• Journal of Astronomy and Space Sciences
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• v.27 no.4
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• pp.359-366
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• 2010

In this study, we developed a global ionosphere model based on measurements from a worldwide network of global positioning system (GPS). The total number of the international GPS reference stations for development of ionospheric model is about 100 and the spherical harmonic expansion approach as a mathematical method was used. In order to produce the ionospheric total electron content (TEC) based on grid form, we defined spatial resolution of 2.0 degree and 5.0 degree in latitude and longitude, respectively. Two-dimensional TEC maps were constructed within the interval of one hour, and have a high temporal resolution compared to global ionosphere maps which are produced by several analysis centers. As a result, we could detect the sudden increase of TEC by processing GPS observables on 29 October, 2003 when the massive solar flare took place.

• Proceedings of KOSOMES biannual meeting
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• 2006.11a
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• pp.131-135
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• 2006

The objective of the project is to model and study the geomagnetic field structure and its secular variation in space and in time due to sources in the dynamic fluid outer core. the Earth's spherical harmonic model of the main field and of the secular variation gives the intensity and geomagnetic structure at any location around the Earth, assuming an undistorted, steady state field that no external sources or localized earth anomalies. To consider the practical use of a ship's digital compass in Earth's magnetic field, Earth's spherical harmonic model is searched for the related practical methods and procedures as a basic study in this work.

• Proceedings of the Korean Institute of Navigation and Port Research Conference
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• 2006.06b
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• pp.87-90
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• 2006

The Earth's spherical harmonic model of the main field and of the secular variation, of the geomagnetic field gives the intensity and geomagnetic structure at any location around the earth, assuming an undistorted, steady state field that no external sources or localized earth anamalies. To consider the practical use of a ship's digital compass in earth's magnetic field, Earth's spherical harmonic model is searched for the related practical methods and procedures as a basic study in this work.

• Journal of the Korean earth science society
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• v.37 no.2
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• pp.107-116
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• 2016

Stability of the barotropic Rossby-Haurwitz wave is investigated using the numerical models on the global domain. The Rossby-Haurwitz wave under investigation is composed of the basic zonal flow of super-rotation and a finite amplitude spherical harmonic wave. The Rossby-Haurwitz wave is given as either steady or unsteady wave by adjusting the strength of the super-rotating zonal flow. Stability as well as the growth rate of the wave in the numerical simulation is determined by comparing the perturbation amplitude at two different time stages. Unstable modes of the Rossby-Haurwitz wave exhibited a horizontal structure composing of various zonal-wavenumber components. The vorticity perturbation for some modes showed a discontinuity around the area of weak flow, which was found robust regardless of the horizontal resolution of the model. Fourier finite element model was shown to generate the unstable mode in earlier stage of the time integration due to less accuracy compared to the spherical harmonic spectral model. Taking the overall accuracy of the models into consideration, the time by which the unstable mode begin to dominate over the spherical harmonic wave was estimated.

• Advances in nano research
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• v.15 no.2
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• pp.141-153
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• 2023

The main objective of this paper is to develop the finite element study on the nonlinear free vibration of functionally graded nanocomposite spherical shells reinforced with graphene platelets under the first-order shear deformation shell theory and von Kármán nonlinear kinematic relations. The governing equations are presented by introducing the full asymmetric nonlinear strain-displacement relations followed by the constitutive relations and energy functional. The extended Halpin-Tsai model is utilized to specify the overall Young's modulus of the nanocomposite. Then, the finite element formulation is derived and the quadrilateral 8-node shell element is implemented for finite element discretization. The nonlinear sets of dynamic equations are solved by the use of the harmonic balance technique and iterative method to find the nonlinear frequency response. Several numerical examples are represented to highlight the impact of involved factors on the large-amplitude vibration responses of nanocomposite spherical shells. One of the main findings is that for some geometrical and material parameters, the fundamental vibrational mode shape is asymmetric and the axisymmetric formulation cannot be appropriately employed to model the nonlinear dynamic behavior of nanocomposite spherical shells.

• Journal of the Korean earth science society
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• v.38 no.3
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• pp.173-181
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• 2017

The stability of the steady Rossby-Haurwitz wave (R-H wave) in the nondivergent barotropic model (NBM) on the sphere was investigated with the normal mode method. The linearized NBM equation with respect to the R-H wave was formulated into the eigenvalue-eigenvector problem consisting of the huge sparse matrix by expanding the variables with the spherical harmonic functions. It was shown that the definite threshold R-H wave amplitude for instability could be obtained by the normal mode method. It was revealed that some unstable modes were stationary, which tend to amplify without the time change of the spatial structure. The maximum growth rate of the most unstable mode turned out to be in almost linear proportion to the R-H wave amplitude. As a whole, the growth rate of the unstable mode was found to increase with the zonal- and total-wavenumber. The most unstable mode turned out to consist of more-than-one zonal wavenumber, and in some cases, the mode exhibited a discontinuity over the local domain of weak or vanishing flow. The normal mode method developed here could be readily extended to the basic state comprised of multiple zonalwavenumber components as far as the same total wavenumber is given.

• Journal of Information Processing Systems
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• v.10 no.1
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• pp.23-35
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• 2014

Recently, novel application areas in digital geometry processing, such as simulation, dynamics, and medical surgery simulations, have necessitated the representation of not only the surface data but also the interior volume data of a given 3D object. In this paper, we present an efficient framework for the shape approximations of spherical solid objects based on trivariate B-splines. To do this, we first constructed a smooth correspondence between a given object and a unit solid cube by computing their harmonic mapping. We set the unit solid cube as a rectilinear parametric domain for trivariate B-splines and utilized the mapping to approximate the given object with B-splines in a coarse-to-fine manner. Specifically, our framework provides user-controllability of shape approximations, based on the control of the boundary condition of the harmonic parameterization and the level of B-spline fitting. Experimental results showed that our method is efficient enough to compute trivariate B-splines for several models, each of whose topology is identical to a solid sphere.

• Journal of the Institute of Electronics Engineers of Korea CI
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• v.43 no.2 s.308
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• pp.72-80
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• 2006

In this paper, we propose a new descriptor for 3D model retrieval based on shape information. The proposed method consists of two steps including ray casting method and spherical harmonic function, considering geometric properties of model. In the ray casting method, an adaptive sampling is performed for external shape information. By increasing shape information included in the descriptor, we improve the discriminating power of the proposed descriptor. The coefficients of spherical harmonic function are adaptively calculated, considering geometric frequency characteristics. This makes the descriptor more compact and concise without decreasing the retrieval performance. By combining two methods, we achieve more improved retrieval results.

• Journal of the Korean Society of Surveying, Geodesy, Photogrammetry and Cartography
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• v.24 no.2
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• pp.183-191
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• 2006

The accuracy of the upward continuation is assessed through the gravity modeling using an ultra-high degree spherical harmonic expansion. The difficulties in the numerical calculation of Legendre function with ultra-high degree, underflow and/or overflow, is successfully resolved in 128 bit calculation scheme. Using the generated Legendre function, the gravity anomaly with spatial resolution of $1'{\times}1'$ on the geoid is calculated. The generated gravity anomaly is degraded and extracted with various noise levels and data intervals, then upward continuation is applied to each data sets. The comparison between the upward continued gravity disturbances and the directly calculated from the spherical harmonics showed that the accuracy on the direct method was significantly better than that of Poisson method. In addition, it is verified that the denser and less noised gravity data on the geoid generates better gravity disturbance vectors at an altitude. Especially, it is found that the gravity noise level less than 5mGal, and the data interval less than 2arcmin is necessary for next generation precision INS navigation which requires the accuracy of 5mGal or better at an altitude.

• Journal of the Korean Society of Surveying, Geodesy, Photogrammetry and Cartography
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• v.15 no.1
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• pp.131-139
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• 1997

Geopotential models were used to determine the reference surface in geoid modelling and until now, OSU91A model has been most widely used in the world. But what so called EGM96, GSFC/DMA geopotential model published in the latter half of the 1996 by GSFC/DMA project. In this paper, we intended to compare the results of spherical harmonic analyses using the both geopotential model and the spherical harmonic analyses performed up to degree and order 300 and the gravimetric geoidal heights considering gravity data on each $3'\times{3'}$ grid point in and around Korean peninsula. The results showed that the average geoidal height of study area computed from EGM96 is larger 0.40 m than that computed from OSU91A and the gravimetric geoidal heights us-ing EGM96 is larger 0.35 m than that using OSU91A model.