• Journal of Positioning, Navigation, and Timing
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• v.2 no.1
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• pp.59-65
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• 2013

The signal broadcast from a GPS satellite experiences code delay and carrier phase advance while passing through the ionosphere, which causes a signal error. Many ionosphere models have been studied to correct this ionospheric delay error. In this paper, the ionosphere modeling for the Korean Peninsula was carried out using a spherical harmonics based model. In contrast to the previous studies, we considered a real-time ionospheric delay correction model using fewer number of basis functions. The modeling performance was evaluated by comparing with a grid model. Total number of basis functions was set to be identical to the number of grid points in the grid model. The performance test was conducted using the GPS measurements collected from 5 reference stations during 24 hours. In the test result, the modeling residual error was smaller than that of the existing grid model. However, when the number of measurements was small and the measurements were not evenly distributed, the overall trend was found to be problematic. For improving this problem, we implemented the modeling with additional virtual measurements.

• 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.

• Investigative Magnetic Resonance Imaging
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• v.11 no.2
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• pp.95-102
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• 2007

Purpose: To acquire high-resolution spiral-scan images at higher magnetic field, high homogeneous magnetic field is needed. Field inhomogeneity mapping and in-vivo shimming are important for rapid imaging such as spiral-scan imaging. The rapid scanning sequences are very susceptible to inhomogeneity. In this paper, we proposed a higher-order shimming method to obtain homogeneous magnetic field. Materials and Methods: To reduce measurement time for field inhomogeneity mapping, simultaneous axial/ sagittal, and coronal acquisitions are done using multi-slice based Fast Spin echo sequence. Acquired field inhomogeneity map is analyzed using the spherical harmonic functions, and shim currents are obtained by the multiplication of the pseudo-inverse of the field pattern with the inhomogeneity map. Results: Since the field inhomogeneity is increasing in proportion to the magnetic field, higher order shimming to reduce the inhomogeneity becomes more important in high field imaging. The shimming technique in which axial, sagittal, and coronal section inhomogeneity maps are obtained in one scan is developed, and the shimming method based on the analysis of spherical harmonics of the imhomogenity map is applied. The proposed technique is applicable to a localized shimming as well. High resolution spiral-scan imaging was successfully obtained with the proposed higher order shimming. Conclusion: Proposed pulse sequence for rapid measurement of inhomogeneity map and higher order shimming based on the inhomogeneity map work very well at 3 Tesla MRI system. With the proposed higher order shimming and localized higher order shimming techniques, high resolution spiral-scan images are successfully obtained at 3 T MRI system.

• 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.

• Journal of Korean Society for Geospatial Information Science
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• v.22 no.3
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• pp.113-119
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• 2014

The positioning accuracy of GNSS surveys deteriorates due to various error factor, and many users sometimes ignore Phase Center Variation (PCV) of antennas. IGS provides an ANTEX file which contains PCV correction information to correct for PCVs. But it is not directly applicable because PCV correction information is provided at 5-degree intervals in the azimuth and elevation directions for the case of receiver antennas, and at 1-degree intervals in the nadir angle for the case of satellite antennas. So, we devised new and optimal ways of interpolating PCV in any desired line of sight to the GNSS satellite. We used spherical harmonics fitting methods in terms of the azimuth and elevation angle for interpolation, and found an optimal degree and order. It is shown that the best accuracy was obtained from the 8 by 8 spherical harmonics. If one requires lower burden on computing resources, the order and degree less than 8 could produce resonable accuracy except for 1st and 5th order.

• Journal of the Korean Chemical Society
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• v.22 no.4
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• pp.229-238
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• 1978

Two methods for evaluation of the dipole moment matrix elements are developed, one using the expansion method for spherical harmonics and the other the transformation method of the dipole moment matrix elements into overlap integrals for Mulliken. The numerical values of the dipole moment matrix elements evaluated by two methods are in agreement with each other.

• 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.

• 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.

• Bulletin of the Korean Mathematical Society
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• v.50 no.5
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• pp.1451-1469
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• 2013

We present various new sharp assertions on multipliers in mixed norm, weighted Hardy and new Lizorkin-Triebel spaces of harmonic functions in higher dimension. Some results are new even in onedimensional case.