• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.25 no.4
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• pp.173-195
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• 2021

A new implicit discontinuous Galerkin spectral element method (DGSEM) based on the first order hyperbolic system(FOHS) is presented for solving elliptic type partial different equations, such as the Poisson problems. By utilizing the idea of hyperbolic formulation of Nishikawa[1], the original Poisson equation was reformulated in the first-order hyperbolic system. Such hyperbolic system is solved implicitly by the collocation type DGSEM. The steady state solution in pseudo-time, which is the solution of the original Poisson problem, was obtained by the implicit solution of the global linear system. The optimal polynomial orders of 𝒪(𝒽^𝑝+1)) are obtained for both the solution and gradient variables from the test cases in 1D and 2D regular grids. Spectral accuracy of the solution and gradient variables are confirmed from all test cases of using the uniform grids in 2D.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2014.10a
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• pp.743-744
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• 2014

Hyperbolic metamaterials in which waves can only propagate through the radial direction have achieved much attention these days due to their capability of sub-wavelength resolution. In this work, the realization and optimization of hyperbolic elastic metamaterials are mainly studied. To obtain a new hyperbolic elastic metamaterial, a specially-engineered mass-spring system is introduced. Based on the mass-spring system, the hyperbolic elastic metamaterials are proposed and realized. In addition, the sub-wavelength resolution of the proposed hyperbolic elastic metamaterial is verified by ultrasonic elastic wave experiments. For the experiments, specially-designed magnetostrictive patch transducers are developed to realize two sub-wavelength elastic wave sources. Furthermore, the proposed hyperbolic elastic metamaterial is optimized to maximize its operating frequency ranges by the topology optimization method.

• Current Optics and Photonics
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• v.1 no.4
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• pp.336-343
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• 2017

A wide field-of-view (FOV) image contains more visual information than a conventional image. This study proposes a new type of hyperbolic mirror for wide FOV image acquisition. The proposed mirror consists of a hyperbolic cylindrical section and a bowl-shaped hyperbolic omnidirectional section. Using an imaging system with this mirror, it is possible to achieve a $213.8^{\circ}$ horizontal and a $126.94^{\circ}$ vertical maximum FOV. Parameters of each section of the mirror are designed to be continuous at the junction of the two parts, and the resultant image is seamless. The image-acquisition model is obtained using ray-tracing optics. To rectify the geometrical distortion of the original image due to the mirror, an image-restoration algorithm based on conformal projection is presented in this study. The performance of the proposed imaging system with the hyperbolic mirror and its image-restoration algorithm are verified by experiments.

• The Journal of Korea Robotics Society
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• v.10 no.3
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• pp.146-153
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• 2015

In order to contain as much information as possible in a single image, a wide FOV(Field-Of-View) imaging system is required. The catadioptric imaging system with hyperbolic cylinder mirror can acquire over 180 degree horizontal FOV realtime panorama image by using a conventional camera. Because the hyperbolic cylinder mirror has a curved surface in horizontal axis, the original image acquired from the imaging system has the geometrical distortion, which requires the image processing algorithm for reconstruction. In this paper, the image reconstruction algorithms for two cases are studied: (1) to obtain an image with uniform angular resolution and (2) to obtain horizontally rectilinear image. The image acquisition model of the hyperbolic cylinder mirror imaging system is analyzed by the geometrical optics and the image reconstruction algorithms are proposed based on the image acquisition model. To show the validity of the proposed algorithms, experiments are carried out and presented in this paper. The experimental results show that the reconstructed images have a uniform angular resolution and a rectilinear form in horizontal axis, which are natural to human.

• East Asian mathematical journal
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• v.16 no.2
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• pp.317-330
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• 2000

In this paper we consider the optimal control problem of both operators and parameters for nonlinear hyperbolic systems. For the identification problem, we show that for every value of the parameter and operators, the optimal control problem has a solution. Moreover we obtain the necessary conditions of optimality for the optimal control problem on the system.

• Journal of the Korean Institute of Navigation
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• v.13 no.1
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• pp.1-10
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• 1989

Nowadays Hyperbolic Navigation System-LORAN, DECCA, OMEGA, OMEGA-is available on the ocean, and Spherical Navigation System, GPS (Global Positioning System) is operated partially. Hyperbolic Navigation System has the blind area near the base line extention because divergence rate of hyperbola is infinite theoretically. The Position Accuracy is differ from the cross angle of LOP although each LOP has the same error of quantity. GDOP(Geometric Dilution of Precisoin) is used to estimate the position accuracy according to the cross angle of LOP and LOP error. Hyperbola and ellipse are crossed at right angle everywhere. Hyperbola and ellipse are used to LOP in Rectangular Navigation System. The equation calculating the GDOP of rectangular Navigation System is induced and GDOP diagram is completed in this paper. A scheme that can improve the position accuracy in the blind area of Hyperboic Navigation System using the Rectangular Navigation System is proposed through the computer simulation.

• Journal of Power System Engineering
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• v.3 no.3
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• pp.14-21
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• 1999

The wave nature of heat conduction has been developed in situations involving extreme thermal gradients, very short times, or temperatures near absolute zero. Under the excitation of a periodic surface heating in a finite medium, the hyperbolic and parabolic heat conduction equations and the damped wave equations in heat flux are presented for comparative analysis by using the Green's function with the integral transform technique. The Kummer transformation is also utilized to accelerate the rate of convergence of these solutions. On the other hand, the temperature distributions are obtained through integration of the energy conservation law with respect to time. For hyperbolic heat conduction, the heat flux distribution does not exist throughout all the region in a finite medium within the range of very short times(${\xi}<{\eta}_l$). It is shown that due to the thermal relaxation time, the hyperbolic heat conduction equation has thermal wave characteristics as the damped wave equation has wave nature.

• Nuclear Engineering and Technology
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• v.35 no.1
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• pp.45-54
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• 2003

A hyperbolic two-phase, two-fluid equation system developed in the previous work has been implemented in an existing nuclear safety analysis code, MARS. Although the implicit treatment of interfacial pressure force term introduced in momentum equation of the hyperbolic equation system is required to enhance the numerical stability, it is very difficult to implement in the code because it is not possible to maintain the existing numerical solution structure. As an alternative, two-step approach with stabilizer momentum equations has been selected. The results of a linear stability analysis by Von-Neumann method show the equivalent stability improvement with fully-implicit solution method. To illustrate the applicability, the new solution scheme has been implemented into the best-estimate thermal-hydraulic analysis code, MARS. This paper also includes the comparisons of the simulation results for the perturbation propagation and water faucet problems using both two-step method and the original solution scheme.

• International Journal of Aerospace System Engineering
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• v.3 no.1
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• pp.1-4
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• 2016

Functionally graded materials (FGMs) are becoming very popular in various industries due to their effectiveness of the utilization of their constituent elements. However, the modelling of these materials is difficult due to the complex nature of variation of material properties across the thickness. Many shear deformation theories have been developed and employed for the analysis of such functionally graded plates (FGPs). A recently developed inverse hyperbolic shear deformation theory has been successfully employed by Grover et al. [1] for the analysis of laminated composites and sandwich plates. The objective of the study is to obtain finite element solution for the structural analysis of functionally graded plates using inverse hyperbolic shear deformation theory. Finite element analysis facilitates the analysis of complex problems such as functionally graded plates with different boundary conditions and different loadings.

• Bulletin of the Korean Chemical Society
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• v.20 no.1
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• pp.35-41
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• 1999

Stability characteristics of hyperbolic reaction-diffusion equations with a reversible Brusselator model are investigated as an extension of the previous work. Intensive stability analysis is performed for three important parameters, Nrd, β and Dx, where Nrd is the reaction-diffusion number which is a measure of hyperbolicity, β is a measure of reversibility of autocatalytic reaction and Dx is a diffusion coefficient of intermediate X. Especially, the dependence on Nrd of stability exhibits some interesting features, such as hyperbolicity in the small Nrd region and parabolicity in the large Nrd region. The hyperbolic reaction-diffusion equations are solved numerically by a spectral method which is modified and adjusted to hyperbolic partial differential equations. The numerical method gives good accuracy and efficiency even in a stiff region in the case of small Nrd, and it can be extended to a two-dimensional system. Four types of solution, spatially homogeneous, spatially oscillatory, spatio-temporally oscillatory and chaotic can be obtained. Entropy productions for reaction are also calculated to get some crucial information related to the bifurcation of the system. At the bifurcation point, entropy production changes discontinuously and it shows that different structures of the system have different modes in the dissipative process required to maintain the structure of the system. But it appears that magnitude of entropy production in each structure give no important information related for states of system itself.