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Multifractals in physics: Successes, dangers and challenges

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  • Aharony, Amnon

Abstract

The multifractal formalism for describing distributions of measures on sets which may be fractal is reviewed, with particular attention to random resistor networks, diffusion limited aggregates and mass fractals. The formalism has been very successful in describing crossover phenomena, but its use is somewhat dangerous due to problems with negative moments, with averaging procedures and with finite size effects.

Suggested Citation

  • Aharony, Amnon, 1990. "Multifractals in physics: Successes, dangers and challenges," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 168(1), pages 479-489.
    • Handle: RePEc:eee:phsmap:v:168:y:1990:i:1:p:479-489
    DOI: 10.1016/0378-4371(90)90400-M
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    References listed on IDEAS

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    1. Aharony, Joseph & Saunders, Anthony & Swary, Itzhak, 1988. "The effects of DIDMCA on bank stockholders' returns and risk," Journal of Banking & Finance, Elsevier, vol. 12(3), pages 317-331, September.
    2. Stanley, H.E. & Bunde, A. & Havlin, S. & Lee, J. & Roman, E. & Schwarzer, S., 1990. "Dynamic mechanisms of disorderly growth: Recent approaches to understanding diffusion limited aggregation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 168(1), pages 23-48.
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    1. Aharony, Amnon & Hinrichsen, Einar L. & Hansen, Alex & Feder, Jens & J∅ssang, Torstein & Hardy, H.H., 1991. "Effective renormalization group algorithm for transport in oil reservoirs," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 177(1), pages 260-266.
    2. Pastor-Satorras, R & Wagensberg, J, 1998. "The maximum entropy principle and the nature of fractals," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 251(3), pages 291-302.

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