• The Journal of the Acoustical Society of Korea
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• v.25 no.5
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• pp.229-238
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• 2006

This paper shows the analytic error caused by the inconsistency of the approximation order between the non local boundary condition (NLBC) and the parabolic governing equation. To obtain the analytic error, we first transform the NLBC to the half space domain using plane wave analysis. Then, the analytic error is derived on the boundary between the true numerical domain and the half space domain equivalent to the NLBC. The derived analytic error is physically expressed as the artificial reflection. We examine the characteristic of the analytic error for the grazing angle, the approximation order of the PE or the NLBC. Our main contribution is to present the analytic method of error estimation and the application limit for the high order parabolic equation and the NLBC.

• Steel and Composite Structures
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• v.27 no.6
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• pp.777-788
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• 2018

An investigation on the thermal buckling resistance of simply supported FGM beams having parabolic-concave thickness variation and temperature dependent material properties is presented in this paper. An analytical formulation based on the first order beam theory is derived and the governing differential equation of thermal stability is solved numerically using finite difference method. a function of thickness variation is introduced which controls the parabolic variation intensity of the beam thickness without changing its original material volume. The results showed the high importance of taking into account the temperature-dependent material properties in the thermal buckling analysis of such critical beam sections. Different Influencing parametric on the thermal stability are studied which may help in design guidelines of such complex structures.

• 한국전산유체공학회:학술대회논문집
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• 2003.10a
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• pp.48-49
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• 2003

In the present research a high order Gudonov-type method has been used for the simulation of very high pressure flow fields, as well as the capturing of strong shocks, which usually occur in explosion of high explosives. The treatment strong shocks and the flow field behind the shocks needs a very high resolution scheme. To resolve accurately the shock and the release waves behind the shock the piece­wise parabolic method (PPM) of Colella [1] was utilized in this research. A major problem which encountered in very high pressure problems is the equation of state which differs completely form the ideal-gas equation of state (EOS). Here, the original PPM is extended for real gas effect consideration.

• The Journal of the Acoustical Society of Korea
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• v.25 no.7
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• pp.339-345
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• 2006

We suggest new 2D two-way Parabolic equation algorithm for multiple scattering. Our method is based on the successive performance of the single scattering approach. First. as the single scattering algorithm, the reflected and transmitted fields are calculated at the vertical interface of a range independent sector. Then. the reflected field is saved and the transmitted field Propagated to the next vertical interface with the split-step Pade method. After one step ends, the same Process is repeatedly performed with the change of the Propagation direction until the reflected field at the vertical interface is close to zero. Final incoming and outgoing fields are obtained as the sum of the wave fields obtained for each step. Our algorithm is relatively simple for the numerical implementation and requires less computational resources than the existing algorithm for multiple scattering

• Korean Journal of Soil Science and Fertilizer
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• v.25 no.4
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• pp.342-356
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• 1992

Kinetic studies using stirred-flow methods were conducted with the Luisiana soil at three pH levels(pH 5, 6.5, and 8) and three temperature levels(10, 25, and $40^{\circ}C$) to explore effects on the rate of silica retention and release and to find out reaction mechanisms. In this study the maximum silica retention could not be obtained for long enough experimental time. The silica sorption isorption was C type fitted well to Freundlich equation. The pH of the soil suspension increased by the silica release process at low pH treatments(pH 5 and 6.5), while decreased at high pH treatment(pH 8). From the above findings It can be deduced that the mechanism of silica retention is a multilayer forming process to change the ligand form depending on pH condition. In the proposed mechanism the sorbed silica provide new binding sites for additional sorption of silica, while the activation energy for the formation of subsequent layers increases correspondingly. The silica retention and release process were well described by first-order and parabolic diffusion equation. However, clear interpretation for silica sorption mechanism using these equations could not be made. The validity of the fraction term (Fa and Fd) included in first-order and parabolic diffusion equation requires further examinations because the temperature effect on apparent rate constant shows no constant trends among temperature treatments, while there was a good trend in Elovich and modified Freundlich equation where the fraction term was not included.