• Journal of Advanced Research in Ocean Engineering
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• v.1 no.3
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• pp.157-167
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• 2015

In order to provide simple and accurate wave theory in design of offshore structure, an analytical approximation is introduced in this paper. The solution is limited to flat bottom having a constant water depth. Water is considered as inviscid, incompressible and irrotational. The solution satisfies the continuity equation, bottom boundary condition and non-linear kinematic free surface boundary condition exactly. Error for dynamic condition is quite small. The solution is suitable in description of breaking waves. The solution is presented with closed form and dispersion relation is also presented with closed form. In the last century, there have been two main approaches to the nonlinear problems. One of these is perturbation method. Stokes wave and Cnoidal wave are based on the method. The other is numerical method. Dean's stream function theory is based on the method. In this paper, power series method was considered. The power series method can be applied to certain nonlinear differential equations (initial value problems). The series coefficients are specified by a nonlinear recurrence inherited from the differential equation. Because the non-linear wave problem is a boundary value problem, the power series method cannot be applied to the problem in general. But finite number of coefficients is necessary to describe the wave profile, truncated power series is enough. Therefore the power series method can be applied to the problem. In this case, the series coefficients are specified by a set of equations instead of recurrence. By using the set of equations, the nonlinear wave problem has been solved in this paper.

• Economic and Environmental Geology
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• v.30 no.5
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• pp.395-406
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• 1997

Some RE (Zr, Nb, REE) ore deposits are located in the middle part of the Korean peninsula. Geotectonically, the RE ore deposits situated on the Kyemyeongsan Formation of northern margin of the Okcheon geosynclinal belt and in the transitional zone between Kyeonggi massif and Okcheon belt. The rare metal deposits distributed in Kyemyeongsan Formation which consists of schist and alkaline granite. The alkali granite has suffered extensive post-magmatic metasomatism and hydrothermal processes. The ore contains mainly Ce-La, Ta-Nb, Y, Y-Nb, Ti-Nb-(U), Nd-Th group minerals. Fergusonite, one of Nb-Y rich REE minerals belonging to the A-B oxides, is most common mineral in the rare metal deposits. The fergusonite bearing rocks may be devided into four types by occurrence features and mineral association, that is, zircon type, allanite vein, feldspar type, and fluorite type. Fergusonites show wide variations in optical properties, due to part of differences in their chemical composition (depending on the types), but also the degree of crystalinity of the individual specimens. Fergusonite metamicts enclosed in biotite are generally surrounded by well developed pleochroic haloes. Usually, fergusonite is accompanied with zircon and other REE-bearing minerals. Petrographical and chemical data are presented for fergusonites which collected different types. $Nb_2O_3$ and $Y_2O_3$ contents range from 48.51 to 53.01 wt.% and 29.18 to 42.02 wt.% respectively. Also, $ThO_2$, (1.83~6.93), $UO_2$, (0.17~2.84), ${\sum}RE_2O_3$ (except to Y) (1.11~8.73), and $TiO_2$, (0.19~1.19 wt.%) contents show variational compositions according to fergusonite types. The ${\sum}RE_2O_3$ of fergusonites are positive relation with $Y_2O_3$ and negative relaton with $ThO_2$ and $({\sum}{RE_2O_3}-{Y_2O_3})$. The $Nb_2O_3$ is sightly negative relation with $Ta_2O_3$. Back-scattered electron microscope images (BEI) of fergusonite show the mineral composition and textural feature is very complicated. The variation of Nb, Th and REE content of fergusonite and the modes of occurrence of mineral, suggests that REE may have been mobilized during the circulation of hydrothermal fluids related to contact metamorphism (metasomatism). The chemical variation of the fergusonites with occurrences and mineral association can be related to metasomatism of alkaline fluid was probably the dominant ore-forming process in Chungju district.