• Title/Summary/Keyword: Self-Affine

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AFFINE TRANSFORMATION OF A NORMAL ELEMENT AND ITS APPLICATION

  • Kim, Kitae;Namgoong, Jeongil;Yie, Ikkwon
    • Korean Journal of Mathematics
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    • v.22 no.3
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    • pp.517-527
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    • 2014
  • In this paper, we study affine transformations of normal bases and give an explicit formulation of the multiplication table of an affine transformation of a normal basis. We then discuss constructions of self-dual normal bases using affine transformations of traces of a type I optimal normal basis and of a Gauss period normal basis.

A Study on the Holter Data Compression Algorithm -Using Piecewise Self-Affine Fractal Model- (Holter Data 압축 알고리즘에 관한 연구 -Piecewise Self-Affine Fractal Model을 이용한-)

  • 전영일;정형만
    • Journal of Biomedical Engineering Research
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    • v.16 no.1
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    • pp.17-24
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    • 1995
  • This paper presents a new compression method (or ECG data using iterated contractive transformations. The method represents any range of ECG signal by piecewise self-afrine fractal Interpolation (PSAFI). The piecewise self-afrine rractal model is used where a discrete data set is viewed as being composed of contractive arfine transformation of pieces of itself. This algorithm was evaluated using MIT/BIH arrhythmia database. PSAFI is found to yield a relatively low reconstruction error for a given compression ratio than conventional direct compression methods. The compression ratio achieved was 883.9 bits per second (bps) - an average percent rms difference (AFRD) of 5.39 percent -with the original 12b ECG samples digitized at 400 Hz.

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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.

Image Coding by Block Based Fractal Approximation (블록단위의 프래탈 근사화를 이용한 영상코딩)

  • 정현민;김영규;윤택현;강현철;이병래;박규태
    • Journal of the Korean Institute of Telematics and Electronics B
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    • v.31B no.2
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    • pp.45-55
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    • 1994
  • In this paper, a block based image approximation technique using the Self Affine System(SAS) from the fractal theory is suggested. Each block of an image is divided into 4 tiles and 4 affine mapping coefficients are found for each tile. To find the affine mapping cefficients that minimize the error between the affine transformed image block and the reconstructed image block, the matrix euation is solved by setting each partial differential coefficients to aero. And to ensure the convergence of coding block. 4 uniformly partitioned affine transformation is applied. Variable block size technique is employed in order to applynatural image reconstruction property of fractal image coding. Large blocks are used for encoding smooth backgrounds to yield high compression efficiency and texture and edge blocks are divided into smaller blocks to preserve the block detail. Affine mapping coefficinets are found for each block having 16$\times$16, 8$\times$8 or 4$\times$4 size. Each block is classified as shade, texture or edge. Average gray level is transmitted for shade bolcks, and coefficients are found for texture and edge blocks. Coefficients are quantized and only 16 bytes per block are transmitted. Using the proposed algorithm, the computational load increases linearly in proportion to image size. PSNR of 31.58dB is obtained as the result using 512$\times$512, 8 bits per pixel Lena image.

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A NUMERICAL STUDY ON CHARACTERISTICS OF FLUID FLOW AND SOLUTE TRANSPORT IN A SELF-AFFINE VARIABLE-APERTURE FRACTURE UNDER NORMAL COMPLIANCE EFFECT

  • JEONG WOOCHANG;HWANG MANHA;KO ICKHWAN;SONG JAIWOO
    • Water Engineering Research
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    • v.6 no.2
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    • pp.49-61
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    • 2005
  • This paper presents the numerical study to examine characteristics of fluid flow and solute transport in a rough fracture subject to effective normal stresses. The aperture distribution is generated by using the self-affine fractal model. In order to represent a nonlinear relationship between the supported normal stress and the fracture aperture, we combine a simple mechanical model with the local flow model. The solute transport is simulated using the random walk particle following algorithm. Results of numerical simulations show that the flow is significantly affected by the geometry of aperture distribution varying with the effective normal stress level while it is slightly affected by the fractal dimension that determines the degree of the fracture surface roughness. However, solute transport is influenced by the effective normal stress as well as the fracture surface roughness.

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A CPW-Fed Self-Affine Cross Shape Fractal Antenna (자기 아파인 프랙탈 구조를 이용한 CPW 급전 크로스 안테나)

  • Kim Tae-Hwan;Lee Jae-Wook;Cho Choon-Sik;Lee Yun-Hyun
    • The Journal of Korean Institute of Electromagnetic Engineering and Science
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    • v.16 no.9 s.100
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    • pp.949-956
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    • 2005
  • In this paper, a new CPW-fed cross shape fractal antenna having a self-affinity is presented. This novel configuration, which has anisotropic scaling symmetry, makes smaller profile characteristic compared to the fractal antenna using a self-similarity. Increase of the iteration coefficient, which leads to decrease of the fundamental resonant frequency, shows a good impedance matching condition and multi-band characteristics due to new surface current paths. The radiation patterns are similar to those of monopole antennas. In the K3 stage of iteration, the proposed antenna shows a measured maximum gain 2.27 dBi at 940 MHz. A commercially available software based on the FDTD algorithm has been used to obtain the predicted results. In addition, an RT/Duroid 5880 substrate has been employed for the experimental results.

On-line Learnign control of Nonlinear Systems Usig Local Affine Mapping-based Networks

  • Chio, Jin-Young;Kim, Dong-Sung
    • Journal of the Korean Institute of Intelligent Systems
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    • v.5 no.3
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    • pp.3-10
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    • 1995
  • This paper proposedan on-line learning controller which can be applied to nonlinear systems. The proposed on-line learning controller is based on the universal approximation by the local affine mapping-based neural networks. It has self-organizing and learning capability to adapt itself to the new environment arising from the variation of operating point of the nonlinear system. Since the learning controller retains the knowledge of trained dynamics, it can promptly adapt itself to situations similar to the previously experienced one. This prompt adaptability of the proposed control system is illustrated through simulations.

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Microcontacting behaviour of material with fractal rough surface (프랙탈 표면을 가진 공구와 재료의 마이크로 접촉거동해석)

  • Kim, Young-Suk;Hyun, Sang-Il
    • Proceedings of the Korean Society for Technology of Plasticity Conference
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    • 2009.10a
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    • pp.33-37
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    • 2009
  • Finite-element methods are used to study non-adhesive, frictionless rough contact of elastic and plastic solids. Roughness on spherical surfaces is realized by self-affine fractal. True contact area between the rough surfaces and flat rigid surfaces increases with power law under external normal loads. The power exponent is sensitive to surface roughness as well as the curvature of spherical geometry. Surface contact pressures are analyzed and compared for the elastic and plastic solids. Distributions of local contact pressure are shown dependent on the surface roughness and the yield stress of plastic solids.

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