Fractal Function

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Alain Iost - One of the best experts on this subject based on the ideXlab platform.

  • Roughness signature of tribological contact calculated by a new method of peaks curvature radius estimation on Fractal surfaces
    Tribology International, 2013
    Co-Authors: Maxence Bigerelle, Denis Najjar, Alain Iost, Jean-marie Nianga, C. Hubert, K.j. Kubiak
    Abstract:

    This paper proposes a new method of roughness peaks curvature radii calculation and its application to tribological contact analysis as characteristic signature of tribological contact. This method is introduced via the classical approach of the calculation of radius of asperity. In fact, the proposed approach provides a generalization to Fractal profiles of the Nowicki's method [Nowicki. Wear Vol. 102, p. 161-176, 1985] by introducing a Fractal concept of curvature radii of surfaces, depending on the observation scale and also numerically depending on horizontal lines intercepted by the studied profile. It is then established the increasing of the dispersion of the measures of that lines with that of the corresponding radii and the dependence of calculated radii on the Fractal dimension of the studied curve. Consequently, the notion of peak is mathematically reformulated. The efficiency of the proposed method was tested via simulations of Fractal curves such as those described by Brownian motions. A new Fractal Function allowing the modelling of a large number of physical phenomena was also introduced, and one of the great applications developed in this paper consists in detecting the scale on which the measurement system introduces a smoothing artifact on the data measurement. New methodology is applied to analysis of tribological contact in metal forming process.

  • Multiscale Functional analysis of wear
    Wear, 2005
    Co-Authors: Maxence Bigerelle, Denis Najjar, Alain Iost
    Abstract:

    In this paper, we propose to create a Fractal Function defined by an infinite series to model worn surfaces obtained by a grinding process. In this series, each elementary term characterizes a wear process at a given scale. This series is only defined by two parameters: an amplitude parameter and the Fractal dimension. This model is tested on worn profiles obtained by using different grinding paper grades and roughness is assessed by tactile profilometry. Then an inverse method is developed to obtain simulated profiles that present the same morphology as the experimental ones. The results from this study prove that our method allows simulation of profiles with elementary Functions that characterize the wear process. © 2004 Elsevier B.V. All rights reserved.

  • Multiscale Functional analysis of wear: A Fractal model of the grinding process
    Wear, 2005
    Co-Authors: Maxence Bigerelle, Denis Najjar, Alain Iost
    Abstract:

    In this paper, we propose to create a Fractal Function defined by an infinite series to model worn surfaces obtained by a grinding process. In this series, each elementary term characterizes a wear process at a given scale. This series is only defined by two parameters: an amplitude parameter and the Fractal dimension. This model is tested on worn profiles obtained by using different grinding paper grades and roughness is assessed by tactile profilometry. Then an inverse method is developed to obtain simulated profiles that present the same morphology as the experimental ones. The results from this study prove that our method allows simulation of profiles with elementary Functions that characterize the wear process.

Maxence Bigerelle - One of the best experts on this subject based on the ideXlab platform.

  • Roughness signature of tribological contact calculated by a new method of peaks curvature radius estimation on Fractal surfaces
    Tribology International, 2013
    Co-Authors: Maxence Bigerelle, Denis Najjar, Alain Iost, Jean-marie Nianga, C. Hubert, K.j. Kubiak
    Abstract:

    This paper proposes a new method of roughness peaks curvature radii calculation and its application to tribological contact analysis as characteristic signature of tribological contact. This method is introduced via the classical approach of the calculation of radius of asperity. In fact, the proposed approach provides a generalization to Fractal profiles of the Nowicki's method [Nowicki. Wear Vol. 102, p. 161-176, 1985] by introducing a Fractal concept of curvature radii of surfaces, depending on the observation scale and also numerically depending on horizontal lines intercepted by the studied profile. It is then established the increasing of the dispersion of the measures of that lines with that of the corresponding radii and the dependence of calculated radii on the Fractal dimension of the studied curve. Consequently, the notion of peak is mathematically reformulated. The efficiency of the proposed method was tested via simulations of Fractal curves such as those described by Brownian motions. A new Fractal Function allowing the modelling of a large number of physical phenomena was also introduced, and one of the great applications developed in this paper consists in detecting the scale on which the measurement system introduces a smoothing artifact on the data measurement. New methodology is applied to analysis of tribological contact in metal forming process.

  • Multiscale Functional analysis of wear
    Wear, 2005
    Co-Authors: Maxence Bigerelle, Denis Najjar, Alain Iost
    Abstract:

    In this paper, we propose to create a Fractal Function defined by an infinite series to model worn surfaces obtained by a grinding process. In this series, each elementary term characterizes a wear process at a given scale. This series is only defined by two parameters: an amplitude parameter and the Fractal dimension. This model is tested on worn profiles obtained by using different grinding paper grades and roughness is assessed by tactile profilometry. Then an inverse method is developed to obtain simulated profiles that present the same morphology as the experimental ones. The results from this study prove that our method allows simulation of profiles with elementary Functions that characterize the wear process. © 2004 Elsevier B.V. All rights reserved.

  • Multiscale Functional analysis of wear: A Fractal model of the grinding process
    Wear, 2005
    Co-Authors: Maxence Bigerelle, Denis Najjar, Alain Iost
    Abstract:

    In this paper, we propose to create a Fractal Function defined by an infinite series to model worn surfaces obtained by a grinding process. In this series, each elementary term characterizes a wear process at a given scale. This series is only defined by two parameters: an amplitude parameter and the Fractal dimension. This model is tested on worn profiles obtained by using different grinding paper grades and roughness is assessed by tactile profilometry. Then an inverse method is developed to obtain simulated profiles that present the same morphology as the experimental ones. The results from this study prove that our method allows simulation of profiles with elementary Functions that characterize the wear process.

Hieu Trinh - One of the best experts on this subject based on the ideXlab platform.

Xavier Otazu - One of the best experts on this subject based on the ideXlab platform.

  • Image compression algorithm based on Hilbert Scanning of Embedded quadTrees: An introduction of the Hi-SET coder
    2011 IEEE International Conference on Multimedia and Expo, 2011
    Co-Authors: Jaime Moreno, Xavier Otazu
    Abstract:

    In this work we present an effective and computationally simple algorithm for image compression based on Hilbert Scanning of Embedded quadTrees (Hi-SET). It allows to represent an image as an embedded bitstream along a Fractal Function. Embedding is an important feature of modern image compression algorithms, in this way Salomon in [1, pg. 614] cite that another feature and perhaps a unique one is the fact of achieving the best quality for the number of bits input by the decoder at any point during the decoding. Hi-SET possesses also this latter feature. Furthermore, the coder is based on a quadtree partition strategy, that applied to image transformation structures such as discrete cosine or wavelet transform allows to obtain an energy clustering both in frequency and space. The coding algorithm is composed of three general steps, using just a list of significant pixels. The implementation of the proposed coder is developed for gray-scale and color image compression. Hi-SET compressed images are, on average, 6.20dB better than the ones obtained by other compression techniques based on the Hilbert scanning. Moreover, Hi-SET improves the image quality in 1.39dB and 1.00dB in gray-scale and color compression, respectively, when compared with JPEG2000 coder.

  • Image Coder Based on Hilbert Scanning of Embedded QuadTrees
    2011 Data Compression Conference, 2011
    Co-Authors: Jaime Moreno, Xavier Otazu
    Abstract:

    In this work we present an effective and computationally simple algorithm for image compression based on Hilbert Scanning of Embedded quadTrees (Hi-SET). It allows to represent an image as an embedded bitstream along a Fractal Function. Embedding is an important feature of modern image compression algorithms, in this way Salomon in [1, pg. 614] cite that another feature and perhaps a unique one is the fact of achieving the best quality for the number of bits input by the decoder at any point during the decoding. Hi-SET possesses also this latter feature. Furthermore, the coder is based on a quadtree partition strategy, that applied to image transformation structures such as discrete cosine or wavelet transform allows to obtain an energy clustering both in frequency and space. The coding algorithm is composed of three general steps, using just a list of significant pixels.

Y Zheng - One of the best experts on this subject based on the ideXlab platform.

  • An analytical model of thermal contact resistance based on the Weierstrass—Mandelbrot Fractal Function:
    Proceedings of the Institution of Mechanical Engineers Part C: Journal of Mechanical Engineering Science, 2020
    Co-Authors: S Jiang, Y Zheng
    Abstract:

    AbstractA Fractal model for analysing the thermal contact resistance (TCR) of rough surfaces is presented; it is based on the classical heat conduction theory and Fractal geometry for the surface topography description, elastic—plastic deformation of contacting asperities, and size-dependent constriction resistance. Relations for the TCR in terms of contact load are obtained for heat conductive surfaces with known material properties and surface topography. With the real contact area being approximately 1 per cent of the apparent contact area or less, the microcontact area distribution has a dominant influence on the TCR. Useful design guidelines for heat contacts are extracted from the numerical results. The analytical results agree well with previous experiments.

  • an analytical model of thermal contact resistance based on the weierstrass mandelbrot Fractal Function
    Proceedings of the Institution of Mechanical Engineers Part C: Journal of Mechanical Engineering Science, 2010
    Co-Authors: S Jiang, Y Zheng
    Abstract:

    AbstractA Fractal model for analysing the thermal contact resistance (TCR) of rough surfaces is presented; it is based on the classical heat conduction theory and Fractal geometry for the surface topography description, elastic—plastic deformation of contacting asperities, and size-dependent constriction resistance. Relations for the TCR in terms of contact load are obtained for heat conductive surfaces with known material properties and surface topography. With the real contact area being approximately 1 per cent of the apparent contact area or less, the microcontact area distribution has a dominant influence on the TCR. Useful design guidelines for heat contacts are extracted from the numerical results. The analytical results agree well with previous experiments.