- About this Journal
- Abstracting and Indexing
- Aims and Scope
- Annual Issues
- Article Processing Charges
- Articles in Press
- Author Guidelines
- Bibliographic Information
- Citations to this Journal
- Contact Information
- Editorial Board
- Editorial Workflow
- Free eTOC Alerts
- Publication Ethics
- Reviewers Acknowledgment
- Submit a Manuscript
- Subscription Information
- Table of Contents
Mathematical Problems in Engineering
Volume 2012 (2012), Article ID 706326, 10 pages
Study of the Fractal and Multifractal Scaling Intervening in the Description of Fracture Experimental Data Reported by the Classical Work: Nature 308, 721–722(1984)
1Physics Faculty, University of Bucharest, P.O. Box MG-11, 077125 Bucharest, Romania
2Physics Department, University “Politehnica” of Bucharest, Splaiul Independenţei, 060042 Bucharest, Romania
Received 9 September 2011; Accepted 4 October 2011
Academic Editor: Cristian Toma
Copyright © 2012 Liliana Violeta Constantin and Dan Alexandru Iordache. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
- Santa Fe Institute for Studies in the Sciences of Complexity: (i) Bulletin, 2-3 issues/year, 1987-present, (ii) Lectures, 1989-present, (iii) Proceedings, 1986-present.
- R. Dobrescu and D. A. Iordache, Complexity Modeling, Politehnica Press, Bucharest, Romania, 2007.
- R. Dobrescu and D. A. Iordache, Complexity and Information, Romanian Academy Printing House, Bucharest, Romania, 2010.
- P. W. Anderson, “More is different,” Science, vol. 177, no. 4047, pp. 393–396, 1972.
- P. W. Anderson, “Physics: the opening to complexity,” Proceedings of the National Academy of Sciences of the United States of America, vol. 92, no. 15, pp. 6653–6654, 1995.
- K. G. Wilson, “Renormalization group and critical phenomena,” Physical Review B, vol. 4, no. 9, pp. 3174–3183, 1971.
- I. Prigogine and G. Nicolis, Self-Organization in Non-Equilibrium Systems: From Dissipative Structures to Order through Fluctuations, Wiley, New York, NY, USA, 1977.
- S. Solomon and E. Shir, “Complexity; a science at 30,” Europhysics News, vol. 34, no. 2, pp. 54–57, 2003.
- S. Solomon, “Evolving uniform and nonuniform cellular automata networks,” in Annual Reviews of Computational Physics, D. Stauffer , Ed., pp. 243–294, World Scientific, River Edge, NJ, USA, 1995.
- A. L. Barabási and R. Albert, “Emergence of scaling in random networks,” Science, vol. 286, no. 5439, pp. 509–512, 1999.
- R. Albert, H. Jeong, and A. L. Barabási, “Diameter of the world-wide web,” Nature, vol. 401, no. 6749, pp. 130–131, 1999.
- A. L. Barabási, “Complex networks: from the cell to human diseases,” in Proceedings of the International Workshop on Quantitative Biology, Bucharest, Romania, May 2007.
- K. Bhattacharya, G. Mukherjee, and S. S. Manna, “The international trade network,” in Econo-Physics of Markets and Business Networks, A. Chatterjee and B. K. Chakrabarti, Eds., New Economic Windows Series, p. 139, Springer, New York, NY, USA, 2008.
- S. Y. Chen, Wei Huang, and C. Cattani, “Traffic dynamics on complex networks: a survey,” Mathematical Problems in Engineering, vol. 2012, Article ID 732698, 23 pages, 2012.
- E. G. Backhoum and C. Toma, “Dynamical aspects of macroscopic andquantum transitions due to coherence function and time series events,” Mathematical Problems in Engineering, vol. 2010, Article ID 428903, 13 pages, 2010.
- E. G. Backhoum and C. Toma, “Specific mathematical aspects of dynamics generated by coherence functions,” Mathematical Problems in Engineering, vol. 2011, Article ID 436198, 10 pages, 2011.
- C. Cattani and P. Sterian, “Modelling the hyperboloid elastic shell,” Scientific Bulletin of University “Politehnica” of Bucharest, Series A, vol. 71, no. 4, pp. 37–44, 2009.
- A. A. Gukhman, Introduction to the Theory of Similarity, Academic Press, New York, NY, USA, 1965.
- G. I. Barenblatt, Dimensional Analysis, Gordon and Breach, New York, NY, USA, 1987.
- G. I. Barenblatt, Scaling, Self-Similarity and Intermediate Asymptotics, Cambridge Texts in Applied Mathematics, Cambridge University Press, Cambridge, UK, 1996.
- C. Shannon, “The mathematical theory of communication,” Bell System Technical Journal, vol. 27, no. 3, pp. 379–423, 1948.
- C. Shannon, “The mathematical theory of communication,” Bell System Technical Journal, vol. 27, no. 4, pp. 623–656, 1948.
- C. Shannon, “Prediction and entropy of printed English,” Bell System Technical Journal, vol. 30, no. 1, pp. 50–64, 1951.
- A. Carpinteri and B. Chiaia, “Multifractal nature of concrete fracture surfaces and size effects on nominal fracture energy,” Materials and Structures, vol. 28, no. 8, pp. 435–443, 1995.
- A. Carpinteri and B. Chiaia, “Multifractal scaling laws in the breaking behaviour of disordered materials,” Chaos, Solitons and Fractals, vol. 8, no. 2, pp. 135–150, 1997.
- D. A. Iordache, P. P. Delsanto, Şt. Puşcă, and V. Iordache, “Complexity, similitude, and fractals in physics,” in Proceedings of the 2nd International Symposium on “Interdisciplinary Applications of Fractal Analysis” (IAFA '05), vol. 3, pp. 7–12, Politehnica Press Publishing House, Bucharest, Romania, May 2005.
- P. P. Delsanto, D. A. Iordache, and Şt. Puşcă, “Study of the correlations between different effective fractal dimensions used for fracture parameters descriptions,” in Interdisciplinary Applications of Fractal and Chaos, R. Dobrescu and C. Vasilescu, Eds., pp. 136–153, Romanian Academy Printing House, Bucharest, Romania, 2004.
- P. P. Delsanto, A. S. Gliozzi, C. L. E. Bruno, N. Pugno, and A. Carpinteri, “Scaling laws and fractality in the framework of a phenomenological approach,” Chaos, Solitons and Fractals, vol. 41, no. 5, pp. 2782–2786, 2009.
- B. B. Mandelbrot, D. E. Passoja, and A. J. Paullay, “Fractal character of fracture surfaces of metals,” Nature, vol. 308, no. 5961, pp. 721–722, 1984.
- Y. Ma and T. G. Langdon, “Observations on the use of a fractal model to predict superplastic ductility,” Scripta Metallurgica et Materiala, vol. 28, no. 2, pp. 241–246, 1993.
- D. A. Iordache, Şt. Puşcă, G. Toma, V. Păun, A. Sterian, and C. Morarescu, “Analysis of compatibility with experimental data of Fractal descriptions of the fracture parameters,” Lecture Notes in Computer Science, vol. 3980, pp. 804–813, 2006.
- E. E. Underwood and K. Banerji, “Fractals in fractography,” Materials Science and Engineering, vol. 80, no. 1, pp. 1–14, 1986.
- C. S. Pande, L. E. Richards, N. Louat, B. D. Dempsey, and A. J. Schwoeble, “Fractal characterization of fractured surfaces,” Acta Metallurgica, vol. 35, no. 7, pp. 1633–1637, 1987.
- C. W. Lung and Z. Q. Mu, “Fractal dimension measured with perimeter-area relation and toughness of materials,” Physical Review B, vol. 38, no. 16, pp. 11781–11784, 1988.
- Z. H. Huang, J. F. Tian, and Z. G. Wang, “Study of the slit island analysis as a method for measuring fractal dimension of fractured surface,” Scripta Metallurgica et Materialia, vol. 24, no. 6, pp. 962–972, 1990.
- R. E. Williford, “Multifractal fracture,” Scripta Metallurgica, vol. 22, no. 11, pp. 1749–1754, 1988.
- Z.Q. Mu and C. W. Lung, “Studies on the fractal dimension and fracture toughness of steel,” Journal of Physics D, vol. 21, no. 5, p. 848, 1988.
- H. Su, Y. Zhang, and Z. Yan, Acta Metallurgica Sinica, vol. 3, p. 226, 1990.
- Şt. Puşcă, V. Solcan, and D. A. Iordache, “Procedure of extraction of numerical data from experimental plots. Application to the numerical analysis of some fractal studies,” in Proceedings of the 5th General Conference of the Balkan Physical Union, pp. 259–264, Vrnjacka Banja, Serbia, August 2003.
- J. F. Gouyet, Physique et Structures Fractales, Masson, Paris, France, 1992.
- D. L. Davidson, “Fracture surface roughness as a gauge of fracture toughness: aluminium-particulate SiC composites,” Journal of Materials Science, vol. 24, no. 2, pp. 681–687, 1989.
- K. Levenberg, “A method for the solution of certain problems in least squares,” Quarterly of Applied Mathematics, vol. 2, pp. 164–168, 1944.
- D. W. Marquardt, “An algorithm fot least-squares estimation of nonlinear parameters,” Journal of the Society for Industrial and Applied Mathematics, vol. 11, no. 2, pp. 431–441, 1963.
- E. Bodegom, D. W. McClure, P. P. Delsanto et al., Computational Physics Guide, Politehnica Press, Bucharest, Romania, 2009.
- W.T. Eadie, D. Drijard, F. E. James, M. Roos, and B. Sadoulet, Statistical Methods in Experimental Physics, North-Holland, Amsterdam, The Netherlands, 1982.
- W. Ledermann, Ed., Handbook of Applied Mathematics, vol. 6 of Statistics, John Wiley & Sons, New York, NY, USA, 1984.
- P. W. M. John, Statistical Methods in Engineering and Quality Assurance, John Wiley & Sons, New York, NY, USA, 1990.
- D. A. Iordache and V. Iordache, “Compatibility of multi-fractal and similitude descriptions of the fracture parameters relative to the experimental data for concrete specimens,” in Proceedings of the 1st South-East European Symposium on Interdisciplinary Approaches in Fractal Analysis, pp. 55–60, Bucharest, Romania, May 2003.
- A. Carpinteri and G. Ferro, “Scaling behaviour amd dual renormalization of experimental tensile softening responses,” Materials and Structures, vol. 31, no. 5, pp. 303–309, 1998.
- M. R. A. van Vliet, Size effects in tensile fracture of concrete and rock, Ph.D. thesis, University of Delft, 2000.