• Title/Summary/Keyword: Fractal Theory

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A Study on the Development of Geometry as the Natural Laws and the Concepts of Space - Focus on the Whitehead's theories of natural laws - (자연법칙으로서 기하학과 공간 개념의 전개에 관한 연구 - 화이트헤드의 자연법칙 학설을 중심으로 -)

  • Hwang, Tae-Joo
    • Korean Institute of Interior Design Journal
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    • v.19 no.2
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    • pp.90-98
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    • 2010
  • The concepts of laws like regularity or persistence or recurrence those are discovered in nature, became the essential elements in speculative philosophy, study and scientific technology. Western civilization was spread out by these natural laws. As this background, this study is aimed to research the theories of natural laws and the development of geometry as the descriptive tools and the development aspects of the concepts of space. According to Whitehead's four theories on the natural laws, the result of this study that aimed like that as follows. First, the theories on the immanence and imposition of the natural laws were the predominant ideas from ancient Greek to before the scientific revolution, the theory on the simple description like the positivism made the Newton-Cartesian mechanism and an absolutist world view. The theory on the conventional interpretation made the organicism and relativism world view according to non-Euclidean geometry. Second, the geometrical composition of ancient Greek architecture was an aesthetics that represented the immanence of natural laws. Third, in the basic symbol of medieval times, the numeral symbol was the frame of thought and was an important principal of architecture. Fourth, during the Renaissance, architecture was regarded as mathematics that made the order of universe to visible things and the geometry was regarded as an important architectural principal. Fifth, according to the non-Euclidean geometry, it was possible to present the natural phenomena and the universe. Sixth, topology made to lapse the division of traditional floor, wall and ceiling in contemporary architecture and made to build the continuous space. Seventy, the new nature was explained by fractal concepts not by Euclidean shapes, fractal presented that the essence of nature had not mechanical and linear characteristic but organic and non-linear characteristic.

The Grid System of Women's Jeogori in Joseon Dynasty (조선시대 여성저고리의 그리드체계)

  • Han, Eun-Hye
    • Journal of the Korean Society of Costume
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    • v.62 no.6
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    • pp.200-217
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    • 2012
  • The purpose of this research is to examine the specificity of grids to define the characteristics of clothes styles in the Joseon Dynasty period. The significance of examining of the specificity of grids is to find out arbitrary types of the features of grids involved in structuring the Jeogori in the Joseon Dynasty period one by one. The Visual Linguistic Theory was introduced as a methodological tool to exquisitely analyze the characteristics of grids in deep structures of Jeogori in the Joseon Dynasty period. This theory strives to examine sample distribution, the distribution of samples by quality and the distribution of the types of ploidy features. Through the examination, the results are as follows. The grid systems of the Jeogori consisted of diverse proportion systems reaching 86 cases, that is, sequence systems composed of multi-functional, multi-combined bodies. Most ornamental grids had feature angles distributed in a range of $2-20^{\circ}$ that showed a common preference for low sloped diagonal lines or small curvature. Although the preference for certain feature angles were prominent, the feature angles that were used were generally distributed evenly among diverse feature angles to show the characteristics of separation. Therefore, Jeogori makers in the Joseon Dynasty period can be considered as having experimented with many proportion systems to show their aesthetics. In conclusion, based on the results of the examination of feature distributions and related methods to allocate ploidy features, O-type accounted for 66% and thus it was identified that the Jeogori was characterized by O-type. Therefore, it was identified that the characteristic of the Jeogori in the Joseon Dynasty period consisted of O-type fractal structures which are formative structures unique to our nation.

High Precision Character Recognition System using The Chaos Theory (카오스 이론을 이용한 고정도 문자 인식 시스템)

  • 손영우
    • Journal of Korea Multimedia Society
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    • v.4 no.6
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    • pp.518-523
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    • 2001
  • This paper proposes the new method which is adopted in extracting character features and recognizing characters using fractal dimension of the Chaos theory which highly recolonizes a minute difference with strange attractor created from Henon system. This paper implements a high precision character recognition system. firstly, it gets features of mesh, projection and cross distance feature from character images. And their feature is converted into data of time series. Then using modified Henon system suggested in this paper, each characters attractor about standard Korean Character, KSC 5601 is reconstructed. Secondly, in order to analyze the Chaotic degree of each characters attractor, it gets last features of character image after calculating box-counting Dimension, Natural Measure, Information Bit, Information Dimension which are meant fractal dimension. An experimental result shows 97.49% character classification rates for 2350 Korean characters using proposed method in this paper.

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A new approach for quantitative damage assessment of in-situ rock mass by acoustic emission

  • Kim, Jin-Seop;Kim, Geon-Young;Baik, Min-Hoon;Finsterle, Stefan;Cho, Gye-Chun
    • Geomechanics and Engineering
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    • v.18 no.1
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    • pp.11-20
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    • 2019
  • The purpose of this study was to propose a new approach for quantifying in situ rock mass damage, which would include a degree-of-damage and the degraded strength of a rock mass, along with its prediction based on real-time Acoustic Emission (AE) observations. The basic approach for quantifying in-situ rock mass damage is to derive the normalized value of measured AE energy with the maximum AE energy, called the degree-of-damage in this study. With regard to estimation of the AE energy, an AE crack source location algorithm of the Wigner-Ville Distribution combined with Biot's wave dispersion model, was applied for more reliable AE crack source localization in a rock mass. In situ AE wave attenuation was also taken into account for AE energy correction in accordance with the propagation distance of an AE wave. To infer the maximum AE energy, fractal theory was used for scale-independent AE energy estimation. In addition, the Weibull model was also applied to determine statistically the AE crack size under a jointed rock mass. Subsequently, the proposed methodology was calibrated using an in situ test carried out in the Underground Research Tunnel at the Korea Atomic Energy Research Institute. This was done under a condition of controlled incremental cyclic loading, which had been performed as part of a preceding study. It was found that the inferred degree-of-damage agreed quite well with the results from the in situ test. The methodology proposed in this study can be regarded as a reasonable approach for quantifying rock mass damage.

A Study of Nonlinear Structure in Visual Design (시각디자인에 있어서 비선형적 구조에 관한 연구)

  • 정원일
    • Archives of design research
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    • v.11 no.2
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    • pp.167-176
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    • 1998
  • The modern contains many problems that cannot be solved by the reductionism based on western natual science. Up until now, it has been formed determinism over the basis of empiricism or rationalism, this can be called a mechanical view of the world. In the field of natural science since 20C, however, raised the standard of revolt in traditional determinism, plural theory headed up. Consequently, in the name of post modernity, western reason became to deconstruct, further, new theory came to need. This new paradigm also affected design, and was studied to overcome the limitation of modern design.

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A Proposal of a Model for the Generation of Weathered Residual Soils (풍화잔류토의 생성모델의 제안)

  • Min Tuk-Ki;Lee Wan-Jin
    • Journal of the Korean Geotechnical Society
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    • v.20 no.9
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    • pp.47-56
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    • 2004
  • A new fragmentation model, called the GRS (the generation model of weathered residual soils) model, was proposed in this study, This model could identify the formation of a residual soil. This model is based on the phenomena that as the soil was weathered more highly, soil particles were smaller and pores were more expanded simultaneously. The possibility of fragmentation, $P_F,$ which was based on the fractal theory, was introduced in this model. There were some fundamental notions in the GRS model that soil particles were generated as the rock is fragmented, and the fragmentation of the rock was performed step by step. The $P_F,$ of the rock was not constant at each fragmentation steps. As a result of application on the GRS model, there were more residue where $P_{Fi}s$ were small at any particle size. There was a S-shape of PSD curve at the concave shape of $P_{Fi},$ and the PSD curve goes to a gaped graded curve at the convex shape of $P_{Fi}.$ The shape of PSD curve was concave in the case of small $P_{Fi}s.$ The value of $P_{Fi}$ increased with the coefficient of uniformity $(C_u)$ and the fragmentation fractal dimension $(D_r),$ but had no relation with the coefficient of gradation $(C_C)$.

Research On Technical Writing Educational Methods Based On Complex Learning Systems (학습복잡계 기반의 공학적 글쓰기 교수 방법 연구)

  • Kim, Hae-Kyung;Kim, Cha-Jong
    • Journal of the Korea Institute of Information and Communication Engineering
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    • v.14 no.7
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    • pp.1521-1528
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    • 2010
  • This paper examines technical writing and teaching methods based on the perspectives of the complex learning system theory. So, the paper first discusses the constituent elements and characteristics of the complex learning system theory and continues to examine the potential of applying the complex learning system theory to new teaching methods. As a result, not only did the research expand the approach methods of providing technical writing education but also confirmed the potential of actual implementation. Such results will provide a leeway to start applying new teaching methods for technical writing education. Furthermore, the paper proposes more detailed case studies related to this topic as well as development of this research to produce textbooks and other higher level researches.

Eddy Diffusion in Coastal Seas: Observation and Fractal Diffusion Modelling (연안역와동확산: 관측 및 프랙탈 확산 모델링)

  • 이문진;강용균
    • Journal of Korean Society of Coastal and Ocean Engineers
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    • v.9 no.3
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    • pp.115-124
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    • 1997
  • We measured the variance of eddy diffusion and associated ‘diffusion coefficients’ in coastal regions of Korea by observing the separation distances among multiple drifters deployed simultaneously at the same initial position. The variance of eddy diffusion was found to be proportional to $t^m$, where t is the time and m is a non-integer scaling exponent between 1.5 and 3.5. The observed scaling exponent of eddy diffusion cannot be reproduced by diffusion models employing constant eddy diffusivity. In this study, we applied fractal theory in simulating exponential increase of variance of eddy diffusion. We employed the fGn(fractional Gaussian noise) as a ‘modified’ random walks corresponding to the oceanic eddy diffusion. The variance of eddy diffusion, which corresponds to the fBm(fractional Brown motion) of our diffusion model, is proportional to $t^{2H}$, where H is Hurst scaling exponent. The temporal increase of the variance. with scaling exponent between 1 and 2, was successfully reproduced by our fractal diffusion model. However, our model cannot reproduce scaling exponent greater than 2. The scaling exponents greater than 2 are associated with the velocity shear of the mean flow.

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Predictive Study of Rubber Friction Considering Large Deformation Contact (대변형 접촉을 고려한 고무 마찰 예측 연구)

  • Nam, Seungkuk
    • Tribology and Lubricants
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    • v.34 no.1
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    • pp.1-8
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    • 2018
  • This paper presents the analysis of friction master curves for a sliding elastomer on rough granite. The hysteresis friction is calculated using an analytical model that considers the energy spent during the local deformation of the rubber due to surface asperities. The adhesion friction is also considered for dry friction prediction. The viscoelastic modulus of the rubber compound and the large-strain effective modulus are obtained from dynamic mechanical analysis (DMA). We accurately demonstrate the large strain of rubber that contacts with road substrate using the GW theory. We found that the rubber block deforms approximately to 40% strain. In addition, the viscoelastic master curve considering nonlinearity (at 40% strain) is derived based on the above finding. As viscoelasticity strongly depends on temperature, it can be assumed that the influence of velocity on friction is connected to the viscoelastic shift factors gained from DMA using the time-temperature superposition. In this study, we apply these shift factors to measure friction on dry granite over a velocity range for various temperatures. The measurements are compared to simulated hysteresis and adhesion friction using the Kluppel friction theory. Although friction results in the low-speed band match well with the simulation results, there are differences in the predicted and experimental results as the velocity increases. Thus, additional research is required for a more precise explanation of the viscoelastic material properties for better prediction of rubber friction characteristics.

Sliding Friction of Elastomer Composites in Contact with Rough Self-affine Surfaces: Theory and Application (자기-아핀 표면 특성을 고려한 유기탄성체 복합재료 마찰 이론 및 타이어 트레드/노면 마찰 응용)

  • Bumyong Yoon;Yoon Jin Chang;Baekhwan Kim;Jonghwan Suhr
    • Composites Research
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    • v.36 no.3
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    • pp.141-153
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    • 2023
  • This review paper presents an introduction of contact mechanics and rubber friction theory for sliding friction of elastomer composites in contact with rough surfaces. Particularly, Klüppel & Heinrich theory considers the self-affine (or fractal) characteristic for rough surfaces to predict adhesion and hysteresis frictions of elastomers based on the contact mechanics of Greenwood & Williamson. Due to dynamic excitation process of elastomer composites while sliding in contact with multiscale surface roughness (or asperity), viscoelastic properties in a wide frequency range becomes major contributor to friction behaviors. A brief description and examples are provided to construct a viscoelastic master curve considering nonlinear viscoelasticity of elastomer composites. Finally, application of rubber friction theory to tire tread compounds in traction with road surfaces is discussed with several experimental and theoretical results.