• Bulletin of the Korean Mathematical Society
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• v.53 no.5
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• pp.1327-1339
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• 2016

Self-organizing systems arise very naturally in artificial intelligence, and in physical, biological and social sciences. In this paper, we modify the classic Cucker-Smale model at both microscopic and macroscopic levels by taking the target motion pattern driving forces into consideration. Such target motion pattern driving force functions are properly defined for the line-shaped motion pattern and the ball-shaped motion pattern. For the modified Cucker-Smale model with the prescribed line-shaped motion pattern, we have analytically shown that there is a flocking pattern with an asymptotic flocking velocity. This is illustrated by numerical simulations using both symmetric and non-symmetric pairwise influence functions. For the modified Cucker-Smale model with the prescribed ball-shaped motion pattern, our simulations suggest that the solution also converges to the prescribed motion pattern.

• Communications of the Korean Mathematical Society
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• v.36 no.3
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• pp.447-463
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• 2021

In this paper we study the existence and long-time behavior of weak solutions to a class of quasilinear degenerate parabolic equations involving weighted p-Laplacian operators with a new class of nonlinearities. First, we prove the existence and uniqueness of weak solutions by combining the compactness and monotone methods and the weak convergence techniques in Orlicz spaces. Then, we prove the existence of global attractors by using the asymptotic a priori estimates method.

• Journal of the Korean Geotechnical Society
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• v.21 no.6
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• pp.93-100
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• 2005

The occurrence of multi-segmented hydraulic fractures that show different behavior from the single fracture is common phenomenon. However, it is not easy to evaluate the behavior of multiple fractures computed by most numerical techniques because of complicated process computation. This study presents how to efficiently calculate the displacement of the multi-segmented hydraulic fractures using the boundary collocation method (BCM). First of all, asymptotic solutions are obtained for the closely spaced overlapping fractures and are compared with those by the BCM where the number of collocation points is varied. As a result, the BCM provides an excellent agreement with the asymptotic solutions even when the number of collocation points is reduced ten times as many as that of conventional implementations. Accordingly, the numerical simulation of more realistic and, hence, more complex fracture geometries by the BCM would be valid with such a significant reduction of the number of collocation points.

• Proceedings of the Earthquake Engineering Society of Korea Conference
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• 2000.10a
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• pp.143-150
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• 2000

A physical lumped parameter model is proposed for the time domain analysis of dam-reservoir system. The exact solution of transmitting boundary is derived for a semi-infinite 2-D reservoir of constant depth. The characteristics of the solution are examined in both frequency and the domains. Mass and damping coefficient are obtained from asymptotic behavior of the frequency domain solution. Further refinement to the lumped model is made by approximating the kernel function of the convolution integral in the exact solution. Finally a new physical lumped parameter model is proposed that consists of two masses, a spring and two dampers for each mode. It is demonstrated that new lumped parameter model of transmitting boundary can give excellent results.

• Communications of the Korean Mathematical Society
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• v.26 no.4
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• pp.695-708
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• 2011

Based on the multiple-time-scale (MTS) method, a general formula has been presented for solving an n-th, n = 2, 3, ${\ldots}$, order ordinary differential equation with strong linear damping forces. Like the solution of the unified Krylov-Bogoliubov-Mitropolskii (KBM) method or the general Struble's method, the new solution covers the un-damped, under-damped and over-damped cases. The solutions are identical to those obtained by the unified KBM method and the general Struble's method. The technique is a new form of the classical MTS method. The formulation as well as the determination of the solution from the derived formula is very simple. The method is illustrated by several examples. The general MTS solution reduces to its classical form when the real parts of eigen-values of the unperturbed equation vanish.

• 제어로봇시스템학회:학술대회논문집
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• 1989.10a
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• pp.913-917
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• 1989

In this paper, the selection method of weighting matrices in the discrete-time LQ problem are suggested in order to improve the guaranteed stability margins, i.e. the gain and phase margins. The asymptotic properties of the solution of the algebraic Riccati equations are investigated by using the closed form solution of the difference Riccati equations. It is shown that the solution of the algebraic Riccati equations monotonically increases as the state weighting matrix Q or the control weighting matrix R increase. The increasing rate of the solution is shown to be much less than that of R for large R. It is also proven that the guaranteed stability margins increases as the ratio between Q and R decreases.

• Structural Engineering and Mechanics
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• v.33 no.5
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• pp.621-633
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• 2009

In this paper we compare the solution of the one-dimensional beam model and the numerical solution of the two-dimensional linearized elasticity problem for rectangular domain of the beam-like form. We first derive the beam model starting from the two-dimensional linearized elasticity, the same way it is derived from the three-dimensional linearized elasticity. Then we present the numerical solution of the two-dimensional problem by finite element method. As expected the difference of two approximations becomes smaller as the thickness of the beam tends to zero. We then analyze the applicability of the one-dimensional model and verify the main properties of the beam modeling for thin beams.

• Korean Journal of Air-Conditioning and Refrigeration Engineering
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• v.7 no.2
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• pp.184-195
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• 1995

A theoretical one-dimensional model for the charging process in stratified thermal storage tanks is established presuming that the fluid ensuing from the tank inlet creates a perfectly mixed, layer above the thermocline. Both the generic and asymptotic closed-form solutions are obtained via the Laplace transformation. The asymptotic solution describes the nature of the charging pertaining to the case of no thermal diffusion, whereas the generic solution is of practical importance to understand the role of operating parameters on the stratification. The present model is validated through comparison with available experimental data, where they agree well with each other within a reasonable limit. An interpretation of the exact solution entails two important features associated with the charging process. The first is that an in-crease in the mixing depth $h_m$ causes a relatively slow temperature rise in the perfectly mixed region, but on the other hand it results in a faster decay of the overall temperature gradient across the thermocline. Next is the predominance of the mixing depth in the presence of the prefectly mixed region. In such a case the effect of the Peclet number is marginal and there-fore the thermal characteristics are solely dependent on the mixing depth paticularly for large $h_m$. The Peclet number affects significantly only for the case without mixing. Variation of the storage efficiency in response to the change in the mass flow rate agrees favorably with the published experimental results, which confirms the utility of the present study.

• Journal of the Korean Mathematical Society
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• v.57 no.6
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• pp.1347-1372
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• 2020

We study bifurcation for the following fractional Schrödinger equation $$\{\left.\begin{eqnarray}(-{\Delta})^su+V(x)u&=&{\lambda}f(u)&&{\text{in}}\;{\Omega}\\u&>&0&&{\text{in}}\;{\Omega}\\u&=&0&&{\hspace{32}}{\text{in}}\;{\mathbb{R}}^n{\backslash}{\Omega}\end{eqnarray}\right$$ where 0 < s < 1, n > 2s, Ω is a bounded smooth domain of ℝⁿ, (-∆)^s is the fractional Laplacian of order s, V is the potential energy satisfying suitable assumptions and λ is a positive real parameter. The nonlinear term f is a positive nondecreasing convex function, asymptotically linear that is $\lim_{t{\rightarrow}+{\infty}}\;{\frac{f(t)}{t}}=a{\in}(0,+{\infty})$. We discuss the existence, uniqueness and stability of a positive solution and we also prove the existence of critical value and the uniqueness of extremal solutions. We take into account the types of Bifurcation problem for a class of quasilinear fractional Schrödinger equations, we also establish the asymptotic behavior of the solution around the bifurcation point.

• Journal of applied mathematics & informatics
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• v.36 no.3_4
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• pp.331-348
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• 2018

In this paper, an initial value method for solving a class of singularly perturbed delay differential equations with layer behavior is proposed. In this approach, first the given problem is modified in to an equivalent singularly perturbed problem by approximating the term containing the delay using Taylor series expansion. Then from the modified problem, two explicit Initial Value Problems which are independent of the perturbation parameter, ${\varepsilon}$, are produced: the reduced problem and boundary layer correction problem. Finally, these problems are solved analytically and combined to give an approximate asymptotic solution to the original problem. To demonstrate the efficiency and applicability of the proposed method three linear and one nonlinear test problems are considered. The effect of the delay on the layer behavior of the solution is also examined. It is observed that for very small ${\varepsilon}$ the present method approximates the exact solution very well.