• 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.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.26 no.4
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• pp.333-342
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• 2022

In this paper, we perform a direct comparison study of real experimental data for domain rearrangement and the Cahn-Hilliard (CH) equation on the dynamics of morphological evolution. To validate a mathematical model for physical phenomena, we take initial conditions from experimental images by using an image segmentation technique. The image segmentation algorithm is based on the Mumford-Shah functional and the Allen-Cahn (AC) equation. The segmented phase-field profile is similar to the solution of the CH equation, that is, it has hyperbolic tangent profile across interfacial transition region. We use unconditionally stable schemes to solve the governing equations. As a test problem, we take domain rearrangement of lipid bilayers. Numerical results demonstrate that comparison of the evolutions with experimental data is a good benchmark test for validating a mathematical model.

• Journal of the Korean Mathematical Society
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• v.37 no.6
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• pp.1031-1042
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• 2000

The equations prescribed in Ω⊂R(sup)n are called loaded, if they contain some operations of the traces of desired solution on manifolds (of dimension which is strongly less than n) from closure Ω. These equations result from approximations of nonlinear equations by linear ones, in the problems of optimal control when the control when the control actions depends on a part of independent variables, in investigations of the inverse problems and so on. In present work we study the nonlocal boundary value problems for first-order loaded differential operator equations. Criterion of unique solvability is established. We illustrate the obtained results by examples.

• Bulletin of the Korean Mathematical Society
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• v.53 no.6
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• pp.1725-1739
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• 2016

Abstract. Numerical solutions for the evolutionary space fractional order differential equations are considered. A predictor corrector method is applied in order to obtain numerical solutions for the equation without solving nonlinear systems iteratively at every time step. Theoretical error estimates are performed and computational results are given to show the theoretical results.

• Communications of the Korean Mathematical Society
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• v.22 no.4
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• pp.623-640
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• 2007

The Lotka-McKendrick model which describes the evolution of a single population is developed from the well known Malthus model. In this paper, we introduce the Lotka-McKendrick model. We approximate the solution to the model using hp-discontinuous Galerkin finite element method. The numerical results show that the presented hp-discontinuous Galerkin method is very efficient in case that the solution has a sharp decay.

• 제어로봇시스템학회:학술대회논문집
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• 2004.08a
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• pp.1769-1775
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• 2004

In presence of collision between two rigid bodies, they exhibit impulsive behavior to generate physically feasible state. When the frictional impulse is involved, collision resolution can not be easily made based on a simple Newton's law or Poisson's law, mainly due to possible change of collision mode during collision, For example, sliding may change to sticking, and then sliding resumes. We first examine two conventional methods: the method of mode evolution by differential equation, and the other by linear complementarity programming. Then, we propose a new method for mode evolution by solving only algebraic equations defining mode changes. Further, our method attains the original nonlinear impulse cone constraint. The numerical simulation will elucidate the advantage of the proposed method as an alternative to conventional ones.

• Journal of Ocean Engineering and Technology
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• v.7 no.1
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• pp.156-161
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• 1993

Structures built in the coastal area often cause unexpectedly severe shoreline change on the adjacent beaches. Therefore, beach evolution is one of the most important problem in the coastal engineering. Beach evolution in the coastal area consisted of wave transform model and sediment transport model. Ebersoale's elliptic mild slope equation which considered the effect of combind wave refraction and perline and Dean's one line theory for the sediment transport model were used in this study. Kwangan beach was selected as study area and field observations were done. Numerical simulation for beach evolution in the Kwangan beach was performed and shoreline change predictions were suggested as results.

• Publications of The Korean Astronomical Society
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• v.30 no.2
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• pp.573-576
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• 2015

Recent discovery of $2M_{\odot}$ neutron stars in white dwarf-neutron star binaries, PSR J1614-2230 and PSR J0348+0432, has given strong constraints on the maximum mass of neutron stars. On the other hand, all well-measured neutron star masses in double neutron star binaries are still less than $1.5M_{\odot}$. These observations suggest that the neutron star masses in binaries may depend on the evolution process of neutron star binaries. In addition, recent works on LMXB (low-mass X-ray binaries) provides us the possibility of estimating the masses and radii of accreting neutron stars in LMXBs. In this talk, we discuss the implications of recent neutron star observations to the neutron star equation of states and the related astrophysical problems. For the evolution of neutron star binaries, we also discuss the possibilities of super-Eddington accretion onto the primary neutron stars.

• Structural Engineering and Mechanics
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• v.54 no.4
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• pp.725-740
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• 2015

This study presents critical buckling load optimization of the axially graded layered uniform columns. In the first place, characteristic equations for the critical buckling loads for all boundary conditions are obtained using the transfer matrix method. Then, for each case, square of this equation is taken as a fitness function together with constraints. Due to explicitly unavailable objective function for the critical buckling loads as a function of segment length and volume fraction of the materials, especially for the column structures with higher segment numbers, initially, prescribed value is assumed for it and then the design variables satisfying constraints are searched using Differential Evolution (DE) optimization method coupled with eigen-value routine. For constraint handling, Exterior Penalty Function formulation is adapted to the optimization cycle. Different boundary conditions are considered. The results reveal that maximum increments in the critical buckling loads are attained about 20% for cantilevered and pinned-pinned end conditions and 18% for clamped-clamped case. Finally, the strongest column structure configurations will be determined. The scientific and statistical results confirmed efficiency, reliability and robustness of the Differential Evolution optimization method and it can be used in the similar problems which especially include transcendental functions.

• Bulletin of the Korean Chemical Society
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• v.16 no.9
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• pp.845-850
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• 1995

A systematic method is presented to analyze the bandgaps of conjugated polymers in terms of geometrical relaxations and electronic effect of moieties using the equation of Eg=ΔEδr + ΔE1-4 + ΔEel. The relationship between ΔEδr and δr is derived from trans-PA and is transferred to other conjugated polymeric systems. By applying this method to heterocyclic polymers, very useful information is obtained to understand the evolution of bandgaps of PT, PPy and PF in connection with the chemical structures and electronic effect of the heteroatoms. We believe that this method is very helpful to understand the evolution of bandgaps of various conjugated polymers in connection with the chemical structures and electronic effect of moieties. Also, the method is expected to provide valuable information to design a small bandgap polymers.