• Journal of Ocean Engineering and Technology
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• v.10 no.3
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• pp.50-61
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• 1996

The breaking phenomenon of regular periodic waves generated by a numerical wave maker is simulated by finite-difference method which can cope with strong interface motions. The air and water flows are simultaneously solved in the time-marching solution procedure for the Navier-Stokes equation. A density-function technique is devised for the implemenation of the interface conditions. The accuracy is examined and applied to the simulation of two-dimensional breaking phenomena of periodic gravity waves.

• Journal of applied mathematics & informatics
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• v.27 no.3_4
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• pp.501-515
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• 2009

A second order nonlinear ordinary differential equation is obtained by solving the initial-boundary value problem of a class of elas-todynamics equations, which models the radially symmetric motion of a incompressible hyper-elastic solid sphere under a suddenly applied surface tensile load. Some new conclusions are presented. All existence conditions of nonzero solutions of the ordinary differential equation, which describes cavity formation and motion in the interior of the sphere, are presented. It is proved that the differential equation has singular periodic solutions only when the surface tensile load exceeds a critical value, in this case, a cavity would form in the interior of the sphere and the motion of the cavity with time would present a class of singular periodic oscillations, otherwise, the sphere remains a solid one. To better understand the results obtained in this paper, the modified Varga material is considered simultaneously as an example, and numerical simulations are given.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.24 no.8 s.179
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• pp.1991-1999
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• 2000

This research has been performed to reveal the hysteresis phenomena of the hunting motion in a railway passenger car having a bolster. Since linear analysis can not explain them, bifurcation analysis is used to predict its outbreak velocities in this paper. However bifurcation analysis is attended with huge computing time, thus this research proposes more effective numerical algorithm to reduce it than previous researches. Stability of periodic solution is obtained by adapting of Floquet theory while stability of equilibrium solutions is obtained by eigen-value analysis. As a result, linear and nonlinear critical speed are acquired. Full scale roller rig test is carried out for the validation of the numerical result. Finally, it is certified that there are many similarities between numerical and test results.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.15 no.2
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• pp.143-150
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• 2011

We consider the global existence of strong solutions of the 3D incompressible Navier-Stokes equations in a thin periodic domain. We present a simple proof that a strong solution exists globally in time when the initial velocity in $H^1$ and the forcing function in $L^p$(0,${\infty}$;$L^2$), $2{\leq}p{\leq}{\infty}$ satisfy certain condition. This condition is basically similar to that by Iftimie and Raugel[7], which covers larger and larger initial data and forcing functions as the thickness of the domain ${\epsilon}$ tends to zero.

• Journal of applied mathematics & informatics
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• v.27 no.3_4
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• pp.779-793
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• 2009

This paper deals with a delayed SEIRS epidemic model with pulse vaccination and crowded incidence rate. Moreover, the case of vertical and horizontal transmission is considered. By using the discrete dynamical system determined by the stroboscopic map, the exact infection-free periodic solution of the SEIRS model is obtained. Further, by employing the comparison arguments, we prove that under the condition that $R_*$ < 1 the infection-free periodic solution is globally attractive, and that under the condition that $R^*$ > 1 the disease is uniformly persistent, which means that after some period of time the disease will become endemic.

• Journal of Institute of Control, Robotics and Systems
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• v.4 no.6
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• pp.802-810
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• 1998

The purpose of this study is to find the analytic solution of determining the optimal capacity of processes and storages to meet the product demand. Recent trend to reduce product delivery time and to provide high quality product to customer requires the increasing capacity of storage facilities. However, the cost of constructing and operating storage facilities is becoming substantial because of increasing land value, environmental and safety concern. Therefore, reasonable decision making about the capacity of processes and storages is important subject for industries. The industrial solution for this subject is to use the classical economic lot sizing method, EOQ(Economic Order Quantity) model, trimmed with practical experience but the unrealistic assumption of EOQ model is not suitable for the chemical plant design with highly interlinked processes and storages. This study, a first systematic attempt for this subject, clearly overcomes the limitation of classical lot sizing method. The superstructure of the plant consists of the network of serially and/or parallelly interlinked processes and storages. A novel production and inventory analysis method, PSW(Periodic Square Wave) model, is applied. The objective function of optimization is minimizing the total cost composed of setup and inventory holding cost. The advantage of PSW model comes from the fact that the model provide a set of simple analytic solution in spite of realistic description of material flow between process and storage. The resulting simple analytic solution can greatly enhance the proper and quick investment decision for the preliminary plant design confronting diverse economic situation.

• Communications for Statistical Applications and Methods
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• v.21 no.6
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• pp.513-520
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• 2014

We study numerical methods to obtain the stationary probabilities of continuous-time Markov chains whose embedded chains are periodic. The power method is applied to the balance equations of the periodic embedded Markov chains. The power method can have the convergence speed of exponential rate that is ambiguous in its application to original continuous-time Markov chains since the embedded chains are discrete-time processes. An illustrative example is presented to investigate the numerical iteration of this paper. A numerical study shows that a rapid and stable solution for stationary probabilities can be achieved regardless of periodicity and initial conditions.

• Journal of applied mathematics & informatics
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• v.26 no.1_2
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• pp.263-273
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• 2008

For the discrete version of an artificial neural network of two neurons with piecewise constant argument, we obtain some sufficient conditions that every solution is either periodic or convergent.

• Corrosion Science and Technology
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• v.3 no.6
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• pp.251-256
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• 2004

Exposure of zinc samples in simulated acid rain solution (SARS) was investigated under a periodic wet-dry conditions using an AC impedance technique. The periodic wet and dry exposure consisted of the immersion of zinc samples in SARS for one hour followed by exposure to 7 hours drying at 60% RH. Phases of the corrosion products were indentified by X-ray diffraction (XRD). The influence of relative humdiity (RH), temperature, and surface inclination on the atmospheric corrosion of zinc is described. The reciprocal of polarization resistance (1/Rp) decreases rapidly during the initial stages then slowly and eventually attains a steady state as exposure time progresses. The average of reciprocal of polarization resistance per cycle, (ARPR) was calculated and found to decrease as number of exposure cycle increases. An increase of temperature enhances the corrsion rate of zinc. The values of ARPR, of a sample inclined at 30 o are lower than those for a sample oriented horizontally. The experiment result shows a pronounced dependence of reciprocal of polarization resistance on RH. Exposure in the presence of carbonate anions gives rise to more protective corrosion products than in nitrate anion solution. The corrosion mechanism during the initial stages of atmospheric zinc corrosion under wet-dry cyclic conditions is suggested.

• Bulletin of the Korean Chemical Society
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• v.29 no.3
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• pp.609-614
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• 2008

A periodic mesoporous organosilica material was synthesized by microwave heating (PMO-M) using 1,2-bis(trimethoxysilyl)ethane as a precursor in a cationic surfactant solution, and textural properties were compared with those of the product produced by conventional convection heating (PMO-C). These synthesized materials were characterized using XRD, TEM/SEM, N2 adsorption isotherm, 29Si and 13C NMR, and TGA, which confirmed their good structural orders and clear arrangements of uniform 3D-channels. Synthesis time was reduced from 21 h in PMO-C to 2-4 h in PMO-M. PMO-M was made of spherical particles of 1.5-2.2 m m size, whereas PMO-C was made of decaoctahedron-shaped particles of ca. 8.0 m m size. Effect of synthesis temperature, time, and heating mode on the PMO particle morphology was examined. The particle size of PMO-M could be controlled by changing the heating rate by adjusting microwave power level. PMO-M demonstrated improved separation of selected organic compounds compared to PMO-C in a reversed phase HPLC experiment. Ti-grafted PMO-M also resulted in higher conversion in liquid phase cyclohexene epoxidation than by Ti-PMO-C.