• Magazine of the Korean Society of Agricultural Engineers
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• v.9 no.2
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• pp.1301-1305
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• 1967

Ground water flow can be studied with model test. Model test of ground water works are necessary for economic and safe design of the works. Also influence of the ground water flow to the durability and safety of hydraulic structures can be studied with this model. a. Sand model ; Water flow through porous media is the principle of sand model. Darcy's formula is the basic equation, $q=k{\frac{dh}{ds}}^{\circ}. The effect of the ground water flow on the grain system itself is represented with this model only. b. Hele-Shaw model ; In this model use is made of the viscous flow analogy. Viscous fluid such as glycerine flowing through two parallel plates depends on Poiseuille law, $q=-c{\frac{dh}{ds}}$. The analogue can be used vertically and horizontally. c. Heat model ; This is based on the analogy of the Fourier's law for heat conduction and Darcy's law for ground water flow. Especially unsteady problem can be studied with this model. A difficulty of the construction of this model is the isolation, which has to prevent losses of the heat. d. Electirc model ; Ohm's law for electric current is analogous to Darcy's law. Resistance material such as metal foil, graphite block, water with salt added, gelatine with salt added, ete. is connected to electric sources and resistor, and equi-voltage line is detected with galvanometer, $N_aCl$, $CuSo_4$, etc. are used as salt in the model. e. Membrane model ; This model is based on the facts that the deflection of a thin membrane obeys Laplace's equation if there is no load in the direction perpendicular to the membrane, and if the dellection is small.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.15 no.4
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• pp.619-628
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• 2002

This paper deals with the FE analysis for the free vibration of sloshing in horizontal cylindrical tank with baffles. We use Laplace equation based on potential theory as governing equation. This problem is solved by FEM using lineal isoparametric elements. We assume that the tank as well as baffles is rigid body and by separating nodes into two at the baffle location, baffle effect is obtained by separating nodes into two at the baffle location. For the calculation of natural frequencies and mode shapes, we introduce Lanczos transformation and Jacobi iteration methods. Numerical results of the first longitudinal and transverse modes, while comparing with literature cited, are very good. In order for the baffle effects on the free vibration of sloshing, various combinations of baffle parameters, which are location, inner diameter and number, are examined.

• Journal of the Korean Institute of Gas
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• v.2 no.1
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• pp.40-46
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• 1998

Mathematical modeling on the corrosion of the steel casing and main pipe due to the protection current resulting from a cathodic protection system was carried out using boundary element method. The model is consisted of Laplace's equation with non-linear boundary conditions(Tafel equations) and the iterative technique to determine the miexed potential of the steel casing. The model is applied to the normal steel casing section as well as abnormal one with defects such as metal touch and insulation defects. From the modeling procedure, we can calculate the potential distributions and current density distributions of the system. The theoretical results of the qualitatiive corrosion aspect along the steel casing and main pipe agree well with the experimental results within the experimental conditions studied.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.32 no.4
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• pp.249-256
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• 2019

This paper presents an optimization framework of electrical impedance tomography for characterizing electrical conductivity profiles of concrete structures in two dimensions. The framework utilizes a partial-differential-equation(PDE)-constrained optimization approach that can obtain the spatial distribution of electrical conductivity using measured electrical potentials from several electrodes located on the boundary of the concrete domain. The forward problem is formulated based on a complete electrode model(CEM) for the electrical potential of a medium due to current input. The CEM consists of a Laplace equation for electrical potential and boundary conditions to represent the current inputs to the electrodes on the surface. To validate the forward solution, electrical potential calculated by the finite element method is compared with that obtained using TCAD software. The PDE-constrained optimization approach seeks the optimal values of electrical conductivity on the domain of investigation while minimizing the Lagrangian function. The Lagrangian consists of least-squares objective functional and regularization terms augmented by the weak imposition of the governing equation and boundary conditions via Lagrange multipliers. Enforcing the stationarity of the Lagrangian leads to the Karush-Kuhn-Tucker condition to obtain an optimal solution for electrical conductivity within the target medium. Numerical inversion results are reported showing the reconstruction of the electrical conductivity profile of a concrete specimen in two dimensions.

• Journal of the Society of Naval Architects of Korea
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• v.37 no.1
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• pp.67-81
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• 2000

An accurate and efficient numerical method for two-dimensional nonlinear radiation problem has been developed. The wave motion due to a moving body is described by the assumption of ideal fluid flow, and the governing Laplace equation can be effectively solved by the higher-order boundary element method with the help of the GMRES (Generalized Minimal RESidual) algorithm. The intersection or corner problem is resolved by utilizing the so-called discontinuous elements. The implicit trapezoidal rule is used in updating solutions at new time steps by considering stability and accuracy. Traveling waves caused by the oscillating body are absorbed downstream by the damping zone technique. It is demonstrated that the present method for time marching and radiation condition works efficiently for nonlinear radiation problem. To avoid the numerical instability enhanced by the local gathering of grid points, the regriding technique is employed so that all the grids on the free surface may be distributed with an equal distance. This makes it possible to reduce time interval and improve numerical stability. Special attention is paid to the local flow around the body during time integration. The nonlinear radiation force is calculated by the "acceleration potential technique". Present results show good agreement with other numerical computations and experiments.

• Journal of Soil and Groundwater Environment
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• v.21 no.6
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• pp.46-55
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• 2016

This experimental study was aimed to estimate interfacial tension of brine-$CO_2$ by using a pendant bubble method and image analysis. Measurements were performed for wide ranges of temperatures, pressures, and salinities covering reservoir conditions in Pohang basin, a possible candidate for $CO_2$ storage operation in Korea. The profiles of $CO_2$ bubbles in brine obtained from image analysis with the densities of brine and $CO_2$ from previous studies were applied to Laplace-Young equation for calculating interfacial twnsion in brine-$CO_2$ system. The experimental results reveals that the interfacial tension is significantly affected by reservoir conditions such as pressure, temperature and water salinity. For conditions of constant temperature and water salinity, the interfacial tension decreases as pressure increases for low pressures (P < $P_c$), and approaches to a constant value for high pressures. For conditions of constant pressure and water salinity, the interfacial tension increases as temperature increases for T < $T_c$, with an asymptotic trend towards a constant value for high temperatures. For conditions of constant pressure and temperature, the interfacial tension increases with increasing water salinity. The trends in changes of interfacial tension can be explained by the effects of the reservoir conditions on the density difference of brine and $CO_2$, and the solubility of $CO_2$ in brine. The information on interfacial tensions obtained from this research can be applied in predicting the migration and distribution of injecting and residual fluids in brine-$CO_2$-rock systems in deep geological environments during geological $CO_2$ sequestrations.

• Journal of the Korean Institute of Telematics and Electronics D
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• v.36D no.5
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• pp.44-53
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• 1999

This paper are reported a methodology and application for extracting parasitic capacitances in a multi-level interconnect semiconductor structure by a numerical technique. To calculate the parasitic capacitances between the interconnect lines, we employed finite element method (FEM) and calculated the distrubution of electric potential in the inter-metal layer dielecric(ILD) by solving the Laplace equation. The three-dimensional multi-level interconnect structure is generated directly from two-dimensional mask layout data by specifying process sequences and dimension. An exemplary structure comprising two metal lines with a dimension of 8.0$\times$8.0$\times$5.0$\mu\textrm{m}^3/TEX>, which is embedded in three dielectric layer, was simulated to extract the parasitic capacitances. In this calculation, 1960 nodes with 8892 tetrahedra were used in ULTRA SPARC 1 workstation. The total CPU time for the simulation was 28 seconds, while the memory size of 4.4MB was required.

• International Journal of Reliability and Applications
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• v.12 no.1
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• pp.15-39
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• 2011

This paper deals with the reliability analysis of a complex system with three possibilities at the time of repair. The considered system consists of two subsystems A and Bin series configuration (1-out-of-2: F). Subsystem A has n units which are connected in series whereas subsystem B consists of n units in parallel configuration. The configuration of subsystem A is of 1-out-of-n: F whereas subsystem B is of k-out-of-n: D and k+1-out-of-n: F nature. System has three states: Good, degraded and failed. Supplementary variable technique has been used for mathematical formulation of the model. Laplace transform is being utilized to solve the mathematical equation. Reliability, Availability, M.T.T.F., Busy Period and Cost effectiveness of the system have been computed. The repairs from state $S_7$ to $S_0$, $S_8$ to $S_0$, $S_9$ to $S_0$ and $S_{11}$ to $S_0$ have two types namely exponential and general. Joint probability distribution of repair rate from $S_7$ to $S_0$, $S_8$ to $S_0$, $S_9$ to $S_0$ and $S_{11}$ to $S_0$ is computed by Gumbel-Hougaard family of copula. Some particular cases of the system have also been derived to see the practical importance of the model.

• Investigative Magnetic Resonance Imaging
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• v.14 no.2
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• pp.87-94
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• 2010

Purpose : To calculate the appearance of the image distortion from metallic artifacts and to determine the location of a metallic needle from a distorted MR image. Materials and Methods : To examine metal artifacts, an infinite metal cylinder in a strong magnetic field are assumed. The cylinder’s axis leaned toward the magnetic field along some arbitrary angle. The Laplace equation for this situation was solved to investigate the magnetic field distortion, and the simulation was performed to evaluation the image artifact caused by both readout and slice-selection gradient field. Using the result of the calculation, the exact locations of the metal cylinder were calculated from acquired images. Results : The distances between the center and the folded point are measured from images and calculated. Percentage errors between the measured and calculated distance were less than 5%, except for one case. Conclusion : The simulation was successfully performed when the metal cylinder was skewed at an arbitrary tilted angle relative to the main magnetic field. This method will make it possible to monitor and guide both biopsy and surgery with real time MRI.

• Transactions of the Korean Society of Mechanical Engineers
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• v.12 no.5
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• pp.1158-1174
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• 1988

A numerical technique is developed for the solution of fully developed turbulent recirculating flow in the passage of variable area using the non-orthogonal coordinate transformation. In the numerical analysis, primitive pressure-velocity finite difference equations were solved by SIMPLER algorithm with 2-equation turbulence model and algebraic stress model (ASM). QUICK scheme on the differencing of convective terms which is free from the inaccuracies of numerical diffusion has been applied to the variable grids and the results compared with those from HYBRID scheme. In order to test the effect of streamline curvatures on turbulent diffusion Lee and Choi streamline curvature correction model which has been obtained by modifying the Leschziner and Rodi's model is testes. The ASM was also employed and the results are compared to those from another turbulence model. The results show that difference of convective differencing schemes and turbulence models give significant differences in the prediction of velocity fields in the expansion region and outlet region of the combustor, however show little differences in the parallel flow region.