• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.9 no.1
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• pp.63-77
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• 2005

The Dirichlet-Neumann problem for the dissipative Helmholtz equation in a connected plane region bounded by closed curves and containing cuts is studied. The Neumann condition is given on the closed curves, while the Dirichlet condition is specified on the cuts. The existence of a classical solution is proved by potential theory. The integral representation of the unique classical solution is obtained. The problem is reduced to the Fredholm equation of the second kind and index zero, which is uniquely solvable. Our results hold for both interior and exterior domains.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.14 no.9 s.90
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• pp.910-918
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• 2004

The vibration analysis of an axially moving membrane are investigated when the membrane has the two sets of in-plane boundary conditions, which are free and fixed constraints in the lateral direction. Since the in-plane stiffness is much higher than the out-of-plane stiffness, it is assumed during deriving the equations of motion that the in-plane motion is in a steady state. Under this assumption, the equation of out-of-plane motion is derived, which is a linear partial differential equation influenced by the in-plane stress distributions. After discretizing the equation by using the Galerkin method, the natural frequencies and mode shapes are computed. In particular, we put a focus on analyzing the effects of the in-plane boundary conditions on the natural frequencies and mode shapes of the moving membrane.

• Journal of the Korean Society of Safety
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• v.10 no.2
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• pp.56-63
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• 1995

A simulation of contaminant dispersion in a water reservoir has been done using 2-D finite difference method(FDM). The steady state velocity field of the reservoir was computed using stream function-vorticity formulation of Wavier-Stokes equation and continuity equation. Based on the computed steady state velocity field, the transient convective diffusion equation of the contaminant dispersion was computed. For the 1m$\times$1m reservoir model with inlet and outlet attached, it was shown that the center of circulation located toward right. For the numerical values of v =0.01($\textrm{cm}^2$/s) and D=0.6($\textrm{cm}^2$/s) and the flow of 50($\textrm{cm}^3$/s ), it was determined that the outflow had to be shut down in 18 seconds to prevent from severe pollution. Also the required time was computed to be 6 seconds for the inflow of 100 ($\textrm{cm}^3$/s). The result of this study is considered, hopefully, to be useful for the design of the water reservoir systems that are the subjects to various contamination.

• Biotechnology and Bioprocess Engineering:BBE
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• v.7 no.6
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• pp.362-366
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• 2002

A mathematical model has been developed for describing the oxygen concentration during the exponential growth of microorganisms, in a static solid substrate bed supported on a tray fermentor. The model equations comprise of one partial differential equation for mass transfer and an ordinary differential equation of growth. After nondimensionlisation, analytical solution tn the model has been obtained by the method of Laplace transforms. An expression for critical thickness of bed is deduced from the model equation. The significance of the model in the design of tray fermentors is discussed. The validity of the discussion is verified by taking an illustration from the literature.

• Honam Mathematical Journal
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• v.44 no.2
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• pp.281-295
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• 2022

This paper deals with the long - time behavior of global bounded solutions for a non-autonomous dispersive-dissipative equation with time-dependent nonlinear damping terms under the null Dirichlet boundary condition. By a new Lyapunov functional and Łojasiewicz-Simon inequality, we show that any global bounded solution converges to a steady state and get the rate of convergence as well, which depends on the decay of the non-autonomous term g(x, t), when damping coefficients are integral positive and positive-negative, respectively.

• Transactions of the Korean Society of Mechanical Engineers
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• v.17 no.5
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• pp.1150-1160
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• 1993

The behavior of polystyrene in the strip cavity during the packing and cooling stages for an injection molding process is examined numerically. The mathematical model is based on the unified post-filling model and finite element/finite difference methods are used to solve simultaneously the continuity, momentum and energy equations coupled to an equation of state. Simulated results show that the density of the molded parts is lower in the core than at the skin, and that the hotter the melt or the higher the packing pressure, the higher the density in the core. The density variation during the packing stage comes up to 50% compared with the total density variation. Also, the density variation after gate sealing and the effect of cooling rate on the equation of state are negligible.

• Geomechanics and Engineering
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• v.12 no.6
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• pp.983-1001
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• 2017

The extent by which economy and safety concerns can be addressed in earth retaining structure design depends on the accuracy of the assumed failure surface. Accordingly, this study attempts to investigate and quantify mechanical backfill properties that control failure surface geometry of cohesionless backfills at the active state for translational mode of wall movements. For this purpose, a small scale 1 g physical model study was conducted. The experimental setup simulated the conditions of a backfill behind a laterally translating vertical retaining wall in plane strain conditions. To monitor the influence of dilative behavior on failure surface geometry, model tests were conducted on backfills with different densities corresponding to different dilation angles. Failure surface geometries were identified using particle image velocimetry (PIV) method. Friction and dilation angles of the backfill are calculated as functions of failure stress state and relative density of the backfill using a well-known empirical equation, making it possible to quantify the influence of dilation angle on failure surface geometry. As a result, an empirical equation is proposed to predict active failure surface geometry for cohesionless backfills based on peak dilatancy angle. It is shown that the failure surface geometries calculated using the proposed equation are in good agreement with the identified failure surfaces.

• Proceedings of the Korean Institute of Electrical and Electronic Material Engineers Conference
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• 2002.05c
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• pp.185-188
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• 2002

This paper describes the information for quantitative simulation of weakly ionized plasma. We should grasp the meaning of the plasma state condition to utilize engineering application and to understand materials of plasma state. In this paper, the drift velocity of electron in $SF_6+O_2$ mixture gas calculated for range E/N values l~900[Td] at the temperature is 300[$^{\circ}K$] and pressure is 1[Torr], using a set of electron collision cross sections determined by the authors and the values of drift velocity of electrons are obtained for TOF, PT, SST sampling method of Backward Prolongation by two term approximation Boltzmann equation method. It has also been used to predict swarm parameter using the values of cross section as input. The result of Boltzmann equation, the drift velocity of electrons, has been compared with pure $SF_6$, pure $O_2$ and mixture gas.

• Journal of Korean Society of Steel Construction
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• v.9 no.4 s.33
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• pp.523-533
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• 1997

Current limit state design method for encased composite columns contains irrational and uncertain design equations in defining section and material properties of composite members. Through investigating previous research used in formulating the design equation, this paper explores the irrationality and uncertainty such as 1) transformation of yield stress and elastic modulus for composite section, 2) an equation influencing buckling strength in terms of area rather than moment of inertia, and 3) selection of larger radius of gyration between steel and concrete sections. Improving the design equations this paper proposes two design methods which can be directly used in practical design.

• Proceedings of the Korean Institute of Electrical and Electronic Material Engineers Conference
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• 2001.05c
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• pp.201-203
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• 2001

This paper describes the information for quantitative simulation of weakly ionized plasma. We must grasp the meaning of the plasma state condition to utilize engineering application and to understand materials of plasma state. In this paper, the drift velocity of electron in Xenon gas calculated for range of E/N values from 0.01~500[Td] at the temperature is $300[^{\circ}K]$ and pressure is 1[Torr], using a set of electron collision cross sections determined by the authors and the values of drift velocity of electrons are obtained for TOF, PT, SST sampling method of Backward Prolongation by two term approximation Boltzmann equation method. it has also been used to predict swarm parameter using the values of cross section as input. The result of Boltzmann equation, the drift velocity of electrons, has been compared with experimental data by L. S. Frost and A. V. Phelps for a range of E/N. The swarm parameter from the study are expected to server as a critical test of current theories of low energy scattering by atoms and molecules.