• The Journal of Engineering Geology
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• v.4 no.2
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• pp.139-151
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• 1994

Rocks are composed of the discrete elements of microstructures such as different grains and microcracks. The studies of these microstructures are of increasing interest in engineering geology and civil engineering related to construction of a deep under-ground space. Accordingly, instead of a simplified continuum approach, discrete structural elements and mechanical properties of various grains must be accounted. But it is difficult to analyse crack and discontinuity surfaces in Euclidean geometry. So, Mandelbrot( 1983) developed fractal theory to manage irregular body in nature. In this study, geometrical properties of microstructures to estimate a relation between crack propagation and stress were calculated. Then it is shown that fractal theory can be applied to research real mechanical behavior of rocks.

• Proceedings of the Korean Institute of Electrical and Electronic Material Engineers Conference
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• 2002.07b
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• pp.927-930
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• 2002

The HFPD measurement method is a technique to analyze aging state of high voltage insulation materials and detect higher frequency signals than conventional PD measurement method therefore it takes less noise effect and could execute active line measurement. It is possible to analyze main discharge phenomena and obtain access to aging progress occurred in insulation materials through accumulation of HFPD signals during determined interval and expression of fractal dimension using statistical process of accumulated signals. In this study, the statistical parameters (skewness & kurtosis) and fractal dimensions are changed by discharge patterns that is shown up different characteristics with applied voltages and times.

• Journal of the Mineralogical Society of Korea
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• v.23 no.4
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• pp.367-375
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• 2010

Understanding the interactions between earth materials and fluids is essential for studying the diverse geological processes in the Earth's surface and interior. In order to better understand the interactions between earth materials and fluids, we explore the effect of specific surface area and porosity on structural parameters of pore structures. We obtained 3D pore structures, using random packing simulations of porous media composed of single sized spheres with varying the particle size and porosity, and then we analyzed configurational entropy for 2D cross sections of porous media and cube counting fractal dimension for 3D porous networks. The results of the configurational entropy analysis show that the entropy length decreases from 0.8 to 0.2 with increasing specific surface area from 2.4 to $8.3mm^2/mm^3$, and the maximum configurational entropy increases from 0.94 to 0.99 with increasing porosity from 0.33 to 0.46. On the basis of the strong correlation between the liquid volume fraction (i.e., porosity) and configurational entropy, we suggest that elastic properties and viscosity of mantle melts can be expressed using configurational entropy. The results of the cube counting fractal dimension analysis show that cube counting fractal dimension increases with increasing porosity at constant specific surface area, and increases from 2.65 to 2.98 with increasing specific surface area from 2.4 to $8.3mm^2/mm^3$. On the basis of the strong correlation among cube counting fractal dimension, specific surface area, and porosity, we suggest that seismic wave attenuation and structural disorder in fluid-rock-melt composites can be described using cube counting fractal dimension.

• Kyungpook Mathematical Journal
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• v.45 no.4
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• pp.503-510
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• 2005

Let $\left{K_{\alpha}\right}_{{\alpha}{\in}{\mathbb{R}}}$ be the multifractal spectrums of a perturbed Cantor set K. We find the set of values ${\alpha}$ of nonempty set $K_{\alpha}$ by using the Birkhoff ergodic theorem. And we also show that such $K_{\alpha}$ is a fractal set in the sense of Taylor [12].

• Korean Journal of Remote Sensing
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• v.23 no.2
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• pp.131-135
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• 2007

The tidal channel is influenced by sediment type, grain size, grain composition and tidal currents in tidal flat. The development of tidal channel including density, shape and order can be used to analyze the characteristics of tidal channel. The quantitative investigation to the tidal channel is insufficiency. In this paper, we represented the fractal analysis method according to the quantitatively analysis in tidal channel and compared with the different intertidal channel patterns. The tidal channel was extracted from the IKONOS image of the southern part of the Kanghwa-do. We used the Box-counting method to estimate fractal dimensions for each tidal channel. As a result, the fractal dimension values (D) were 1.31 in the southern Kanghwa-Do. Linear pattern and less dense channel development area had low D values (from 1.0563 to 1.0672). Dendritic pattern and dense channel development area had high D values (from 1.2550 to 1.3016). In other words, fractal dimension values had difference about 0.2 values according to the characteristic of tidal channel development. We concluded that fractal analysis can be able to quantitatively classification in tidal channel.

• Journal of Korean Dental Science
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• v.6 no.1
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• pp.4-12
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• 2013

Purpose: This study sought to verify the usefulness of mini-implant and surgical steel wire in the treatment of mandibular fracture through the objective identifi cation of the change of bone structure and bone density before and after reduction by evaluating radiological change through fractal analysis when mandibular fracture is treated using mini-implant and surgical wire. Materials and Methods: This study looked at 45 patients (males: 38, female: 7) diagnosed with mandibular fracture in the oral and maxillofacial surgery division of Chung-Ang University Dental Hospital and who received open reduction and intra-osseous fi xation. Result: The average fracture dimension values were higher for the group of the patients who had mini-implants and surgical wire treatment. Conclusion: Based on the results of the study on the usefulness of the reduction technique using mini-implant and surgical steel wire in the treatment of mandibular fracture through the fractal analysis method, the reduction technique using mini-implant and surgical steel wire is regarded as an effective method of minimizing the gap between mandibular fracture fragments.

• Journal of the Institute of Electronics Engineers of Korea TC
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• v.39 no.12
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• pp.566-574
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• 2002

In this paper, the scattered field from a perfectly conducting fractal surface by the Monte-Carlo moment method was computed. An one-dimensional fractal surface was generated by using the fractional Brownian motion model. Back scattering coefficients are calculated with different values of the spectral parameter(S$\_$0/), and fractal dimension(D) which determine characteristics of the fractal surface. The number of surface realization for the computed field, the point number, and the width of surface realization are set to be 80, 2048, and 64L, respectively. In order to verify the computed results these results are compared with those of small perturbation methods, which show good agreement between them.

• Journal of Veterinary Clinics
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• v.24 no.4
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• pp.568-572
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• 2007

This study was carried out to show at the fractal analysis complements the practical disadvantage of gray level histogram which is designed to measure the quantitative classification of echo patterns in ultrasonographic image of parenchymal organs such as spleen and kidney and it is a practical method of measurement for quantitative classification. By using ultrasonographs, kidney and spleen of 21 healthy Beagles were fixed under different gain settings to be scanned for echo patterns and results were analyzed with body gray level histogram and fractal analysis. Then it was compared based on the statistical data obtained. Although there was a proportionate increase in histogram along with gain settings, there were consistencies in the fractal dimension. In terms of quantitative analysis in ultrasonographic images, fractal analysis is concluded to complement the practical disadvantage of gray level histogram.

• Imaging Science in Dentistry
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• v.50 no.1
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• pp.31-36
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• 2020

Purpose: The purpose of this study was to investigate the impact of radiotherapy on mandibular bone tissue in head and neck cancer patients through an analysis of pixel intensity and fractal dimension values on digital panoramic radiographs. Materials and Methods: Thirty patients with radiographic records from before and after 3-dimensional (3D) conformational radiotherapy were selected. A single examiner carried out digital analyses of pixel intensity values and fractal dimensions, with the areas of interest unilaterally located in the right angle medullary region of the mandible below the mandibular canal and posterior to the molar region. Results: Statistically significant decreases were observed in the mean pixel intensity (P=0.0368) and fractal dimension (P=0.0495) values after radiotherapy. Conclusion: The results suggest that 3D conformational radiotherapy for head and neck cancer negatively affected the trabecular microarchitecture and mandibular bone mass.

• Geomechanics and Engineering
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• v.3 no.3
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• pp.219-231
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• 2011

Waste fills resulting from coal mining should consist of large, free-draining sedimentary rocks fragments. The successful performance of these fills is related to the strength and durability of the individual rock fragments. When fills are made of shale fragments, some fragments will be durable and some will degrade into soil particles resulting from slaking and inter-particle point loads. The degraded material fills the voids between the intact fragments, and results in settlement. A laboratory program with point load and slake durability tests as well as thin section examination of sixty-eight shale samples from the Appalachian region of the United States revealed that pore micro-geometry has a major influence on degradation. Under saturated and unsaturated conditions, the shales absorb water, and the air in their pores is compressed, breaking the shales. This breakage was more pronounced in shales with smooth pore boundaries and having a diameter equal to or smaller than 0.060 mm. If the pore walls were rough, the air-pressure breaking mechanism was not effective. However, pore roughness (measured by the fractal dimension) had a detrimental effect on point load resistance. This study indicated that the optimum shales to resist both slaking as well as point loads are those that have pores with a fractal dimension equal to 1.425 and a diameter equal to or smaller than 0.06 mm.