• Bulletin of the Korean Mathematical Society
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• v.57 no.3
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• pp.649-660
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• 2020

This paper proves a new regularity criterion for solutions to the Cauchy problem of the 3D Boussinesq equations via one directional derivative of the horizontal component of the velocity field (i.e., (∂_iu₁; ∂_ju₂; 0) where i, j ∈ {1, 2, 3}) in the framework of the anisotropic Lebesgue spaces. More precisely, for 0 < T < ∞, if $$\large{\normalsize\displaystyle\smashmargin{2}{\int\nolimits_o}^T}({\HUGE\left\|{\small{\parallel}{\partial}_iu_1(t){\parallel}_{L^{\alpha}_{x_i}}}\right\|}{\small^{\gamma}_{L^{\beta}_{x_{\hat{i}}x_{\bar{i}}}}+}{\HUGE\left\|{\small{\parallel}{\partial}_iu_2(t){\parallel}_{L^{\alpha}_{x_j}}}\right\|}{\small^{\gamma}_{L^{\beta}_{x_{\hat{i}}x_{\bar{i}}}}})dt<{{\infty}},$$ where ${\frac{2}{{\gamma}}}+{\frac{1}{{\alpha}}}+{\frac{2}{{\beta}}}=m{\in}[1,{\frac{3}{2}})$ and ${\frac{3}{m}}{\leq}{\alpha}{\leq}{\beta}<{\frac{1}{m-1}}$, then the corresponding solution (u, θ) to the 3D Boussinesq equations is regular on [0, T]. Here, (i, ${\hat{i}}$, ${\tilde{i}}$) and (j, ${\hat{j}}$, ${\tilde{j}}$) belong to the permutation group on the set 𝕊₃ := {1, 2, 3}. This result reveals that the horizontal component of the velocity field plays a dominant role in regularity theory of the Boussinesq equations.

• Proceedings of the KSME Conference
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• 2003.11a
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• pp.658-663
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• 2003

A process of 3-D stereo particle image velocimetry(PIV)was developed for the measurement of an illuminated sliced section field of 3-D complex flows. The present method includes modeling of camera by a calibrator based on the homogeneous coordinate system, transformation of the oblique-angled image to the right-angled image, identification of 2-D velocity vectors by 2-D cross-correlation equation, stereo matching of 2-D velocity vectors of two cameras, accurate calculation of 3-D velocity vectors by homogeneous coordinate system, removal of error vectors by a statistical method followed by a continuity equation criteria, and finally 3-D display as the post processing. An experimental system was also used for the application of the proposed method. Two high speed digital CCD cameras and an Argon-Ion Laser for the illumination were adopted to clarify the time-dependent characteristics of the leading edge extension(LEX) in a highly swept shape applied to a delta wing found in modern air-fighters.

• Journal of Biosystems Engineering
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• v.30 no.4 s.111
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• pp.229-234
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• 2005

Kinetic friction coefficient, bulk density, dynamic and static angle of repose, and terminal velocity of rice husk at the moisture range 7 to $23\%$ w.b. were determined. It could lead to better design and operation of the processing machinery and handling facilities. Friction coefficient was determined from the horizontal traction force measured by pulling the container holding a mass of rice husk on various plate materials. Dynamic angle of repose was calculated from the photos of bulk samples piled by gravity flow on a circular platform. Static angle of repose was determined by measuring the side angle of the bulk material which was left in a cylindrical container after natural discharge of the bulk sample through a circular hole in the bottom plate. Kinetic friction coefficients of rice husk were in the range of $0.254\~0.410,\;0.205\~0.520,\;0.229\~0.400,\;and 0.133\~0.420$ on PVC, mild steel, galvanized steel, and stainless steel, respectively. Bulk density, dynamic and static angle of repose, and terminal velocity were in the range of $91.7\~98.3$ $kg/m^3$, $40.2\~47.6^{\circ},\;52.8\~83.7^{\circ},$ and $1.36\~1.73$ m/s, respectively. These physical properties of rice husk increased linearly as the moisture content increased.

• Journal of Biosystems Engineering
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• v.23 no.6
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• pp.583-590
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• 1998

This study was performed to determine the kinetic friction coefficient bulk density, dynamic and static angle of repose, and terminal velocity of the chopped rice straw in the moisture range of 8~23%, which could be used for better design and operation of the processing machinery and handling facilities. Friction coefficient was determined from the horizontal traction force measured by pulling the container holding the mass of rice straw on the various plate materials. Bulk density was measured with an apparatus consisting of a filling funnel and a receiving vessel. Dynamic angle of repose was calculated from the photos of bulk samples piled by gravity flow on a circular platform. Static angle of repose was determined by measuring the side angle of the bulk material which was left in the cylindrical container after natural discharge of the bulk sample through a circular hole in the bottom plate. Kinetic friction coefficients of rice straw on the PVC, mild steel, stainless steel, and galvanized steel were in the range of 0.303~0.434, 0.222~0.439, 0.204~0.448, and 0.206~0.407, respectively. and indicated linear increase with moisture content. The effects of moisture change on the friction coefficients were in the order of PVC, mild steel, galvanized steel, and stainless steel. Bulk density, dynamic and static angle of repose, and terminal velocity were in the range of 56.8~60.3 kg/m$^3$, 41.4~45.9$^{\circ}$, 94.4~100.8$^{\circ}$, and 1.07~4.48 m/s, respectively, and were increased linearly with the moisture content.

• 한국지구물리탐사학회:학술대회논문집
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• 2007.06a
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• pp.209-214
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• 2007

In Korean geology that crystalline rock is dominant, the properties of subsurface including the anisotropy are distributed complexly and changed abruptly. Because of such geological environments, cross-hole seismic traveltime tomography is widely used to obtain the high resolution image of the subsurface for the engineering purposes in the geotechnical sites. However, because the cross-hole tomography has a wide propagation angle coverage relatively, its data tend to include the seismic velocity anisotropy comparing with the surface seismic methods. It can cause the misinterpretation that the cross-hole seismic data including the anisotropic effects are analyzed and treated with the general processing techniques assuming the isotropy. Therefore, we need to consider the seismic anisotropy in cross-hole seismic traveltime tomography. The seismic anisotropic tomography algorithm, which is developed for evaluation of the velocity anisotropy, includes several inversion schemes in order to make the inversion process stable and robust. First of all, the set of the inversion parameters is limited to one slowness, two ratios of slowness and one direction of the anisotropy symmetric axis. The ranges of the inversion parameters are localized by the pseudo-beta transform to obtain the reasonable inversion results and the inversion constraints are controlled efficiently by ACB(Active Constraint Balancing) method. Especially, the inversion using the Fresnel volume is applied to the anisotropic tomography and it can make the anisotropic tomography more stable than ray tomography as it widens the propagation angle coverage.

• Proceedings of the Korea Crystallographic Association Conference
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• 2002.11a
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• pp.3-3
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• 2002

Many studies on crystal growth mechanisms of the hen egg-white lysozyme protein crystals have mainly performed by optical microscopy and atomic force microscopy (AFM). As results, two types of growth mechanisms, which are a two-dimensional nucleation mechanism and a spiral growth mechanism, were identified. However, there was no direct evidence of grown-in screw dislocations at the spiral sites. We first observed the screw dislocations in tetragonal lysozyme crystals using synchrotron X-ray topography. In addition, to confirm the characteristics of dislocations, we have observed some elastic constants in lysozyme crystals in terms of the sound velocity measurement by pulse echo methods. Tetragonal hen egg-white lysozyme crystals were grown by the concentration gradient method. The crystals were grown in test tubes, with an inner diameter of 8 ㎜ and 80 ㎜ in length, held vertically. The test tubes were kept at 23C for 2 weeks. The maximum size of crystals were 3×3×4 ㎟. The high quality crystals were examined by Laue topography with a water filter using synchrotron radiation. Figure is a X-ray topograph. Several straight screw dislocations were observed. We also determined Burgers vector to be a [110] direction. The measurement of sound velocity was performed by the digital signal processing method. the crystals were placed in stainless steel vessel, which was filled with lysozyme solution used for crystal growth. We observed the longitudinal sound velocity along the [110] direction in the tetragonal is obtained to be 1817 ㎧. Therefore, Young modulus and shear modulus were evaluated to be 2.70 Gpa and 1.02 Gpa, respectively, if we assumed Poisson ratio is 0.33. These results will be discussed at the meeting.

• Journal of Advanced Marine Engineering and Technology
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• v.25 no.4
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• pp.817-824
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• 2001

In the present study, flow characteristics of turbulent oscillatory flows in the exit region connected to the square-sectional $180^{\circ}$curved duct was investigated experimentally. The experimental study for air flows was conducted to measure velocity profiles, shear stress distributions by using the Laser Doppler Velocimetry(L.D.V) system with the data acquisition and processing system of Rotating Machinery Resolver(R.M.R) and PHASE software. The results obtained from the experimentation were summarized as follows : The critical Reynolds number for a change from transitional oscillatory flow to turbulent oscillatory flow was about 75,000 in the 90 region of dimensionless axial position (x/Dh) which was considered as a fully developed flow region. In the turbulent oscillatory flow, velocity profiles of the inflow period in the entrance region were gradually developed, but those of the outflow period were not changed nearly. Shear stress distributions of turbulent oscillatory flow was gradually increased as the flow proceeds to downstream.

• Economic and Environmental Geology
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• v.29 no.6
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• pp.739-744
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• 1996

'Kite' is a newly developed single-channel seismic imaging system capable of producing high resolution three dimensional images of subbottom geology in one traverse of a survey region. The system consists of a horizontally towed hydrophone array and active source. The hydrophone array is towed axis perpendicular to ship direction and the airgun source at the end of the hydrophone array is excited at timed intervals during the progression. The construction of the three dimensional subbottom image was made simply by using conventional multichannel seismic reflection data processing techniques. Common source shot (CSS) gathers of the hydrophone traces are evaluated using Dix's equation for average interval velocity of each subbottom layer. From the interval velocity profile and the normal consolidation stress condition, values of shear modulus, porosity, and shear velocity are deduced from the chosen values of physical constants. The system has been successfully tested at several locations on the North Atlantic continental shelf.

• Korea-Australia Rheology Journal
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• v.17 no.4
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• pp.207-215
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• 2005

We present a finite difference solution for electrokinetic flow in rectangular microchannels encompassing Navier's fluid slip phenomena. The externally applied body force originated from between the nonlinear Poisson-Boltzmann field around the channel wall and the flow-induced electric field is employed in the equation of motion. The basic principle of net current conservation is applied in the ion transport. The effects of the slip length and the long-range repulsion upon the velocity profile are examined in conjunction with the friction factor. It is evident that the fluid slip counteracts the effect by the electric double layer and induces a larger flow rate. Particle streak imaging by fluorescent microscope and the data processing method developed ourselves are applied to straight channel designed to allow for flow visualization of dilute latex colloids underlying the condition of simple fluid. The reliability of the velocity profile determined by the flow imaging is justified by comparing with the finite difference solution. We recognized the behavior of fluid slip in velocity profiles at the hydrophobic surface of polydimethylsiloxane wall, from which the slip length was evaluated for different conditions.

• Transactions of Materials Processing
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• v.11 no.6
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• pp.487-494
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• 2002

A new method of optimal blank shape design using the initial nodal velocity (INOV) has been proposed for the drawings of arbitrary shaped cups. With the given information of tool shape and the final product shape, corresponding initial blank shape has been found from the motion of boundary nodes. Although the sensitivity method, the past work of the present authors, has been proved to be excellent method to find optimal blank shapes, the method has a problem that a couple of deformation analysis is required at each design step and it also exhibits an abnormal behaviors in the rigid body rotation prevailing region. In the present method INOV, only a single deformation analysis per each design stage is required. Drawings of practical products as well as oil-pan, have been chosen as the examples. At every case the optimal blank shapes have been obtained only after a few times of modification without predetermined deformation path. The deformed shape with predicted optimal blank almost coincides with the target shape at every case. Through the investigation the INOV is found to be very effective in the arbitrary shaped drawing process design.