• Journal of applied mathematics & informatics
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• v.13 no.1_2
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• pp.233-245
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• 2003

A time fractional advection-dispersion equation is Obtained from the standard advection-dispersion equation by replacing the firstorder derivative in time by a fractional derivative in time of order ${\alpha}$(0 < ${\alpha}$ $\leq$ 1). Using variable transformation, Mellin and Laplace transforms, and properties of H-functions, we derive the complete solution of this time fractional advection-dispersion equation.

• Journal of Environmental Science International
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• v.11 no.9
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• pp.907-914
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• 2002

Various Eulerian-Lagrangian models for the one-dimensional longitudinal dispersion equation in nonuniform flow were studied comparatively. In the models studied, the transport equation was decoupled into two component parts by the operator-splitting approach; one part is governing advection and the other is governing dispersion. The advection equation has been solved by using the method of characteristics following fluid particles along the characteristic line and the results were interpolated onto an Eulerian grid on which the dispersion equation was solved by Crank-Nicholson type finite difference method. In the solution of the advection equation, Lagrange fifth, cubic spline, Hermite third and fifth interpolating polynomials were tested by numerical experiment and theoretical error analysis. Among these, Hermite interpolating polynomials are generally superior to Lagrange and cubic spline interpolating polynomials in reducing both dissipation and dispersion errors.

• Water for future
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• v.28 no.4
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• pp.195-204
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• 1995

New dispersion coefficient equation which can be used to estimate dispersion coefficient by using only hydraulic data easily obtained in natural streams has been developed. Dimensional analysis was performed to select physically meaningful parameters, One-Step Huber method, which is one of the nonlinear multi-regression method, was applied to derive a regression equation of dispersion coefficient. 59 measured hydraulic data which were collected in 26 streams in the United States and were analyzed in the Part I of this study, were used in developing new dispersion coefficient equation. Among 59 measured data sets, 35 data sets were used in deriving regression equation, and 24 data sets are used for verification. The new dispersion coefficient equation, which has been developed in this study was proven to be superior in explaining dispersion characteristics of natural streams more precisely compared to existing dispersion coefficient equations.

• Journal of Soil and Groundwater Environment
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• v.8 no.3
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• pp.8-12
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• 2003

The centrifuge test result on capped sediment was compared to the advection- dispersion equation proposed for one layered to predict contaminant transport parameters. The fitted contaminant transport parameters for the centrifuge test results were one to three orders of magnitude greater than the estimated parameters from the advection-dispersion equation. This indicates that the centrifuge model over estimated the contaminant transport phenomena. Thus, the centrifuge provides a non-conservative approach to modeling contaminant transport. It should be also noted that the advection-dispersion equation used in this study is a one layered model. Two layered modeling approaches are more appropriate for modeling this data since there are two layers with different partitioning coefficients. Further research is required to model the centrifuge test using two-layered advection-dispersion models.

• Korean Journal of Hydrosciences
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• v.6
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• pp.51-66
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• 1995

Various Eulerian-Lagerangian numerical models for the one-dimensional longtudinal dispersion equation are studied comparatively. In the models studied, the transport equation is decoupled into two component parts by the operator-splitting approach ; one part governing advection and the other dispersion. The advection equation has been solved using the method of characteristics following flud particles along the characteristic line and the result are interpolated onto an Eulerian grid on which the dispersion equation is solved by Crank-Nicholson type finite difference method. In solving the advection equation, various interpolation schemes are tested. Among those, Hermite interpo;ation po;ynomials are superor to Lagrange interpolation polynomials in reducing both dissipation and dispersion errors.

• Water for future
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• v.28 no.3
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• pp.205-216
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• 1995

Existing equations for dispersion coefficient are analyzed in depth to select proper dispersion coefficient which can represent dispersion characteristics of natural streams. Several equations are tested with measured data which were collected in 26 streams in the United States. Findings of this study are as follows. Elder's equation should not be used to estimate dispersion coefficient of the one-dimensional dispersion model because it underestimates significantly. McQuivey and Keefer's equation is overestimating, whereas Magazine et al.'s equation is underestimating. However, Iwasa and Aya's equation predicts relatively well. Fischer's equation is generally overestimating. Liu's equation predicts quite well. The performance of Liu's equation is the best of all especially in terms of accuracy. However, Liu's equation is generally overestimating in case of large river because the square of channel width is included in the equation. Therefore, it is recommended not to use Liu's equation in case of large rivers, especially rivers of which channel width is larger than 200m.

• Water for future
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• v.23 no.1
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• pp.119-127
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• 1990

The concentration of cohesive suspended sediment is determined by the circulation of water and the material dispersion. The equations of the two-dimensional, depth-integrated dispersive transport are the Reynolds equation, continuity equation, and advection-dispersion equation based on the Fick's law. A finite difference method has been applied to two models of circulation and dispersion transport. The circulation model is solved by the explicit scheme and the dispersion transport model is solved by multi-operational scheme. It is investigated wheter advective terms are included when the equation of circulation is applied to the model. For advection-dispersion equation, it was also investigated about variations of suspended sediment concentration with respect to the critical shear stresses.

• Journal of the Korean Institute of Telematics and Electronics A
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• v.32A no.8
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• pp.140-152
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• 1995

Derived was the scalar wave equation of optical fibers. Based on the derived equation, the dispersion characteristics of arbitrarily profiled fibers were analyzed. We applied the 1-D FEM employing quadratic interpolation fucntions to solve the scalar wave equation. To find the optimum index distribution of a fiber that has the ultra-low total dispersion, we analyzed QC fibers as objects. Adding 2$_{nd}$ and 3$_{rd}$ clads to DC fiber, we investigated the change of dispersion characteristics. We found the QC fiber parameters for which the dispersion was ultra-low flattened, less than 0.5 ps/km.nm for ${\lambda}=1.4~1.6{\mu}m$, and the dispersion value was as low as 0.20 ps/km.nm at ${\lambda}=1.55{\mu}m$.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.32 no.6B
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• pp.373-378
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• 2012

In this study, a new empirical equation for the transverse dispersion coefficient has been developed based on the theoretical background in river bends. The nonlinear least-square method was applied to determine regression coefficients of the equation. The estimated dispersion coefficients derived by the new equation were compared with observed transverse dispersion coefficients acquired from natural rivers and coefficients calculated by the other existing empirical equations. From a comparison of the existing transverse dispersion equations and the new proposed equation, it appears that the behavior of the existing formula in a relative sense is very much dependent on the friction factor and the river geometry. However, the new proposed equation does not vary widely according to variation of friction factor. Also, it was revealed that the equation proposed in this study becomes an asymptotic curve as the curvature effect increases.

• Journal of Electrical Engineering and Technology
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• v.1 no.3
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• pp.381-386
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• 2006

In dielectric waveguide analysis and synthesis, we often encounter an awkward task of solving the eigenvalue equation to find the value of propagation constant. Since the dispersion equation is an irrational equation, we cannot solve it directly. Taking advantage of approximated calculation, we attempt here to solve this irrational dispersion equation. A new type of eigenvalue equation, in which guide index is expressed as a function of frequency, has been developed. In practical optical waveguide designing and in calculating the propagation mode, this equation will be used more conveniently than the previous one. To expedite the design of the waveguide, we then solve the eigenvalue equation of a slab waveguide, which is sufficiently accurate for practical purpose.