• Journal of computational fluids engineering
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• v.20 no.4
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• pp.58-62
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• 2015

Recent studies on wall-bounded shear flow have emphasized the significance of the stable manifold of simple nonlinear invariant solutions to the Navier-Stokes equation in the formation of the boundary between the laminar and turbulent regions in state space. In this paper we present newly discovered homoclinic orbits of the Kawahara and Kida(2001) periodic solution in plane Couette flow. We show that as the Reynolds number decreases a pair of homoclinic orbits move closer to each other until they disappear to exhibit homoclinic tangency.

• Proceedings of the KSME Conference
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• 2003.11a
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• pp.109-114
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• 2003

The physical model considered here is a horizontal layer of fluid heated below and cooled above with a periodic array of evenly spaced square cylinders placed at the center of the layer, whose aspect ratio here varies from unity to twelve. Periodic boundary condition is employed along the horizontal direction to allow for lateral freedom for the convection cells. Two-dimensional solution for unsteady natural convection is obtained using an accurate and efficient Chebyshev spectral multi-domain methodology for a given Rayleigh numbers of $10^{6}$.

• Proceedings of the Korean Institute of Information and Commucation Sciences Conference
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• 2013.05a
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• pp.59-60
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• 2013

In order to analyze optical waveguide, the FDTD method can be applied. But structure of optical waveguide is relatively larger than wavelength of center frequency. But optical waveguide system must be periodic structure and the solution of the waveguide can be obtained from a simulation in one period of the structure by applying PBC(Periodic boundary condition). In this paper, an efficient FDTD algorithm incorporating PBC in inhomogeneous medium is introduced and estimated.

• 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.

• Current Photovoltaic Research
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• v.5 no.3
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• pp.75-82
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• 2017

High efficiency thin film solar cells require an absorber layer with high absorption and low defect, a transparent conductive oxide (TCO) film with high transmittance of over 80% and a high conductivity. Furthermore, light can be captured through the glass substrate and sent to the light absorbing layer to improve the efficiency. In this paper, morphology formation on the surface of glass substrate was investigated by using HF, mainly classified as random etching and periodic etching. We discussed about the etch mechanism, etch rate and hard mask materials, and periodic light trapping structure.

• Journal of the Korean institute of surface engineering
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• v.39 no.5
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• pp.223-228
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• 2006

The current efficiency of copper anode containing impurities in copper sulfate solution for electrorefining was studied at various current type such as direct current, variable current and periodic reverse current. The passivity behavior was investigated by galvanostatic technique. The results obtained were that current efficiency of variable current was higher than those of direct current and periodic reverse current. The increased current efficiency could be explained by the formation of slime structure with lower average resistance due to variable current. The frequency of various factors in variable current condition has a greatest effect on current efficiency. It appeared that frequency increased current efficiency when increased from 1 to 4, but further increases did not have an effect.

• Honam Mathematical Journal
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• v.31 no.1
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• pp.75-85
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• 2009

We show the existence of the nontrivial periodic solution for a class of the system of the nonlinear suspension bridge equations with Dirichlet boundary condition and periodic condition by critical point theory and linking arguments. We investigate the geometry of the sublevel sets of the corresponding functional of the system, the topology of the sublevel sets and linking construction between two sublevel sets. Since the functional is strongly indefinite, we use the linking theorem for the strongly indefinite functional and the notion of the suitable version of the Palais-Smale condition.

• Proceedings of the KIEE Conference
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• 1996.07b
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• pp.1140-1142
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• 1996

In this paper, a fixed-horizon $H_{\infty}$ tracking control (HTC) for continuous time-varying systems is proposed in state-feedback case. The solution is obtained via the dynamic game theory. From HTC, an intervalwise receding horizon $H_{\infty}$ tracking control (IHTC) for continuous periodic systems is obtained using the intervalwise strategy. The conditions under which IHTC stabilizes the closed-loop system are proposed. Under proposed stability conditions, it is shown that IHTC guarantees the $H_{\infty}$-norm bound.

• The Pure and Applied Mathematics
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• v.28 no.4
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• pp.297-314
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• 2021

This manuscript is divided into three segments. In the first segment, we formulate a unique common fixed point theorem satisfying generalized Meir-Keeler contraction on partially ordered metric spaces and also give an example to demonstrate the usability of our result. In the second segment of the article, some common coupled fixed point results are derived from our main results. In the last segment, we investigate the solution of some periodic boundary value problems. Our results generalize, extend and improve several well-known results of the existing literature.

• Coupled systems mechanics
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• v.1 no.2
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• pp.155-163
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• 2012

This paper presents analytical approximate solutions for the initial post-buckling deformation of the pipes in oil and gas wells. The governing differential equation with sinusoidal nonlinearity can be reduced to form a third-order-polynomial nonlinear equation, by coupling of the well-known Maclaurin series expansion and orthogonal Chebyshev polynomials. Analytical approximations to the resulting boundary condition problem are established by combining the Newton's method with the method of harmonic balance. The linearization is performed prior to proceeding with harmonic balancing thus resulting in a set of linear algebraic equations instead of one of non-linear algebraic equations, unlike the classical method of harmonic balance. We are hence able to establish analytical approximate solutions. The approximate formulae for load along axis, and periodic solution are established for derivative of the helix angle at the end of the pipe. Illustrative examples are selected and compared to "reference" solution obtained by the shooting method to substantiate the accuracy and correctness of the approximate analytical approach.