2003
DOI: 10.1590/s0103-97332003000300030
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Anisotropy and percolation threshold in a multifractal support

Abstract: Recently a multifractal object, Q mf , was proposed to allow the study of percolation properties in a multifractal support. The area and the number of neighbors of the blocks of Q mf show a non-trivial behavior. The value of the probability of occupation at the percolation threshold, pc, is a function of ρ, a parameter of Q mf which is related to its anisotropy. We investigate the relation between pc and the average number of neighbors of the blocks as well as the anisotropy of Q mf . I IntroductionDue to the … Show more

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Cited by 12 publications
(9 citation statements)
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“…The theory of percolation threshold predicts that, in a medium of randomly distributed porosity, this threshold is met at ∼12% . However, if the organic matters present in the shales are in thin laminations, then the percolation threshold would be higher across lamination and lower in the direction perpendicular to it. Therefore, it suggests that even if the percolation threshold is below or above 12%, the alteration in shale wettability would also be dependent on the direction of organic matter laminations, with respect to the direction of the upward-moving CO 2 . Similarly, the presence and distribution of functional groups within shale surfaces have been observed to strongly influence the shale wettability behavior .…”
Section: Challenges and Perspectivesmentioning
confidence: 99%
“…The theory of percolation threshold predicts that, in a medium of randomly distributed porosity, this threshold is met at ∼12% . However, if the organic matters present in the shales are in thin laminations, then the percolation threshold would be higher across lamination and lower in the direction perpendicular to it. Therefore, it suggests that even if the percolation threshold is below or above 12%, the alteration in shale wettability would also be dependent on the direction of organic matter laminations, with respect to the direction of the upward-moving CO 2 . Similarly, the presence and distribution of functional groups within shale surfaces have been observed to strongly influence the shale wettability behavior .…”
Section: Challenges and Perspectivesmentioning
confidence: 99%
“…The Lucena network starts in the paper [17] that introduces a peculiar multifractal partition of the square, that means, the area lattice distribution of the blocks of the partition follows a multifractal distribution. A review of the properties of multifractal lattice is found in Ref.…”
Section: Introductionmentioning
confidence: 99%
“…In the reference [1,2] a deterministic multifractal tilling is developed to study percolation in multifractal systems. This object is a natural generalization of the square lattice in which it is possible to estimate analytically the full spectrum of fractal dimensions.…”
Section: -Introductionmentioning
confidence: 99%