• Proceedings of the Computational Structural Engineering Institute Conference
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• 1998.04a
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• pp.68-74
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• 1998

A finite element analysis for physical phenomenon which are governed by parabolic equation, has some inefficiencies caused by much computational time and large storage space. In this paper, a comparative study is performed to suggest the best efficient transient analysis algorithms for parabolic equations. First, the general finite element analysis techniques are summarized in views of formulation procedures, treatments of convection terms. and time stepping methods. Results of several combinations applied to one dimensional convection-diffusion equation and Burger equation are represented and compared using some criteria such as accuracy, stability, and computational time. Through the results, some guidelines to select a algorithm for solving parabolic equations are proposed for diffusion dominant and convection dominant cases. Finally applicability of two dimensional extension of the result is also discussed.

• Honam Mathematical Journal
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• v.37 no.3
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• pp.299-315
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• 2015

In this paper, we study the first-order system least-squares (FOSLS) spectral method for parabolic partial differential equations. There were lots of least-squares approaches to solve elliptic partial differential equations using finite element approximation. Also, some approaches using spectral methods have been studied in recent. In order to solve the parabolic partial differential equations in parallel, we consider a parallel numerical method based on a hybrid method of the frequency-domain method and first-order system least-squares method. First, we transform the parabolic problem in the space-time domain to the elliptic problems in the space-frequency domain. Second, we solve each elliptic problem in parallel for some frequencies using the first-order system least-squares method. And then we take the discrete inverse Fourier transforms in order to obtain the approximate solution in the space-time domain. We will introduce such a hybrid method and then present a numerical experiment.

• Advances in Energy Research
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• v.8 no.3
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• pp.155-163
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• 2022

The current study presents experimental research on a parabolic trough collector with tube and cavity receivers. The primary concentrating parabolic reflector is designed for an aperture area of 2×2 m² with mirror-polished stainless steel sheet reflectors. The cavity receiver consists of a compound parabolic secondary reflector and a copper tube. Both the conventional tube receiver and the cavity receiver tube are coated with black powder. The experiments are carried out to compare the efficiency of the cavity receiver with the tube receiver for fluid temperature rise, thermal efficiency, and overall losses. The experiments showed significantly higher fluid temperature rise and overall efficiency and lower thermal losses for the cavity receiver compared to the tube receiver within the parameters explored in this study.

• The Journal of the Institute of Internet, Broadcasting and Communication
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• v.18 no.4
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• pp.49-53
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• 2018

Parabolic offset antenna is widely used for wireless communication system. The general structure of parabolic offset antenna system is composed of supporting stand and RF devices under parabolic reflector. However sidelobe distortion in gain pattern is occurred by supporting stand and RF devices. Depending on position of subsidiary devices, angle of sidelobe distortion can be changed. In this paper we describe method for sidelobe distortion suppression using raytracing. We calculate 3D vector for sidelobe distortion suppression zone by raytracing method and compare when subsidiary device is in sidelobe distortion suppression zone or not. By comparison, we show method for parabolic antenna sidelobe distortion suppression.

• Current Optics and Photonics
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• v.6 no.6
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• pp.627-633
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• 2022

To realize uniform side pumping of solar lasers and improve their output power, a solar concentrating system based on off-axis parabolic mirrors is proposed. Four identical off-axis parabolic mirrors with focal length of 1,000 mm are toroidally arranged as the primary concentrator. Four two-dimensional compound parabolic concentrators (2D-CPCs) are designed as a secondary concentrator to further compress the focused spot induced by the parabolic mirrors, and the focused light is then homogenized by four rectangular diffusers and provides uniform pumping for a laser-crystal rod to achieve solar laser emission. Simulation results show that the solar power received by the laser rod, uniformity of the light spot, and output power of the solar laser are 7,872.7 W, 98%, and 351.8 W respectively. This uniform pumping configuration and concentrator design thus provide a new means for developing high-power side-pumped solid-state solar lasers.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.20 no.1
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• pp.1-7
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• 2007

This study introduces an elastic parabolic cable element for initial shaping analysis of cable-stayed bridges. First, an elastic catenary cable theory is shortly summarized by deriving the compatibility condition and the tangent stiffness matrices of the elastic catenary cable element. Next, the force-deformation relations and the tangent stiffness matrices of the elastic parabolic cable elements are derived from the assumption that sag configuration under self-weights is small. In addition the equivalent cable tension is defined in the chord-wise direction. Finally, to confirm the accuracy of this element, initial shaping analysis of cable-stayed bridges under dead loads is executed using TCUD in which stay cables are modeled by an elastic parabolic cable and an elastic catenary cable element, respectively. Resultantly it turns that unstrained lengths of stay cables, the equivalent cable tensions, and maximum tensions by the parabolic cable element are nearly the same as those by the catenary cable elements.

• Korean Journal of Materials Research
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• v.28 no.6
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• pp.361-364
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• 2018

Binary Ti-Al alloys below 51.0 mass%Al content exhibit a breakaway, transferring from parabolic to linear rate law. The second $Al_2O_3$ layer might have some protectiveness before breakaway. Ti-63.1 mass%Al oxidized at 1173 K under parabolic law. Breakaway oxidation is observed in every alloy, except for Ti-63.1 mass%Al. After breakaway, oxidation rates of the binary TiAl alloys below 34.5 mass%Al obey almost linear kinetics. The corrosion rate of Ti-63.1 mass%Al appears to be almost parabolic. As content greater than 63.0 mass% is found to be necessary to form a protective alumina film. Addition of Mo improves the oxidation resistance dramatically. No breakaway is observed at 1123 K, and breakaway is delayed by Mo addition at 1173 K. At 1123 K, no breakaway, but a parabolic increase in mass gain, are observed in the Mo-added TiAl alloys. The binary Ti-34.5 mass%Al exhibits a transfer from parabolic to linear kinetics. At 1173 K, the binary alloys show vary fast linear oxidation and even the Mo-added alloys exhibit breakaway oxidation. The 2.0 mass%Mo-added TiAl exhibits a slope between linear and parabolic. At values of 4.0 and 6.0 mass% added TiAl alloys, slightly larger rates are observed than those for the parabolic rate law, even after breakaway. On those alloys, the second $Al_2O_3$ layer appears to be persistently continuous. Oxidation resistance is considerably degraded by the addition of Mn. Mn appears to have the effect of breaking the continuity of the second $Al_2O_3$ layer.

• Journal of Korean Society of Coastal and Ocean Engineers
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• v.10 no.1
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• pp.1-9
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• 1998

Among the phenomena of water-wave transformation, the wave diffraction is prominent for waves insidc the harbor. It is important to study how accurately the diffraction can be resolved by the numerical model. Three parabolic mild-slope equations, i.e., simple, wide-ang1e, three-parameter parabolic equations, are compared in view of the diffraction of water-waves around a semi-infinite breakwater. To avoid reflections at lateral boundaries, we apply the perfect boundary condition of Dalrymple and Martin (1992) in case of simple parabolic equation. The numerical results for the case of a semi-infinite breakwater are compared with the analytical solution of Penney and Price (1952). All the results are very accurate when waves attack the breakwater normally. When waves attack the breakwater obliquely, however, the simple parabolic equation yields the worst solution and the three-parameter parabolic equation yields the most accurate solution.

• Korean Journal of Mathematics
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• v.7 no.2
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• pp.139-150
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• 1999

In this paper we establish some bounds for solutions of parabolic one dimensional $p$-Laplacian equation.

• Honam Mathematical Journal
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• v.20 no.1
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• pp.67-78
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• 1998