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Power Laws Variance Scaling of Boolean Random Varieties

Author

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  • Dominique Jeulin

    (PSL Research University, CMM-Centre de Morphologie Mathématique)

Abstract

Long fibers or stratified media show very long range correlations. These media can be simulated by models of Boolean random varieties and their iteration. They show non standard scaling laws with respect to the volume of domains K for the variance of the local volume fraction: on a large scale, the variance of the local volume fraction decreases according to power laws of the volume of K. The exponent γ is equal to n − k n $\frac {n-k}{n}$ for Boolean varieties with dimension k in the space ℝ n $ \mathbb {R}^{n}$ : γ = 2 3 $\gamma =\frac {2}{3}$ for Boolean fibers in 3D, and γ = 1 3 $\gamma =\frac {1}{3}$ for Boolean strata in 3D. When working in 2D, the scaling exponent of Boolean fibers is equal to 1 2 $\frac {1}{2}$ . From the results of numerical simulations, these scaling laws are expected to hold for the prediction of the effective properties of such random media.

Suggested Citation

  • Dominique Jeulin, 2016. "Power Laws Variance Scaling of Boolean Random Varieties," Methodology and Computing in Applied Probability, Springer, vol. 18(4), pages 1065-1079, December.
    • Handle: RePEc:spr:metcap:v:18:y:2016:i:4:d:10.1007_s11009-015-9464-5
    DOI: 10.1007/s11009-015-9464-5
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