• Korean Journal of Mathematics
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• v.20 no.1
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• pp.107-116
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• 2012

We investigate the multiple solutions for a class of the elliptic system with the singular potential nonlinearity. We obtain a theorem which shows the existence of the solution for a class of the elliptic system with singular potential nonlinearity and Dirichlet boundary condition. We obtain this result by using variational method and critical point theory.

• Journal of Institute of Control, Robotics and Systems
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• v.15 no.4
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• pp.385-389
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• 2009

This paper deals with the enhancement of the complex potential navigation for wheeled mobile robots. The circle theorem from complex function theory is used to avoid an obstacle, and the enhancement to avoid multiple obstacles is proposed. The limit cycle navigation can be combined for robot to kick the ball to the intentioned direction. Avoiding step and superposing twin vortices can be applied to adjust the direction of robot's trajectory. The proposed method is verified through a set of simulation works, and the feasibilities for the enhancement of complex potential theory are successful.

• Journal of the Korean Chemical Society
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• v.46 no.6
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• pp.545-549
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• 2002

Many theories for polymeric liquids are based on the concepts of cell, hole, free volume or lattice etc. In the theories, van der Waals potential, Lennard-Jones 6-12 potential and their modified potentials are commonly used.In this work, Mie(p, 6) potential was applied to the Continuous Lattice Fluid Theory (which extends the discrete lattices of Lattice Fluid Theory to classically continuous lattices) and Dee-Walsch's Cell Theory (which modifies Flory's Equa-tion of State Theory). Both of them are known to be successful theories for polymeric liquids. Thus, PVT values chang-ing with p (the exponent in the repulsion potential) were calculated and compared with experimental values. And, calculated values of Lattice Fluid Theory, Flory's Equation of State Theory and Cho-Sanchez Theory using pertubation method were also compared. Through the calculated results, van der Waals potential, Lennard-Jones 6-12 potential and Mie(p, 6) potential for polymeric liquids were compared with each other.

• Journal of Mechanical Science and Technology
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• v.14 no.8
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• pp.845-850
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• 2000

We consider the problem of determining the singular stresses and electric fields in a piezoelectric ceramic strip containing a Griffith crack under in-plane normal loading within the framework of linear piezoelectricity. The potential theory method and Fourier transforms are used to reduce the problem to the solution of dual integral equations, which are then expressed to a Fredholm integral equation of the second kind. Numerical values on the field intensity factors are obtained, and the influences of the electric fields for PZT-6B piezoelectric ceramic are discussed.

• Proceedings of the Korean Institute of Electrical and Electronic Material Engineers Conference
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• 2004.11a
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• pp.218-221
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• 2004

The electronic state of ZnO doped with Al, Ga and In, which belong to III family elements in periodic table, was calculated using the density functional theory. In this study, the program used for the calculation on theoretical structures of ZnO and doped ZnO was Vienna Ab-initio Simulation Package (VASP), which is a sort of pseudo potential method. The detail of electronic structure was obtained by the describe variational $X{\alpha}(DV-X{\alpha})$(DV-Xa) method, which is a sort of molecular orbital full potential method. The optimized crystal structures obtained by calculations were compared to the measured structure. The density of state and energy levels of dopant elements was shown and discussed in association with properties.

• Journal of the Society of Naval Architects of Korea
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• v.28 no.2
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• pp.159-173
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• 1991

This paper describes a potential-based panel method formulated for the analysis of a super-cavitating two-dimensional hydrofoil. The method employs normal dipoles and sources distributed on the foil and cavity surfaces to represent the potential flow around the cavitating hydrofoil. The kinematic boundary condition on the wetted portion of the foil surface is satisfied by requiring that the total potential vanish in the fictitious inner flow region of the foil, and the dynamic boundary condition on the cavity surface is satisfied by requiring thats the potential vary linearly, i.e., the tangential velocity be constant. Green's theorem then results in a potential-based integral equation rather than the usual velocity-based formulation of Hess & Smith type. With the singularities distributed on the exact hydrofoil surface, the pressure distributions are predicted with improved accuracy compared to those of the linearized lilting surface theory, especially near the leading edge. The theory then predicts the cavity shape and cavitation number for an assumed cavity length. To improve the accuracy, the sources and dipoles on the cavity surface are moved to the newly computed cavity surface, where the boundary conditions are satisfied again. This iteration process is repeated until the results are converged. Characteristics of iteration and discretization of the present numerical method are much faster and more stable than the existing nonlinear theories. The theory shows good correlations with the existing theories and experimental results for the super-cavitating flow. In the region of small angles of attack, the present prediction shows and excellent comparison with the Geurst's linear theory. For the long cavity, the method recovers the trends of the Wu's nonlinear theory. In the intermediate regions of the short super-cavitation, the method compares very well with the experimental results of Parkin and also those of Silberman.

• Structural Engineering and Mechanics
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• v.5 no.6
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• pp.775-784
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• 1997

A unified theory is presented for the shape analysis of curved surface with a single layer structure composed by frame, membrane or shell. The shapes produced by the theory have no shear stress in elements, and the stress states in the whole shape are as uniform as possible under an ordinary load. The theory starts from defining an element potential function expressed by the measurement of the element length or the element area. Therefore, the shape analysis can produce various forms according to the definition of the potential function, and each of those form or the cable net form with the potential function of the second power of element length is simply gotten by the linear analysis. The form in tensile stress is mechanically equal to an isotropic tension form.

• Structural Engineering and Mechanics
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• v.89 no.2
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• pp.135-153
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• 2024

In this study, the impact response of a nanobeam with a moving nanoparticle is investigated. Timoshenko beam theory is used to model the nanobeam behavior and nonlocal elasticity theory is used to consider the effects of small dimensions. The interaction between the nanoparticle and nanobeam has been described using Lennard-Jones potential theory and the equations are discretized by the radial basis meshless method and a mathematical model is presented for the nanobeam-nanoparticle system. Validation of the proposed model is achieved by comparing the obtained natural frequencies with reference values, demonstrating good agreement. Dimensionless frequency analysis reveals a decrease with increasing nonlocal parameter, pointing out a toughening effect in nanobeam. The dynamic response of the nanobeam and nanoparticle is obtained by time integration of equations of motion using Newmark and Wilson-𝜃 methods. A comparative analysis of the two methods is conducted to determine the most suitable approach for this study. As a distinctive aspect in this study, the analysis incorporates the deformation of the nanobeam resulting from the nanoparticle-nanobeam interaction when calculating the Lennard-Jones force in the nanobeam-nanoparticle system. The numerical findings explore the impact of various factors, including the nonlocal parameter, initial velocity, nanoparticle mass, and boundary conditions.

• Journal of Ocean Engineering and Technology
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• v.6 no.2
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• pp.94-102
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• 1992

This paper presents the method of numerical analysis concerned with the hydropdynamic forces and moments of the floating bodies exerted by waves. The analytic methods of hydrodynamic wave forces and moments for large volume structures are generally classified into four categories ; the strip method, the boundary element method, the finite element method, and the potential matching method. In the case of the comparatively large structures, diffraction theory can be applied. However, there are no application limits of diffraction theory which have been known concerning with the analytic method of the rectangular structures. In this paper, the two-dimensional B.E.M. is treated for a moored small rectangular structure in order to evaluate applicability of diffraction theory. Numerical calculation is carried out for the structure. The results are compared with some other ones for verification. The result shows that diffraction theory is applicable to structures smaller than 0.15 in the ratio of the representative structure length d to wave length L for rectangular ones.

• Journal of Ocean Engineering and Technology
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• v.38 no.1
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• pp.1-9
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• 2024

The vertical center of gravity (VCG) has a significant impact on the roll motion response of a surface ship, particularly oil tankers based on the oil level in the tanker after discharging oil at several stations or positional changes, such as changes in the superstructure and deck structure. This study examined the motion response of the Korea very large crude carrier 2 (KVLCC2) at various VCGs, especially roll motion when the VCG changed. The potential theory in the Ansys AQWA program was used as a numerical simulation method to calculate the motion response. On the other hand, the calculations obtained through potential theory overestimated the roll amplitudes during resonance and lacked precision. Therefore, roll damping is a necessary parameter that accounts for the viscosity effect by performing an experimental roll decay. The roll decay test estimated the roll damping coefficients for various VCGs using Froude's method. The motion response of the ship in regular waves was evaluated for various VCGs using the estimated roll-damping coefficients. In addition, the reliability of the numerical simulation in motion response was verified with those of the experiment method reported elsewhere. The simulation results showed that the responses of the surge, sway, heave, pitch, and yaw motion were not affected by changing the VCG, but the natural frequency and magnitude of the peak value of the roll motion response varied with the VCG.