• Journal of Korea Water Resources Association
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• v.32 no.6
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• pp.607-616
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• 1999

A fractional step finite difference model for the longitudinal dispersion of nonconservative contaminants is developed. It is based on splitting the longitudinal dispersion equation into a set of three equations each to be solved over a one-third time step. The fourth-order Holly-Preissmann scheme, an analytic solution, and the Crank-Nicholson scheme are used to solve the equations for the pure advection, the first-order decay, and the diffusion, respectively. To test the model, it is applied to simulate the longitudinal dispersion of continuous source released into a nonuniform flow field as well as the dispersion of an instantaneous source in a uniform flow field. The results are compared with the exact solution and those computed by an existing model. Compared to the existing model which uses Euler method for the first-order decay equation, the present model yield more accurate results as the decay coefficient increases.

• Journal of the Society of Cosmetic Scientists of Korea
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• v.33 no.2
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• pp.105-110
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• 2007

The stability of titanium dioxide dispersion was evaluated by zeta ($\zeta$) potential and we intended to apply it for improvement of dispersion stability. Both theories related to $\zeta$ potential (electric double layer, electrophoresis, isoelectric point and electroosmosis) and a method to measure $\zeta$ potential were explained in this study. The change in $\zeta$ potential of $TiO_2$ dispersion was measured by means of Henry's function of Helmholtz-Smoluchowski's equation (H-S equation). The $\zeta$ potentials of $TiO_2$ dispersion were negative in all measured pH values ($3.0{\sim}9.0$), and absolute values of $\zeta$ potentials of $TiO_2$ increased as pH values increased. $TiO_2$ dispersion was maintained in pH 8.0 and 9.0 respectively. From these results, we suggest that $\zeta$ potentials have an effect on $TiO_2$ dispersion and absolute value of $\zeta$ potentials played an important role in the stability of $TiO_2$ dispersion in aqeous medium.

• Journal of Korean Society for Atmospheric Environment
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• v.16 no.2
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• pp.141-150
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• 2000

In order to genralize the vertical dispersion of plume at long distances on mesoscale over complex terrain dispersion coefficients data have been obtained systematically according to lapsed time after release by using a composite turbulence water tank that simulates convective boundary layer. Dispersion experiments have been carried out for various combined conditions of thermal turbulence intensity mechanical turbulence intensity and plume release height at slightly to moderately unstable conditions. Results of tracer dispersion experiments conducted using water tank camera and image processing system have been converted into atmospheric dispersion data through the application of similarity law. The equation $\sigma$z/Zi=aX/(b+c X2)0.5 where $\sigma$2; vertical dispersion coefficient zi : mixing height X : dimen-sionaless downwind distance was confirmed to be an appropriate and general equation for expressing $\sigma$2 variation with turbulence intensity and plume release height, The value of "a" was found to be principally affected by mechanical turbulence intensity and that of "b" by mechanical turbulence intensity and release height. It was confirmed that the magnitude of "c" varies with release height. Results of water tank experiments on the relationship of $\sigma$2 vs downwind distance x have been compared with actual atmospheric dispersion data such as CONDORS data and Bowne's nomogram Operating conditions of a composite turbulence water tank for simulating the field turbulence situations of CONDORS experiments and Bowne's $\sigma$2(x) nomogram for suburban area have also been investigated in terms of water temperature difference between convection water tank and bottom plate heating tank grid plate stroke mixing water depth length scale and velocity scale. Moreover the effect of mechanical turbulence intensity on vertical dispersion has been discussed in the light of release height and downwind distance. height and downwind distance.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 2008.04a
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• pp.39-44
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• 2008

Stress wave propagation plays an important role in many engineering problems for reducing industrial noise and vibrations. In this paper, the dispersion-corrected finite element model is proposed for reducing the dispersion error in simulation of stress wave propagation. At eliminating the numerical dispersion error arising from the numerical simulation of stress wave propagation, numerical dispersion characteristics of the wave equation based finite element model are analyzed and some dispersion control scheme are proposed. The validity of the dispersion correction techniques is demonstrated by comparing the numerical solutions obtained using the present techniques.

• The Journal of the Acoustical Society of Korea
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• v.15 no.6
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• pp.47-51
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• 1996

The Cylindrical Shell Equation is one of the fundamental tools in the study of the noise analysis in the cylindrical shell. Therefore, lot of the acousticians induced many cylindrical shell motion equations.[1] In the Reference[6], we introduced the newly induced cylindrical Shell Equation and Junger and Feit's shell equation[5], and computed the free wave number with the linear Equation with the supposed solution, in the case of the free motion of the shell. In this paper, we compared above cylindrical shell equations by using dispersion curve of free wave number and we describe the physical mean for the dispersion curve with ring-frequency and ring-extention-frequency. With this result, we proves the useful of a newly induced cylindrical shell equation and we can analyse the Structure-Borne Sound of the shell with this equation in the application.

• Geophysics and Geophysical Exploration
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• v.3 no.2
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• pp.39-47
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• 2000

A great deal of computing time and a large computer memory are needed to solve wave equation in a large complex subsurface layers using the finite difference method. The computing time and memory can be reduced by decreasing the number of grid points per minimum wave length. However, the decrease of grids may cause numerical dispersion and poor accuracy. In this study we performed the grid dispersion analysis for several rotated finite difference operators, which was commonly used to reduce grids per wavelength with accuracy in order to determine the solution for the acoustic wave equation in frequency domain. The rotated finite difference operators were to be extended to 81, 121 and 169 difference stars and studied whether the minimum grids could be reduced to 2 or not. To obtain accuracy (numerical errors less than $1\%$) the following was required: more than 13 grids for conventional 5 point difference stars, 9 grids for 9 difference stars, 3 grids for 25 difference stars, and 2.7 grids for 49 difference stars. After grid dispersion analysis for the new rotated finite difference operators, more than 2.5 grids for 81 difference stars, 2.3 grids for 121 difference stars and 2.1 grids for 169 difference stars were needed. However, in the 169 difference stars, there was no solution because of oscillation of the dispersion curves in the group velocity curves. This indicated that the grids couldn't be reduced to 2 in the frequency acoustic wave equation. According to grid dispersion analysis for the determination of grid points, the more rotated finite difference operators, the fewer grid points. However, the more rotated finite difference operators that are used, the more complex the difference equation terms.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.26 no.2B
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• pp.171-178
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• 2006

The finite element model based on the 2-D advection-dispersion equation incorporating the dispersion tensor that is calculated using velocity field data was developed in order to analyze more accurately 2-D mixing of pollutants for meandering streams. The proposed model was tested using the straight channel that inclined at 45o in the Cartesian coordinate system. The simulation results showed that dispersion tensor model using velocity field data gives an accurate solution. The suitability of the proposed model in analyzing actual pollutant mixing in meandering channels was demonstrated by comparing the simulation results with experimental data obtained from the tracer tests in the laboratory flume. Comparison results showed that the proposed model with dispersion tensor can represents more accurately the mixing phenomena of the pollutants in the meandering channels in which the direction of the primary flow is varying periodically along the channel.

• Proceedings of the IEEK Conference
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• 2001.06a
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• pp.81-84
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• 2001

We propose the cascade FBG(Fiber Bragg Grating)s to compensate the dispersion, discuss the dispersion characteristics of such cascaded FBGs, compare with the single FBG dispersion compensator. For these, we theoretically consider the sencond- and third-order group-velocity dispersion(GVD) in the single fiber grating using plane wave solution and the coupled mode equation. We also theoretically find the group-velocity dispersion in the cascaded fiber gratings from the results in the single fiber grating and present the optimum disign data of the cascaded FBGs dispersion compensator in the N-channel WDM system through the numerical simulation.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.21 no.11
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• pp.3012-3023
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• 1996

In this paper, we analyze the compression of optical soliton which is obtained by proceeding the optical pulse in FSDD(Fiber with Slowly Decreasing Dispersion) using both NSE(Nonlinear Schrodinger Equation) and GNSE(General Nonlinear Schrodinger Equation) and compare the results. We replace the FSDD with a sequence of fibers having different dispersion values and pompre the results with those obtained in FSDD. It is found that the same results in peak value and FWHM(Full width Half Maximum) can be obtained by replacing FSDD with a sequence of fibers having proper length. We vary the shape of initial pulse which is the input of FSDD and suggest the condition to obtain higher compression rate.

• Smart Structures and Systems
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• v.17 no.2
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• pp.327-345
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• 2016

The existence of SH-wave in a piezomagnetic layer overlying an initially stressed orthotropic half-space is investigated. The coupled of differential equations are solved for piezomagnetic layer overlying an orthotropic elastic half-space. The general dispersion equation has been derived for both magnetically open circuit and magnetically closed circuits under the four types of boundary conditions. In the absence of the piezomagnetic properties, initial stress and orthotropic properties of the medium, the dispersion equations reduce to classical Love equation. The SH-wave velocity has been calculated numerically for both magnetically open circuit and closed circuits. The effect of initial stress and magnetic permeability are illustrated by graphs in both the cases. The velocity of SH-wave decreases with the increment of wave number.