• Journal for History of Mathematics
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• v.21 no.3
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• pp.1-30
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• 2008

The success of Newton's Gravitational Theory has influenced the theory of capillarity, beginning in the early nineteenth century, by providing a major model of molecular attraction. He used the equation of the attraction of spheroids, which is expressed by second order partial differential equations, to utilize this analogy as the same kind of a particle's force, between gravitational, refractive force of light, and capillarity. The solution of the differential equation corresponds to the geometrical figure of the vessel and the contact angle which is made by the fluid. Unknown abstract functions $\varphi(f)$ represent interaction forces between molecules, giving their potential functions. By conducting several kinds of experimental conditions, it was found that the height of the ascending fluid in the tube is inversely proportional to the rayon of the tube or the distance of the plate. This model is an essential element in the theory of capillarity. Laplace has brought Newtonian mechanics to completion, which relates to the standard model of gravitational theory. Laplace-Young's equation of capillarity is applicable to minimal surfaces in mathematics, to surface tensional phenomena in physics, and to soap bubble experiments.

• Journal of Korean Society for Geospatial Information Science
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• v.16 no.3
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• pp.117-126
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• 2008

Earth geopotential models were used to determine the reference surface in geoid modelling and many global geopotential models were developed after 1980's. Nowadays, EGM96 and EIGEN-GL04C geopotential models have been most widely used in the world, but what so called EGM2008 earth geopotential model were developed in 2008 by NGA. In this paper, we intended to compare the results of spherical harmonic analyses using the three geopotential model, EGM96, EIGEN-GL04C and EGM2008. So, the spherical harmonic analyses were performed up to degree and order 360(in case of EGM2008, up to degree and order 720, 1440, 2190 in addition), on each $1'{\times}1'$grid point in and around Korean peninsula. Geometric geoid were calculated at 464 GPS/leveling points for accuracy evaluation and then the results of three geopotential models were compared to geometric geoid. The results show that the accuracy of EGM2008 is improved considerablely compared to EGM96 and EIGEN-GL04C and it is possible to calculate geoidal heights within 14cm standard deviation and 5.5cm standard deviation after LSC fitting in and around Korean peninsula using EGM2008 geopotential model.

• Journal of Astronomy and Space Sciences
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• v.10 no.2
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• pp.152-162
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• 1993

We developed the S/W which calculate the Planetary and the Moon ephemerides. The ephemeris of the Solar system objects was obtained from a simultaneous numerical integration of the equations of motion for the nine planets and the Moon. The mathematical model includes contributions from (1) point-mass interactions (2) figure effect (3) earth tides (4) the orientations of the Earth and the Moon. The calculated ephemerides are compared with DE200 data produced by JPL (Jet Propulsion Laboratory).

• Transactions of the Korean Society of Mechanical Engineers B
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• v.30 no.6 s.249
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• pp.578-586
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• 2006

Numerical simulations are carried out to investigate the thermal effects of the gravitational potential on the centrifugal instability of a Taylor-Couette flow, and to further study the detailed flow fields and flow bifurcations to spiral vortices. The effects of centrifugal potential on the centrifugal instability are also investigated in the current study. Spiral vortices have various types of mode depending on Grashof number and Reynolds number. The correlation of Richardson number with the spiral angle of the spiral vortices shows that the structure of the spiral vortices strongly depends on the Richardson number. The heat transfer rate of the inner cylinder increases with increasing Grashof number. It is also confirmed that the torque required to rotate the inner cylinder increases as Grashof number increases.

• Journal of the Korean earth science society
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• v.24 no.3
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• pp.205-215
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• 2003

A precise and dense Bouguer anomaly is one of the most important data to improve the knowledge of our environment in the aspect of geophysics and physical geodesy. Besides the precise absolute gravity station net, we should consider two parts; one is to improve the precision in gravity measurement and correction of it, and the other is the density of measurement both in number and distribution. For the precise positioning, we have tested how we could use the GPS properly in gravity measurement, and deduced that the GPS measurement for 5 minutes would be effective when we used DGPS with two geodetic GPS receivers and the baseline was shorter than 40km. In this case we should use a precise geoid model such as PNU95. By applying this method, we are able to reduce the cost, time, and number of surveyors, furthermore we also get the benefit of improving in quality. Two kind of computer programs were developed to correct crossover errors and to calculate terrain effects more precisely. The repeated measurements on the same stations in gravity surveying are helpful not only to correct the drifts of spring but also to approach the results statistically by applying network adjustment. So we can find out the blunders of various causes easily and also able to estimate the quality of the measurements. The recent developments in computer technology, digital elevation data, and precise positioning also stimulate us to improve the Bouguer anomaly by more precise terrain correction. The gravity data of various sources, such as land gravity data (by Choi, NGI, etc.), marine gravity data (by NORI), Bouguer anomaly map of North Korea, Japanese gravity data, altimetry satellite data, and EGM96 geopotential model, were collected and processed to get a precise and dense Bouguer anomaly in and around the Korean Peninsula.

• Economic and Environmental Geology
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• v.43 no.3
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• pp.249-258
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• 2010

In general, a crustal geomagnetic (or gravity) anomaly compiled at one altitude can be estimated at a different altitude by continuation using the Fourier transform (FT). However, in case of continuation with a great distance between the two elevations, or, in particular, in case of downward continuation, the estimated anomalies by the FT are likely to be mathematically unstable so that the estimated values are not realistic. To solve this problem, two independently measured magnetic field anomalies at different altitudes, such as aeromagnetic and satellite magnetic observations, are implemented to estimate values at in-between altitude for better understanding and interpreting geophysical and geological features. This ‘'dual continuation’' technique is straightforward in the FT and gives a more realistic estimate in all altitudes when we simulated with a set of prismatic bodies at different altitudes. This implies that we add up another constraint like satellite-based observations on the geopotential field modeling for the non-unique geological and geophysical problems to a conventional Fourier-type continuation technique with a single set of observations.

• Journal of the Korean earth science society
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• v.30 no.2
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• pp.165-175
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• 2009

The East Sea including the area of this study is identified as a typical back-arc sea located in the backside of the Circum-Pacific volcanic and earthquake belt. Previous studies reported that the East Sea has begun to open by tensile force and formed its current shape. In this study, we investigate the regional tectonic structure of the East Sea using ship-borne gravity, magnetic, and satellite gravity data. The result of three-dimensional depth inversion shows that Moho depth of the study area is approximately 13-25km and inversely proportional to the thickness of the crust. In addition, as approaching to the center of the Ulleung Basin (UB), the thickness of the crust of the UB becomes thinner due to the extension caused by tensile force which had opened the East Sea.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.29 no.5C
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• pp.217-228
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• 2009

In case of application of electrophoresis method for leakage restoration of waste impoundment, main points of consideration were to evaluate the mobility of clay particles by electrophoretic force and capacity of leakage repair in leachate electrolyte system contained with various chemical species. However, the flocculation phenomena of clay particles induced by electrochemical interaction between various chemical species and clay particles would cause the big problems in electrophoresis method. Therefore, a series of laboratory tests such as one-dimensional electrophoresis and gravitational experiments were carried out in order to identify the specific chemical species affected flocculation of clay particles and the range of chemical concentration in leachate. In addition, the characteristics of clay particle behavior with chemical species and concentration range in leachate were analized using the concept of the settling velocity, zeta potential, and electrophoretic velocity.

• Journal of the Korean earth science society
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• v.29 no.1
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• pp.1-12
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• 2008

A geophysical mapping was performed for Hwasan caldera which is located in Euisung Sub-basin of the southeastern part of the Korean Peninsula. In order to overcome the limitation of the previous studies, remote sensing technic was used and dense potential data were obtained and analyzed. First, we analyzed geological lineament for target area using geological map, digital elevation model (DEM) data and satellite imagery. The results were greatly consistent with the previous studies, and showed that N-S and NW-SE direction are the most dominant one in target area. Second, based on the lineament analysis, highly dense gravity data were acquired in Euisung Sub-basin and an integrated interpretation considering air-born magnetic data was made to investigate the regional structure of the target area. The results of power spectrum analysis for the acquired potential data revealed that the subsurface of Euisung Sub-basin have two density discontinuities at about 1 km and 3-5 km depth. A 1 km depth discontinuity is thought as the depth of pyroclastic sedimentary rocks or igneous rocks which were intruded at the ring vent of Hwasan caldera, while a 3-5 km depth discontinuity seems to be associated with the depth of the basin basement. In addition, three-dimensional gravity inversion for the total area of Euisung Sub-basin was carried out, and the inversion results indicated two followings; 1) Cretaceous Palgongsan granite and Bulguksa intrusion rocks, which are located in southeastern part and northeastern part of Euisung Sub-basin, show two major low density anomalies, 2) pyroclastic rocks around Hwasan caldera also have lower density when compared with those of neighborhood regions and are extended to 1.5 km depth. However, a poor vertical resolution of potential survey makes it difficult to accurately delineate the detailed structure caldera which has a vertically developed characteristic in general. To overcome this limitation, integrated analysis was carried out using the magnetotelluric data on the corresponding area with potential data and we could obtain more reasonable geologic structure.

• Journal of Astronomy and Space Sciences
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• v.14 no.1
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• pp.136-141
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• 1997

To calculate the position and velocity of the artificial satellite precisely, one has to build a mathematical model concerning the perturbations by understanding and analysing the space environment correctly and then quantifying. Due to these space environment model, the total acceleration of the artificial satellite can be expressed as the 2nd order differential equation and we build an orbit propagation algorithm by integrating twice this equation by using the Cowell's method which gives the position and velocity of the artificial satellite at any given time. Perturbations important for the orbits of geostationary spacecraft are the Earth's gravitational potential, the gravitational influences of the sun and moon, and the solar radiation pressure. For precise orbit propagation in Cowell' method, 40 x 40 spherical harmonic coefficients can be applied and the JPL DE403 ephemeris files were used to generate the range from earth to sun and moon and 8th order Runge-Kutta single step method with variable step-size control is used to integrate the the orbit propagation equations.