• KSBB Journal
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• v.10 no.2
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• pp.119-125
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• 1995

The morphology of fungal growth, which is an important variable for separability and rheological property of fermented medium, was quantified with fractal geometry Fractal dimensions were determined for submerged growth of two industrially important fungi, Aspergillus niger and Aspergillus oruzae. The tendency of pellet formation was related to the fractal dimension of fungi.

• KSBB Journal
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• v.9 no.5
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• pp.512-517
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• 1994

The morphology of fungal growth, which is an important variable for separability and rheological property of fermented medium, was quantified with fractal geometry. Fractal dimensions were determined for submerged growth of two industrially important fungi, Aspergillus niger and Aspergillus oryzae. The tendency of pellet formation was related to the fractal dimension of fungi.

• Imaging Science in Dentistry
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• v.52 no.1
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• pp.33-41
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• 2022

Purpose: This study aimed to evaluate the structural complexity of craniofacial trabecular bone in multiple myeloma by fractal analysis of panoramic and lateral skull radiography, and to compare the fractal dimension values of healthy patients (HPs), pre-treatment patients (PTPs), and patients during bisphosphonate treatment (DTPs). Materials and Methods: Pairs of digital panoramic and lateral skull radiographs of 84 PTPs and 72 DTPs were selected. After application of exclusion criteria, 43 panoramic and 84 lateral skull radiographs of PTPs, 56 panoramic and 72 lateral skull radiographs of DTPs, and 99 panoramic radiographs of age- and sex-matched HPs were selected. The fractal dimension values from panoramic radiographs were compared among HPs, PTPs, and DTPs and between anatomical locations within patient groups using analysis of variance with the Tukey test. Fractal dimension values from lateral skull radiographs were compared between PTPs and DTPs using the Student t-test. Pearson correlation coefficients were used to assess the relationship between the mandible from panoramic radiographs and the skull from lateral skull radiographs. Intra-examiner agreement was assessed using intraclass correlation coefficients (α=0.05). Results: The fractal dimension values were not significantly different among HPs, PTPs, and DTPs on panoramic radiographs or between PTPs and DTPs on lateral skull radiographs (P>0.05). The mandibular body presented the highest fractal dimension values (P≤0.05). The fractal dimension values of the mandible and skull in PTPs and DTPs were not correlated. Conclusion: Fractal analysis was not sensitive for distinguishing craniofacial trabecular bone complexity in multiple myeloma patients using panoramic and lateral skull radiography.

• Journal of the Korean Association of Geographic Information Studies
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• v.8 no.3
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• pp.1-10
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• 2005

The purpose of this paper is to conduct an experimental measurement and analysis of cities' morphology. Fractal theory that is an effective tool for evaluating self-similarity and complexity of objects was applied. For the comparative analysis of fractailities and computational verification, two totally different cities in Japan were selected. They are Kitakyushu City, which is a big and fully developed city, and Jinguu Machi of which almost all the area is covered with agricultural land use. After converting vector data to raster data within GIS, fractal dimensions of two cases in Kitakyushu City and one case in Jinguu Machi were calculated. The calculation showed that two parts of Kitakyushu City were already fractal. Jinguu Machi, however, was difficult to find fractality. As a conclusion, fractal was proved to be an useful tool to estimate the shape of cities reflecting their internal spatial structure, that is self-similarity and complexity.

• Proceedings of the Korean Society of Tribologists and Lubrication Engineers Conference
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• 2002.10b
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• pp.457-458
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• 2002

The fractal dimension is the characteristics that can quantitatively define the irregularity in natural. It is useful in describing the morphology or various rubbed surface for hydraulic piston motor instead of the stylus profiling method. But fractal parameters had not constructed on the morphological characteristic or rubbed surface because of the insufficient knowledge about a conception of fractal dimension. In this study, for the purpose or applying fractal I parameters practically, we have suggested way to establish the morphological characteristic of rubbed surface with fractal parameters, and we carried out an experiment on the lubricant friction and wear by using Ball-ON-Disk type tester. Materials were the brass and the bronze which are used to slipper-pad in the hydraulic piston motor. We searched for fractal parameters or surface structure with the digital image processing, Surface fractal dimension can be determined by sum of intensity difference of surface pixel. Using the image processing and fractal parameters for rubbed surface in the friction and wear test, morphology of rubbed sur race can be effectively obtained by fractal dimensions.

• Structural Engineering and Mechanics
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• v.23 no.2
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• pp.147-161
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• 2006

Recent developments in fractal theory suggest that fractal may provide a more realistic representation of characteristics of cementitious materials. In this paper, the roughness of fracture surfaces in cementitious material has been characterized by fractal theory. A systematic experimental investigation was carried out to examine the dependency of fracture parameters on the aggregate sizes as well as the loading rates. Three maximum aggregate sizes (4.76 mm, 12.7 mm, and 19.1 mm) and two loading rates (slow and fast loading rate) were used. A total of 25 compression tests and 25 tension tests were performed. All fracture parameters exhibited an increase, to varying degrees, when aggregates were added to the mortar matrix. The fracture surfaces of the specimens were digitized and analyzed. Results of the fractal analysis suggested that concrete fracture surfaces exhibit fractal characteristics, and the fractal geometry provide a useful tool for characterizing nonlinear fracture behavior of concrete. Fractal dimension D was monotonically increased as maximum aggregate sizes increase. A new fractal fracture model was developed which considers the size and shape of aggregate, and the crack paths in the constituent phases. Detailed analyses were given for four different types of fracture paths. The fractal fracture model can estimate fractal dimension for multiphase composites.

• Journal of Periodontal and Implant Science
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• v.43 no.5
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• pp.209-214
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• 2013

Purpose: To assess bony trabecular changes potentially caused by loading stress around dental implants using fractal dimension analysis. Methods: Fractal dimensions were measured in 48 subjects by comparing radiographs taken immediately after prosthesis delivery with those taken 1 year after functional loading. Regions of interest were isolated, and fractal analysis was performed using the box-counting method with Image J 1.42 software. Wilcoxon signed-rank test was used to analyze the difference in fractal dimension before and after implant loading. Results: The mean fractal dimension before loading ($1.4213{\pm}0.0525$) increased significantly to $1.4329{\pm}0.0479$ at 12 months after loading (P<0.05). Conclusions: Fractal dimension analysis might be helpful in detecting changes in peri-implant alveolar trabecular bone patterns in clinical situations.

• Structural Engineering and Mechanics
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• v.20 no.3
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• pp.265-277
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• 2005

This paper is focused on fractal analysis of the surface cracking, a new tool for safety evaluation of corroded reinforced concrete (RC) beams. Comprehensive experimental investigations, including flexural tests, coupon tests on strength evaluation of corroded concrete and rusty rebar, and pullout tests to determine bond strength between concrete and rebar were carried out on nine Corroded Reinforced Concrete Beams (CRCB) exposed to an aggressive environment for more than 10 years. In combination with test results from a previous study on CRCBs fabricated in the laboratory from accelerated methods, it is found that, for both types of beams, the surface cracking distributions are fractal in character at loading and failure stages. Fractal dimension is calculated for all specimens at different corrosion states based on fractal analysis method. Relationships between the fractal dimension and mechanical properties of corroded concrete, rebar corrosion ratio, and ductility of CRCBs are discussed in detail. It is concluded that the fractal dimension can act as a damage index and can be efficiently used to describe the corrosion state of CRCBs.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.25 no.11
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• pp.1737-1742
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• 2001

The fractal-based method for describing rubbed surface texture has aroused great interest. The determination of rubbed surface topography is believed to be extremely important in the areas of contact mechanics, adhesion and friction. In order to describe topography of the rubbed surface, the wear test was carried out with annular surfaces of wear testing specimens in dry friction. furthermore, the relation between the fractal dimensions and the frictional conditions are also investigated and fractal descriptors was applied to rubbed surface with image processing. Fractal dimension can be determined by sum of intensity difference of image surface pixel. Fractal dimension increased according as the applied load and sliding distance increase. Topography of the rubbed surface can be effectively obtained by fractal dimensions.

• Economic and Environmental Geology
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• v.27 no.1
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• pp.81-91
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• 1994

There has been considerable research dealing with the influence of surface roughness along surfaces of rock discontinuities in relation to the peak shear strength of rock masses. Concepts accepted recently for measuring such strength include estimation of a roughness coefficient such as developed by Barton's studies. The method for estimation the Joint Roughness Coefficient (JRC) value of a measured roughness profile is subjective. The aim of this research is to estimate the JRC value of the roughness of a surface profile in a rock mass system using an objective method. The study of roughness of surfaces has included measurement of fractal geometric characteristics. Once the irregularity of the surface has been described by the fractal dimension, the spatial variation of the surface irregularities can be described using variogram and drift analysis. An empirical relationships between the roughness profiles of selected JRC ranges and their fractal dimension with variogram and drift were derived. The application of analyses of fractal dimension, variogram and drift was novel for the analysis of roughness profiles. Also, an empirical equation was applied to experimental data.