• Steel and Composite Structures
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• v.17 no.5
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• pp.561-572
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• 2014

In this paper, we present the scattering characteristics of infinite and finite array using method of moment (MoM) with Floquet harmonics and asymptotic waveform evaluation (AWE) technique. First, infinite cylindrical dipole array is analyzed using the MoM with entire domain basis function and cylindrical Floquet harmonics. To provide the validity of results, we fabricated the cylindrical dipole array and measured the transmission characteristics. The results show good agreements. Second, we analyzed the scattering characteristics of finite array. A large simulation time is needed to obtain the scattering characteristics of finite array over wide frequency range because Floquet harmonics can't be applied. So, we used the MoM with AWE technique using Taylor series and Pade approximation to overcome the shortcomings of conventional MoM. We calculated the radar cross section (RCS) as scattering characteristics using the proposed method in this paper and the conventional MoM for finite planar slot array, finite spherical slot array, and finite cylindrical dipole array, respectively. The compared results agree well and show that the proposed method in this paper is good for electromagnetic analysis of finite FSS.

• Nuclear Engineering and Technology
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• v.49 no.6
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• pp.1114-1124
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• 2017

Acceleration/preconditioning strategies available in the SCEPTRE radiation transport code are described. A flexible transport synthetic acceleration (TSA) algorithm that uses a low-order discrete-ordinates ($S_N$) or spherical-harmonics ($P_N$) solve to accelerate convergence of a high-order $S_N$ source-iteration (SI) solve is described. Convergence of the low-order solves can be further accelerated by applying off-the-shelf incomplete-factorization or algebraic-multigrid methods. Also available is an algorithm that uses a generalized minimum residual (GMRES) iterative method rather than SI for convergence, using a parallel sweep-based solver to build up a Krylov subspace. TSA has been applied as a preconditioner to accelerate the convergence of the GMRES iterations. The methods are applied to several problems involving electron transport and problems with artificial cross sections with large scattering ratios. These methods were compared and evaluated by considering material discontinuities and scattering anisotropy. Observed accelerations obtained are highly problem dependent, but speedup factors around 10 have been observed in typical applications.

• Bulletin of the Korean Chemical Society
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• v.6 no.1
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• pp.3-7
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• 1985

The general formulas for SCF atomic orbitals |5s > and |6p > have been derived separately by expressing the spherical harmonics part in terms of the coordinate($r_1,\;$r_2$) of the reference point, and by translating the exponential part, $r^4\;exp\;(-{\beta}r)$), in terms of $r_1,\;and\;r_2$ and the modified Bessel functions. Master formulas for overlap and dipole moment matrix elements are derived. The computed values of overlap and dipole moment matrix elements for hypothetical NO molecule are exactly in agreement with those for the previous methods.

• Economic and Environmental Geology
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• v.49 no.4
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• pp.269-280
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• 2016

I presented three vector crustal magnetic anomaly components and six gradients by using spherical Slepian functions over the cap area of $20^{\circ}$ of radius centered on the South Pole. The Swarm mission, launched by European Space Agency(ESA) in November of 2013, was planned to put three satellites into the low-Earth orbits, two in parallel in East-West direction and one in cross-over of the higher altitude. This orbit configuration will make the gradient measurements possible in North-South direction, vertical direction, as well as E-W direction. The gravity satellites, such as GRACE and GOCE, have already implemented their gradient measurements for recovering the accurate gravity of the Earth and its temporal variation due to mass changes on the subsurface. However, the magnetic gradients have little been applied since Swarm launched. A localized magnetic modeling method is useful in taking an account for a region where data availability was limited or of interest was special. In particular, computation to get the localized solutions is much more efficient and it has an advantage of presenting high frequency anomaly features with numbers of solutions fewer than the global ones. Besides, these localized basis functions that were done by a linear transformation of the spherical harmonic functions, are orthogonal so that they can be used for power spectrum analysis by transforming the global spherical harmonic coefficients. I anticipate in scientific and technical progress in the localized modeling with the gradient measurements from Swarm and here will do discussion on the results of the localized solution to represent the three vector and six gradient anomalies over the Antarctic area from the synthetic data derived from a global solution of the spherical harmonics for the crustal magnetic anomalies of Swarm measurements.

• 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 earth science society
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• v.41 no.4
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• pp.344-355
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• 2020

Tropical cyclone scale vortices and associated Rossby waves were investigated numerically using high-resolution barotropic models on the global domain. The equations of the barotropic model were discretized using the spectral transform method with the spherical harmonics function as orthogonal basis. The initial condition of the vortex was specified as an axisymmetric flow in the gradient wind balance, and four types of basic zonal states were employed. Vortex tracks showed similar patterns as those on the beta-plane but exhibited more eastward displacement as they moved northward. The zonal-mean flow appeared to control not only the west-east translation but also the meridional translation of the vortex. Such a meridional influence was revealed to be associated with the beta gyre and the Rossby wave, which are formed around the vortex due to the beta effect. In the case of the basic zonal state of climatological mean, the meridional translation speed reached the maximum value when the vortex underwent recurving.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2004.11a
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• pp.1101-1106
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• 2004

This study presents the reconstruction of sound field radiated from an automotive engine using equivalent sources. Basic concept of the method presented is to replace the engine noise source with elementary sources of multipoles, e.g., monopoles and dipoles. The so-called Helmholtz equation least-squares (HELS) method can reconstruct the sound radiation fields from spherical geometries in a series expansion of spherical Hankel functions and spherical harmonics. In this paper, multi-Point, multipole equivalent sources are employed to reconstruct the sound field radiated from an automotive engine with a fixed rotation speed. To ensure and improve the accuracy of reconstruction, the spatial filters of multipole coefficients and wave-vectors are adopted for suppressing the adverse effect of high-order multipoles. Optimal filter shapes are designed with regularization parameters minimizing the generalized cross validation (GCV) function between actual and reproduced model. After regeneration of field pressures using the proposed method as many as necessary, the vibro-acoustic field of an engine could be reconstructed by using the BEM-based near-field acoustic holography (NAH) technique in a cost-effective manner.

• Journal of Astronomy and Space Sciences
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• v.32 no.3
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• pp.247-256
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• 2015

In this work, an efficient method with which to evaluate the high-degree-and-order gravitational harmonics of the non-sphericity of a central body is described and applied to state predictions of a lunar orbiter. Unlike the work of Song et al. (2010), which used a conventional computation method to process gravitational harmonic coefficients, the current work adapted a well-known recursion formula that directly uses fully normalized associated Legendre functions to compute the acceleration due to the non-sphericity of the moon. With the formulated algorithms, the states of a lunar orbiting satellite are predicted and its performance is validated in comparisons with solutions obtained from STK/Astrogator. The predicted differences in the orbital states between STK/Astrogator and the current work all remain at a position of less than 1 m with velocity accuracy levels of less than 1 mm/s, even with different orbital inclinations. The effectiveness of the current algorithm, in terms of both the computation time and the degree of accuracy degradation, is also shown in comparisons with results obtained from earlier work. It is expected that the proposed algorithm can be used as a foundation for the development of an operational flight dynamics subsystem for future lunar exploration missions by Korea. It can also be used to analyze missions which require very close operations to the moon.

• Journal of the Korean Chemical Society
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• v.23 no.5
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• pp.296-306
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• 1979

Operator technique has been applied for calculation of the quadrupole moment matrix-elements. Master formulas for the quadrupole moment matrix elements for pairs of Slater type, orbitals are derived, one using the expansion method for spherical harmonics and the other the transformed of the quadrupole moment matrix elements into overlap integrals for Mulliken. The numerical values of the quadrupole moment matrix elements evaluated by two methods are in agreement with each other and the calculated quadrupole moment for the ground state of HCl molecule is also in agreement with that of Nesbet.

• Journal of the Korean Chemical Society
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• v.23 no.1
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• pp.1-6
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• 1979

The dipole moments for square planar and tetrahedral $[M(II)N_2S_2]$ type complexes are calculated, using the expansion method for spherical harmonics [M(II) = Co(II), Ni(II), Cu(II) or Zn(II)]. The calculated values of the dipole moments for these complexes are in the range of the experimental values. The possible structures for these complexes in benzene solution are discussed on the basis of the calculated dipole moments and the the magnetic properties.