Power Laws Variance Scaling of Boolean Random Varieties

Dominique Jeulin
2015 Methodology and Computing in Applied Probability  
Long ...bers or strati...ed 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 is equal to n k n for Boolean varieties with dimension k in the space R n : = 2 3 for
more » ... ...bers in 3D, and = 1 3 for Boolean strata in 3D. When working in 2D, the scaling exponent of Boolean ...bers is equal to 1 2 . From the results of numerical simulations, these scaling laws are expected to hold for the prediction of the e¤ective properties of such random media.
doi:10.1007/s11009-015-9464-5 fatcat:jyrasvpr2zfsthvtzw6yhla5jq