• Communications of the Korean Mathematical Society
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• v.13 no.3
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• pp.579-587
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• 1998

In this paper we will estimate the lower bound of k-th Dirichlet eigenvalue $ \lambda_{k}$ / of Laplace equation on bounded domain in sphere.

• Computational Structural Engineering
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• v.8 no.4
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• pp.129-136
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• 1995

This paper presents a boundary element method for obtaining approximate solutions of 2-dimensional consolidation problems based on the Biot's linear theory. Laplace transform is applied to differential equation system in order to eliminate the time dependency. The boundary integral equations in transformed space are formulated and the fundamental solutions are shown in a closed form. In order to convert the transformed solutions to the ones in real space, the Hosono's numerical Laplace transform inversion method is applied. As a numerical example, a half-space consolidation problem subjected to a strip local load is selected and the applicability of the method is demonstrated through the comparison with the exact solutions.

• Journal of Korea Water Resources Association
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• v.42 no.12
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• pp.1125-1133
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• 2009

Evanescent modes which are the other solutions of the Laplace equation for the linear dispersion equation may affect the wave transformation especially when a water depth varies abruptly. In this study, the effects of evanescent modes for a three-dimensional depression of seabed are investigated by using the eigenfunction expansion method. A convergence test is first carried out by changing numbers of domains and evanescent modes. The wave transformation for various depressions of seabed is then calculated under condition that the solution of the eigenfunction expansion method is converged.

• Journal of the Institute of Electronics Engineers of Korea SD
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• v.47 no.12
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• pp.17-23
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• 2010

In this paper, a new analytical model for deriving the threshold voltage of a short-channel bulk-type MOSFET is suggested. Using the Fourier coefficient method, the Laplace equation in the oxide region and the Poisson equation in the depleted silicon region have been solved two-dimensionally. Making use of them, the minimum surface potential is derived to describe the threshold voltage. Simulation results show good agreement with the dependencies of the threshold voltage on the various device parameters and applied bias voltages.

• Journal of the Institute of Electronics Engineers of Korea SD
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• v.45 no.7
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• pp.9-16
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• 2008

In this paper, a simple analytical model for deriving the threshold voltage of a short-gate SOI MESFET is suggested. Using the iteration method, the Poisson equation in the fully depleted silicon channel and the Laplace equation in the buried oxide region are solved two-dimensionally, Obtained potential distributions in each region are expressed in terms of fifth-order of $\chi$, where $\chi$ denotes the coordinate perpendicular to the silicon channel direction. From them, the bottom channel potential is used to describe the threshold voltage in a closed-form. Simulation results show the dependencies of the threshold voltage on the various device geometry parameters and applied bias voltages.

• Journal of the Institute of Electronics Engineers of Korea SD
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• v.48 no.10
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• pp.54-61
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• 2011

In this paper, a simple analytical model for deriving the I-V characteristics of a cylindrical surrounding gate SOI MOSFET with intrinsic silicon core is suggested. The Poisson equation in the intrinsic silicon core and the Laplace equation in the gate oxide layer are solved analytically. The surface potentials at both source and drain ends are obtained by means of the bisection method. From them, the surface potential distribution is used to describe the I-V characteristics in a closed-form. Simulation results seem to show the dependencies of the I-V characteristics on the various device parameters and applied bias voltages within a range of satisfactory accuracy.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.7 no.4
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• pp.21-29
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• 1987

In this paper the liquid sloshing effects in vertical storage tanks under earthquake loadings are studied. The study focuses on the investigation of the effect of the flexibility of the tank wall on the hydrodynamic forces exerted on it. The tank structure is modelled using finite elements. The motion of the liquid is expressed by the Laplace equation. The equation of motion of the fluid shell system is formulated including the coupling effect between the shell motion and the sloshing motion. A procedure is developed to obtain the natural frequencies and the mode shapes of the sloshing motion as well as the shell vibration. Dynamic analyses have been carried out for several tanks with different dynamic characteristics utilizing the time history method as well as the response spectra method.

• Nuclear Engineering and Technology
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• v.55 no.8
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• pp.2952-2965
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• 2023

Advanced reactors, such as Small Modular Reactors or existing Nuclear Power Plants, often use Field Programmable Gate Array (FPGA) based controllers in new Instrumentation and Control (I&C) system architectures or as an alternative to existing analog-based I&C systems. Compared to CPU-based Programmable Logic Controllers (PLCs), FPGAs offer better overall performance. However, programming functions on FPGAs can be challenging due to the requirement for a hardware description language that does not explicitly support the operation of real numbers. This study aims to implement the Reactor Trip (RT) functions of the existing analog-based Reactor Protection System (RPS) using FPGAs. The RT equations for Overtemperature delta Temperature and Overpower delta Temperature involve dynamic compensators expressed with the Laplace transform variable, 's', which is not directly supported by FPGAs. To address this issue, the trip equations with the Laplace variable in the continuous-time domain are transformed to the discrete-time domain using the Z-transform. Additionally, a new operation based on a relative value for the equation range is introduced for the handling of real numbers in the RT functions. The proposed approach can be utilized for upgrading the existing analog-based RPS as well as digitalizing control systems in advanced reactor systems.

• Laser Solutions
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• v.5 no.1
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• pp.23-31
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• 2002

The uniform metal droplet generation using Nd-YAG laser was studied and experiment was carried out. The shape and volume of developed droplet was measured and the Young-Laplace equation and equilibrium condition of force were applied this model. The differential equation predicting shape of droplet using equilibrium condition of force instead of Navier-stokes equation was induced and numerical solution of differential equation compared with experimentation data. The differential equation was solved by Runge-Kutta method. Surface tension coefficient of droplet was determined with numerical solution relate to experimental result under the statical condition. In case of dynamic vibration, metal droplet shape and detaching critical volume are predicted by recalculating proposed model. The result revealed that this model could reasonably describe the behavior of molten metal droplet on vibration.

• Journal of Industrial Technology
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• v.9
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• pp.79-85
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• 1989

In this paper, the static limit of Helmhortz equation is discussed in the analysis of acoustic wave scattering in a waveguide. Boundary integral equation method is used to formulate the scattering process in the exerior of the scatterer and finite element method in the interior of the scatterer. And hybrid Ray-Mode Method is used the provide the Green's function of the waveguide. The proposed algorithm is applied to a sample poblem with arbitrary scatterer in a waveguide. The results are compared with those of Laplace's equation which is the governing equation in the static problems.