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Fractals and multifractals: Applications in physics

Author

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  • Coniglio, A.
  • De Arcangelis, L.
  • Herrmann, H.J.

Abstract

Critical fluctuations, growth or disorder can produce fractal structures which have unusual physical properties due to their scale invariance. Particularly interesting are the so called multifractals measures that can exist on these fractals. We will introduce the concept of multifractals and the most common way to formalize them via the function f(α). We will present three situations in which multifractality appears: percolation, growth phenomena and fracture.

Suggested Citation

  • Coniglio, A. & De Arcangelis, L. & Herrmann, H.J., 1989. "Fractals and multifractals: Applications in physics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 157(1), pages 21-30.
    • Handle: RePEc:eee:phsmap:v:157:y:1989:i:1:p:21-30
    DOI: 10.1016/0378-4371(89)90272-0
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    Cited by:

    1. Englman, R. & Jaeger, Z., 1990. "Fracture in concrete due to percolating cracks and pores," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 168(1), pages 655-671.
    2. Moukarzel, C., 1992. "Laplacian growth on a random lattice," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 190(1), pages 13-23.
    3. Charutha, S. & Gopal Krishna, M. & Manimaran, P., 2020. "Multifractal analysis of Indian public sector enterprises," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 557(C).
    4. Caracciolo, Sergio, 1992. "Replica symmetry breaking and Monte Carlo simulations for spin glasses," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 185(1), pages 261-270.
    5. Herrmann, H.J. & Kertész, J., 1991. "Stability analysis of crack propagation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 178(2), pages 227-235.

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