• ETRI Journal
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• 제33권6호
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• pp.849-856
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• 2011

This research introduces three new fractal array configurations that have superior performance over the well-known Sierpinski fractal array. These arrays are based on the fractal shapes Dragon, Twig, and a new shape which will be called Flap fractal. Their superiority comes from the low side lobe level and/or the wide angle between the main lobe and the side lobes, which improves the signal-to-intersymbol interference and signal-to-noise ratio. Their performance is compared to the known array configurations: uniform, random, and Sierpinski fractal arrays.

• 한국항해항만학회지
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• 제35권1호
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• pp.51-56
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• 2011

자연지형의 3D 디지털 지형모델(DTM)을 다루면서 소실된 셀의 데이터를 복원하거나, 저해상도의 DTM 이미지 일부를 컴퓨터 화면상에 확대표시 할 경우에는 존재하지 않는 데이터를 인위적으로 만들어줄 필요가 있다. 기존의 Bilinear법과 Bicubic법은 고도가 완만한 모델에는 잘 맞지만, 자연지형과 같이 무한의 상세함이 내재된 곳에는 부적합하다. 따라서 본 연구에서는 프랙탈 이론(Fractal theory)에 기초하여 자연지형을 보간하는 문제를 다루면서, 보간 전후 지형의 지형정보(프랙탈 차원과 표준편차)가 유지되는 한 방법을 제안한다. 이를 위해 DTM을 다수의 패치로 분할하고 프랙탈 기법으로 지형정보를 추출하고, 이 정보와 원래의 고도와 Random midpoint displacement법으로 보간한다. 제안된 알고리즘의 유효성을 확인하기 위해 가상의 프랙탈 지형을 만들어 시뮬레이션을 실시하고 기존의 방법과 비교한다.

• 대한수학회지
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• 제51권5호
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• pp.1075-1088
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• 2014

We consider random fractal sets with random recursive constructions in which the contracting vectors have different distributions at different stages. We prove that the random fractal associated with such construction has a constant packing dimension almost surely and give an explicit formula to determine it.

• 한국컴퓨터그래픽스학회논문지
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• 제1권2호
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• pp.248-253
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• 1995

Mandelbrot에 의하여 제안된 Random Fractal은 현실감 있는 지형의 모델링을 가능하게 하였으며. Fournier등은 수학적으로 매우 복잡한 Fractal이론을 단순화한 중간점 분할 알고리즘(Midpoint Subdivision Algorithm)을 고안하여 다양한 형태의 지형 모델링에 매우 성공적인 결과를 얻게 되었다. 그러나, Random Fractal을 응용한 여러 종류의 알고리즘들은 이것의 특성으로 인하여, 생성되는 지형의 형태를 예측하기 어려운 단점이 있다. 따라서, 본 논문에서는 중간점 분할 알고리즘을 이용하여 사용자가 원하는 형태의 지형을 모델링할 수 있는 방법에 대하여 논하였다. 전체적인 지형의 모델링 과정을 크게 전역 제어와 지역 제어의 두 단계로 구분하여, 전역 제어 단계에서 전체 지형의 개략적인 형태를 제어하여 모델링한 후 지역 제어 단계에서의 세부적인 형태제어를 통하여 최종적으로 사용자가 원하는 형태의 지형을 모델링할 수 있는 방법을 제안하였다. 또한, GUI(Graphical User Interface)를 이용하여 전역 제어와 지역 제어에서 생성되는 전체 지형의 형태를 wire frame을 이용하여 실시간에 회전시키며 점검할 수 있도록 하여 세부적인 수정을 용이하게 하였다.

• 정보저장시스템학회논문집
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• 제2권1호
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• pp.43-49
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• 2006

Fractal/angle multiplexing is a $LiNBO_3$ crystal using a X-Y Galvano mirror, and the random access concept in fractal/angle multiplexing are discussed in this paper. First, the brief introduction of the designed holographic digital data storage system is presented. Then, the average access time concept for the storage system is newly defined, and the comparison of the average access time between the holographic storage and a conventional optical disk is performed. Second, the basic simulation and experiment to find the X-Y Galvano mirror dynamics are conducted. From this analysis, we find that the average access time in our HDDS which has 6 degree scan angle is about 5 msec. This result is very high performance when it compared with the average access time of a conventional optical disk. Finally, some recording results using fractal/angle multiplexing are presented, then, the relationship between bit error rate and angle mismatch for the each multiplexing are discussed.

• Bulletin of the Korean Chemical Society
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• 제26권11호
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• pp.1723-1727
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• 2005

A generalized fractional diffusion equation (FDE) is presented, which describes the time-evolution of the spatial distribution of a particle performing continuous time random walk (CTRW) on a fractal lattice. For a case corresponding to the CTRW with waiting time distribution that behaves as $\psi(t) \sim (t) ^{-(\alpha+1)}$, the FDE is solved to give analytic expressions for the Green’s function and the mean squared displacement (MSD). In agreement with the previous work of Blumen et al. [Phys. Rev. Lett. 1984, 53, 1301], the time-dependence of MSD is found to be given as < $r^2(t)$ > ~ $t ^{2\alpha/dw}$, where $d_w$ is the walk dimension of the given fractal. A Monte-Carlo simulation is also performed to evaluate the range of applicability of the proposed FDE.

• International Journal of Concrete Structures and Materials
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• 제18권1E호
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• pp.23-28
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• 2006

In this study, the general theory of fractality is discussed to provide a fundamental understanding of fractal geometry applied to heterogeneous material surfaces like pavement surface and rock surface. It is well known that many physical phenomena and systems are chaotic, random and that the features of roughness are found at a wide spectrum of length scales from the length of the sample to the atomic scales. Studying the mechanics of these physical phenomena, it is absolutely necessary to characterize such multi scaled rough surfaces and to know the structural property of such surfaces at all length scales relevant to the phenomenon. This study emphasizes the role of fractal geometry to characterize the roughness of various surfaces. Pavement roughness and rock surface roughness were examined to correlate their roughness property to fractality.

• 대한전기학회:학술대회논문집
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• 대한전기학회 1997년도 하계학술대회 논문집 C
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• pp.1481-1484
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• 1997

This paper describes a electrical tree simulation by fractal theory. Tree patterns produced by computer simulation with random numbers were studied from the point of view of fractal dimension. Tree patterns have a variety of shapes such as branch-like, bush-like, and quasi-bush-like trees. The patterns are determined by origins and probability ratio. The fractal dimensions have been measured a function of discharge number.

• 한국원자력학회:학술대회논문집
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• 한국원자력학회 1999년도 추계학술발표회요약집
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• pp.139.1-139
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• 1999

• Tribology and Lubricants
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• 제33권6호
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• pp.303-308
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• 2017

Most automobile tire companies have not yet considered the geometric information of a road at the design stage of a tire because the topographical characterization of a road surface is very difficult owing to its vastness and randomness. A road surface shows variable surface roughness values according to magnification, and thus, the contact force between the road and tire significantly fluctuates with respect to the scale. In this study, we make an attempt to define a representative value for surface topographical information at multi-scale levels. To represent surface topography, we use a statistical method called power spectral density (PSD). We use the fast Fourier transform (FFT) and PSD to analyze the height profiles of a random surface. The FFT and PSD of a surface help in obtaining a fractal dimension, which is a representative value of surface topography at all length scales. We develop three surfaces with different fractal dimensions. We use finite element analysis (FEA) to observe the contact forces between a tire and the road surfaces with three different fractal dimensions. The results from FEA reveal that an increase in the fractal dimension decreases the contact length between the tire and road surfaces. On the contrary, the average contact force increases. This result indicates that designing and manufacturing a tire considering the fractal dimension of a road makes safe driving possible, owing to the improvement in service life and braking performance of the tire.