• Proceedings of the Korean Society of Precision Engineering Conference
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• 2010.05a
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• pp.869-870
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• 2010

• Journal of Korea Technical Association of The Pulp and Paper Industry
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• v.47 no.4
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• pp.177-186
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• 2015

Until Mandelbrot introduced the concept of fractal geometry and fractal dimension in early 1970s, it has been generally considered that the geometry of nature should be too complex and irregular to describe analytically or mathematically. Here fractal dimension indicates a non-integer number such as 0.5, 1.5, or 2.5 instead of only integers used in the traditional Euclidean geometry, i.e., 0 for point, 1 for line, 2 for area, and 3 for volume. Since his pioneering work on fractal geometry, the geometry of nature has been found fractal. Mandelbrot introduced the concept of fractal geometry. For example, fractal geometry has been found in mountains, coastlines, clouds, lightning, earthquakes, turbulence, trees and plants. Even human organs are found to be fractal. This suggests that the fractal geometry should be the law for Nature rather than the exception. Fractal geometry has a hierarchical structure consisting of the elements having the same shape, but the different sizes from the largest to the smallest. Thus, fractal geometry can be characterized by the similarity and hierarchical structure. A process requires driving energy to proceed. Otherwise, the process would stop. A hierarchical structure is considered ideal to generate such driving force. This explains why natural process or phenomena such as lightning, thunderstorm, earth quakes, and turbulence has fractal geometry. It would not be surprising to find that even the human organs such as the brain, the lung, and the circulatory system have fractal geometry. Until now, a normal frequency distribution (or Gaussian frequency distribution) has been commonly used to describe frequencies of an object. However, a log-normal frequency distribution has been most frequently found in natural phenomena and chemical processes such as corrosion and coagulation. It can be mathematically shown that if an object has a log-normal frequency distribution, it has fractal geometry. In other words, these two go hand in hand. Lastly, applying fractal principles is discussed, focusing on pulp and paper industry. The principles should be applicable to characterizing surface roughness, particle size distributions, and formation. They should be also applicable to wet-end chemistry for ideal mixing, felt and fabric design for papermaking process, dewatering, drying, creping, and post-converting such as laminating, embossing, and printing.

• Proceedings of the Korean Society of Precision Engineering Conference
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• 2005.06a
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• pp.915-918
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• 2005

Advances in Information Technology and in Biomedicine have created new uses for CAD technology with many novel and important biomedical applications. Such applications can be found, for example, in the design and modeling of orthopedics, medical implants, and tissue modeling in which CAD can be used to describe the morphology, heterogeneity, and organizational structure of tissue and anatomy. CAD has also played an important role in computer-aided tissue engineering for biomimetic design, analysis, simulation and freeform fabrication of tissue scaffolds and substitutes. And all the applications require precision geometry of the organs or bones of each patient. But the geometry information currently used is polygon model with none solid geometry and is so rough that it cannot be utilized for accurate analysis, simulation and fabrication. Therefore a case study is performed to deduce a transformation method to build free form surface from a rough polygon data or medical images currently used in the application. This paper describes the transformation procedure in detail and the considerations for accurate organ modeling are discussed.

• International Journal of Korean Welding Society
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• v.1 no.1
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• pp.23-30
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• 2001

Among the various welding conditions, the welding current that is inversely proportional to the tip-to-work-piece distance is an essential parameter as to monitor the GMAW process and to implement the welding automation. Considering the weld pool surface geometry including weld defects, it should modify the signal processing method for automatic seam tracking in horizontal fillet welding. To meet the above necessities, a mathematical model related with the weld pool geometry was proposed as in a conjunction with the two-dimensional heat flow analysis of the horizontal fillet welding. The signal processing method based on the artificial neural network (Adaptive Resonance Theory) was proposed for discriminating the sound weld pool surface from that with the weld defects. The reliability of the numerical model and the signal processing method proposed were evaluated through the experiments of which showed that they are effective for predicting the weld bead shape with or without the weld defects in a horizontal fillet welding.

• Journal of Surface Science and Engineering
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• v.50 no.2
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• pp.108-113
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• 2017

We investigated the effect of graphite electrode geometry and combination on nanocarbon material synthesis using underwater discharge plasma(UDP). The UDP system consists of two graphite electrodes and beaker filled with de-ionized water. A high voltage of 15 kV with a frequency of 25 kHz is applied to produce UDP using an alternating-current power source. The UDP system with conical electrodes produced the largest amount of products due to the concentration of electrical fields between electrodes. In addition, hollow-shaped stationary electrode and conical-shaped moving electrode stores discharge-induced bubbles and maintains longer reaction time. We found from Raman spectroscopy and electron microscopy that high quality carbon nanomaterials including carbon nanotubes are synthesized by the UDP system.

• Journal of Industrial Technology
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• v.27 no.B
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• pp.91-96
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• 2007

Electrical impedance tomography (EIT) is a technique for determining the electrical conductivity and permittivity distribution within the interior of a body from measurements made on its surface. One recent application area of the EIT is the detection of breast cancer by imaging the conductivity and permittivity distribution inside the breast. The present standard for breast cancer detection is X-ray mammography, and it is desirable that EIT and X-ray mammography use the same geometry. A forward model of a simplified mammography geometry for EIT imaging was proposed earlier. In this paper, we propose an iterative algorithm for computing the current pattern that will be applied to the electrodes. The current pattern applied to the electrodes influences the voltages measured on the electrodes. Since the measured voltage data is going to be used in the impedance imaging computation, it is desirable to apply currents that result in the largest possible voltage signal. We compute the eigenfunctions for a homogenous medium that will be applied as current patterns to the electrodes. The algorithm for the computation of the eigenfunctions is presented. The convergence of the algorithm is shown by computing the eigencurrent of the simplified mammography geometry.

• Journal of the Korean Mathematical Society
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• v.55 no.4
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• pp.987-1004
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• 2018

In this paper, we get several centroaffine invariant properties for a ruled surface in ${\mathbb{R}}^4$ with centroaffine theories of codimension two. Then by solving certain partial differential equations and studying a centroaffine surface with some centroaffine invariant properties in ${\mathbb{R}}^4$, we obtain such a surface is centroaffinely equivalent to a ruled surface or one of the flat centered cyclic surfaces. Furthermore, some centroaffine invariant properties for centered cyclic surfaces are considered.

• Journal of the Optical Society of Korea
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• v.18 no.6
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• pp.672-678
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• 2014

We propose a method to estimate the 3-D shape of surfaces with specular reflection, using a model of the difference in appearance between images reflected from a flat surface and a curved surface. First, we analyze the geometry of spatial reflection from a specular surface and how reflected light varies due to a curved surface. This is used to estimate 3-D shape. The proposed method is shown to be effective in experiments using illumination from spatially distributed light sources and a camera capturing the reflected light from curved, specular surfaces.

• Proceedings of the Korean Society of Tribologists and Lubrication Engineers Conference
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• 2000.11a
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• pp.205-211
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• 2000

Friction control is highly desirable for optimization of tribological systems. In this work, the effect of geometric structure of the solid surface on friction is investigated using a Scanning Electron Microscope equipped with a tribotester. Silicon and silicon oxide specimens were used and undulations on the surface were fabricated by mechanical and chemical methods. It is shown that the friction coefficient depends on the relative dimensions of the ball and the width of undualation. By optimizing the geometry of the undulation, friction reduction may be achieved.

• Nuclear Engineering and Technology
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• v.52 no.6
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• pp.1271-1276
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• 2020

The geometrical efficiency of a source-to-detector configuration is considered to be necessary in the calculation of the full energy peak efficiency, especially for NaI(Tl) and HPGe gamma-ray spectroscopy detectors. The geometrical efficiency depends on the solid angle subtended by the radioactive sources and the detector surfaces. The present work is basically concerned to establish a new mathematical approach for calculating the solid angle and geometrical efficiency, based on conversion of the geometrical solid angle of a non-axial radioactive point source with respect to a circular surface of the detector to a new equivalent geometry. The equivalent geometry consists of an axial radioactive point source with respect to an arbitrary elliptical surface that lies between the radioactive point source and the circular surface of the detector. This expression was extended to include coaxial radioactive circular disk source. The results were compared with a number of published data to explain how significant this work is in the efficiency calibration procedure for the γ-ray detection systems, especially in case of using isotropic radiating γ-ray sources in the form of point and disk shapes.