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Non-conservative character of the intersection of self-similar cascades

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  • Vergassola, M.
  • Vespignani, A.

Abstract

When a self-similar cascade is intersected, the resulting cascade process generating the intersection set is in general non-conservative, i.e. in the fragmentation process the related measure is not conserved. It is shown that the non-conservative character of a cascade invalidates the experimental analysis of the process. In particular it is possible to have self-similar cascades which do not show any fractal or multifractal behaviour when the box-counting analysis is performed. In the case of fractals the most relevant example is provided by processes having negative dimensions. With respect to multifractals, our results show that a strict interpretation of dissipation in a fully developed turbulent fluid as a result of a self-similar cascade is untenable.

Suggested Citation

  • Vergassola, M. & Vespignani, A., 1991. "Non-conservative character of the intersection of self-similar cascades," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 174(2), pages 425-437.
    • Handle: RePEc:eee:phsmap:v:174:y:1991:i:2:p:425-437
    DOI: 10.1016/0378-4371(91)90341-9
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    References listed on IDEAS

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    1. Pietronero, L. & Erzan, A. & Evertsz, C., 1988. "Theory of Laplacian fractals: Diffusion limited aggregation and dielectric breakdown model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 151(2), pages 207-245.
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