• Economic and Environmental Geology
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• v.18 no.2
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• pp.159-166
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• 1985

The computation of gravity anomalies by multi pole expansion is derived and compared with exact calculation for right rectangular prisms and right circular cylinders. For sources near field points, the multipole expansion results in a better approximation in volume integrals than in surface integrals. Nonetheless two approximate methods are coincident in the far-field of the general geophyical prospecting.

• Applied Chemistry for Engineering
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• v.20 no.6
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• pp.646-652
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• 2009

Present study deals with a three phase flow problem of determining drag acting on spheres wetted by liquid flow by gas flow through the spheres in simple cubic (SC), body-center cubic (BCC) and face-centered cubic (FCC) array, respectively, when the inertia of gas is negligibly small. The liquid flow driven by gravity on the spheres is assumed to be unaffected by the countercurrent gas flow. A perturbation method coupled with a multipole expansion method is used to calculate the hydrodynamic interactions between spheres and hence determine the effect of liquid film and flow on the gas flow for each periodic array of spheres. An approximate method for evaluating the effect of the liquid film is also presented for simple estimations. It is found that the approximation results are in a reasonable agreement with the numerical calculations.

• Journal of the Korean Institute of Telematics and Electronics
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• v.26 no.4
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• pp.16-26
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• 1989

Diffraction patterns of electromagnetic fields for the incidence of E-polarized plane wave on both interfaces of an arbitrary-angle dielect wedge are obtained by sum of geometric optics term and the edge diffracted fields. The diffraction coefficients of the edge diffracted fields are evaluated by employing the physical optics approximation and then correcting its error with the multipole line source at the dielectric edge. For the wedge angle $120^{circ}$, the incident angle $60^{circ}$, the relative dielectric constant of the dielectric wedge, 2, 5, and 10, and the observation distance from the tip of the wedge, 5 and 10 wavelength, the diffraction coefficients and the diffraction patterns corresponding to geometric optics, physical optics, and the solution corrected by the multipole line source are plotted, respectively. While the corrected solutions presented in this paper are valid only in the far-field region, these asymptotic solutions show to satisfy the boundary condition on the dielectric interfaces.

• 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.

• The Journal of Korean Institute of Electromagnetic Engineering and Science
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• v.29 no.9
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• pp.701-706
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• 2018

The characteristic basis function method, or CFBM, is one of the representative electromagnetic methods widely used today. In this paper, we propose an accelerating algorithm for the far field interaction calculation of CBFM, to efficiently analyze the electromagnetic characteristics of arbitrarily large structures. To effectively analyze the electromagnetic characteristics of a large structure, it is essential to shorten the computation time. In the CBFM analysis method, the complexity can be greatly reduced by using approximations created via the multipole expansion method. The new algorithm proposed in this paper is applied to the computation of radar cross sections of conductor spheres and fighter aircraft, and it is confirmed that calculation time is reduced by 34 % and 74 %, respectively, without loss of accuracy compared with existing CBFM.

• The Bulletin of The Korean Astronomical Society
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• v.38 no.1
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• pp.47.2-47.2
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• 2013

We have performed a set of high-resolution simulations of nuclear star-forming ring that results in an inward gas migration from the galactic disk. Our simulations consider gas heating/cooling, star formation, and supernova feedback. The galactic potential was obtained from a snapshot of a 6.3 million particle simulation of a galactic disk at 1 Gyr, which manifests spiral arms and pseudo-bulge. The potential was modeled with a combination of 3-dimensional spherical (for the pseudo-bulge) and 2-dimensional cylindrical (for the disk) multipole expansion technique. With such a potential model, one can easily set up various realistic 3-dimensional potential models by slightly changing the expansion coefficients. We have performed a set of simulations with a few million gas particles covering the central ~6 kpc of the disk for different pseudo-bulge sizes and non-axisymmetry, and we report the dependence of the gas inflow rate, size of the star-forming ring, and star-formation rate in the ring on the size and strength of the non-axisymmetry in the bulge.

• The Bulletin of The Korean Astronomical Society
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• v.40 no.1
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• pp.59.1-59.1
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• 2015

We present hydrodynamic simulations of gas clouds that inflowing from the disk to a few hundred parsec region of the Milky Way. Realistic Galactic structures are included in our simulations by thousands of multipole expansions that describe 6.4 million stellar particles of a self-consistent Galaxy simulation (Baba, Saitoh & Wada, in prep.). We find that a hybrid multipole expansion model with two different basis sets and a thick disk correction well reproduces the overall structures of the Milky Way. We find that the nuclear ring evolves into 240 pc at T~1500 Myr, regardless of the initial size. For most of simulation runs, gas inflow rate to the nuclear region is equilibrated as ~0.02 Msun/yr, and thus accumulated gas mass and star formation activity is stabilized as $6{\times}10^7Msun$ and ~0.02M/yr, respectively. These stabilized values are in a good agreement with estimations for the CMZ. The nuclear ring is off-centered to the Galactic center by the lopsided central mass distribution of the Galaxy model, and thus an asymmetric mass distribution is arose accordingly. The lopsidedness also leads the nuclear ring to be tilted to the Galactic plane and to precess along the Galaxy rotation. In early evolutionary stage when gas clouds start to inflow and form the nuclear ring, the z-directional oscillations of the gas clouds results in the twisted, infinity-shaped nuclear ring. Since the infinity-shaped feature is transient only for first 100 Myr, the current infinity-shape observed in the CMZ may indicate that the CMZ forms quite recently.

• Journal of Korean Society for Atmospheric Environment
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• v.9 no.E
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• pp.347-357
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• 1993

The Lagrangian grid-free numerical method, the discrete vortex method, was applied to solve the Navier-Stokes euqations. This method avoids the introduction of numerical viscosity swamping the real physical viscosity at high Reynolds number, unlike Eulerian method, e.g. finite difference and element methods. The boundary integral equation method for the potential flow solution was included to make the discrete vortex method more feasible for complex geometries. The fast adaptive multipole expansion method was incorporated to reduce the computational time from $O(N^2)$ to O(N) for the computations of vortex-vortex interactions. The test problems were air flow around one circular cylinder and two circular cylinders in tandem with various gaps. The numerical results were in excellent gareement with the experimental and other computational results. The applicabilty of the method was discussed with the indoor and the outdoor air pollution problems, especially the contaminant transport in the recirculation regions.

• Bulletin of the Society of Naval Architects of Korea
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• v.18 no.1
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• pp.19-27
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• 1981

The surge motion of a freely-floating sphere in a regular wave is studied within the framework of a linear potential theory. The fluid is assumed to be perfect and only the steady-state harmonic motion in a water of infinite depth is considered. A velocity potential describing the fluid motion is decomposed into three parts; the incident wave potential, the diffraction potential and the radiation potential. In this paper the diffraction potential and the radiation potential are analysed by using multipole expansion method. Upon calculating pressures over the immersed surface of the sphere, the hydrodynamic forces are evaluated in terms of Froude-Krylov, diffraction, added mass and damping forces as functions of the frequency of the incident wave. Finally the frequency dependence of two pertinent parameters, the amplitude ratio and the phase lag between the motion of the sphere and that of the incident wave is derived from the equation of motion. As for numerical results the general tendency of the present calculation shows good agreement with Kim's work who also treated this problem utilizing the Green's function method.

• Bulletin of the Korean Chemical Society
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• v.27 no.11
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• pp.1752-1756
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• 2006

This study explores and interprets in a new way the complex solvent and the temperature dependence of the NMR shifts for the N-$CH_2$ protons in tris(N,N-diethyldithiocarbamato) iron(III) in acetone, benzene, carbon disulfide, chloroform, dimethylformamide and pyridine. The NMR shifts are interpreted in terms of the Fermi contact interaction and the dipolar term from the multipole expansion of the interaction of the electron orbital angular momentum and the electron spin dipolar-nuclear spin angular momentum. This analysis yields a direct measure of the effect of the solvent system on the environment of the transition metal ion. The results are analysed in terms of the crystal field environment of the transition metal ion with contributions from (a) the dithiocarbamate ligand (b) the solvent molecules and (c) the interaction of the effective dipole moment of the polar solvent molecule with the transition metal ion complex.