246
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    • 2000
  • The microwave dielectric properties of the complex perovskite (Pb0.5Ca0.5)(Fe0.5Ta0.5)O3 ceramics were investigated with the porosity and the dielectric mixing rule. Assuming that the specimens were mixtures of real dielectrics and pores, with 3-0 connectivity, the ionic polarizabilities modified by Maxwell's equation were more close to the theoretical values rather than those modified by Wiener's equation in porous specimens. The theoretical dielectirc loss were obtained with the infrared reflectivity spectra from 50 to 4000cm-1, which were calculated by Kramers-Kronig analysis and classical osciallator model. The relative tendency of dielectric loss calculated from the theoretical value and Maxwell's equation in the specimens with different porosities was in good agreement with the one by the post resonant method.

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Eulerian-Lagrangian Split-Operator Method for the Longitudinal Dispersion Equation (종확산 방정식에 대한 Eulerian-Lagrangian 연산자 분리방법)

  • Jun, Kyung Soo;Lee, Kil Seong
    • KSCE Journal of Civil and Environmental Engineering Research
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    • v.14 no.1
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    • pp.131-141
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    • 1994
  • Three characteristics-based split-operator methods were applied to a longitudinal pollutant dispersion problem, and the results were compared with those of several Eulerian schemes. The split-operator methods consisted of generalized upwind, two-point fourth-order and sixth-order Holly-Preissmann schemes, respectively, for the advection calculation, and the Crank-Nicholson scheme for the diffusion calculation. Compared with the Eulerian schemes tested, split-operator methods using the Holly-Preissmann schemes gave much more accurate computational results. Eulerian schemes using centered difference approximations for the advection term resulted in numerical oscillations, and those using backward difference resulted in numerical diffusion, both of which were more severe for smaller value of the longitudinal dispersion coefficient.

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Studies on Solid Dispersion System of Ketoconazole (케토코나졸의 고체분산계에 관한 연구)

  • Lee, Chi-Ho;Kim, Ki-Heun;Choi, Woo-Sik;Kim, Jung-Ryang
    • Journal of Pharmaceutical Investigation
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    • v.21 no.1
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    • pp.23-32
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    • 1991
  • Dissolution profiles of ketoconazole in solid dispersion system (SDS) were investigated in the second fluid (pH 6.8) for the dissolution test (KPV). PVP K-30 and methyl cellulose were used as carriers in SDS, and chloroform as a solvent. Computer optimization technique was applied to obtain an optimum formula of SDS, and the following results were obtained; 1) Dissolution rate of ketoconazole in SDS was larger than that of pure ketoconazole in the second fluid of pH 6.8. 2) PVP K-30 and methyl cellulosr were good carriers for SDS of ketoconazole. Moerover PVP K-30 was better than methyl cellulose. 3) The optimum formula of ketoconazole SDS obtained from computer optimization technique was chloroform 175 ml, PVP K-30 5g and methyl cellulose 0.2g per 1g of ketoconazole. 4) The experimental value of $A_{60}$ (Amount released from ketoconazole tablet during 60 minutes) obtained from SDS by optimum formula agreed well with the value calculated by polynomial regression equation.

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