Scaling of cluster mass between two lines in 3d percolation

Luciano R. Da Silva; Gerald Paul; Shlomo Havlin; Don R. Baker; H. Eugene Stanley

doi:10.1016/S0378-4371(02)01387-0

Scaling of cluster mass between two lines in 3d percolation

Luciano R. Da Silva, Gerald Paul, Shlomo Havlin, Don R. Baker, H. Eugene Stanley

Department of Physics

Research output: Contribution to journal › Article › peer-review

4 Scopus citations

Abstract

We consider the cluster mass distribution between two lines of arbitrary orientations and lengths in porous media in three dimensions, and model the porous media by bond percolation at the percolation threshold p_c. We observe that for many geometrical configurations the mass probability distribution presents power law behavior. We determine how the characteristic mass of the distribution scales with such geometrical parameters as the line length, w, the minimal distance between lines, r, and the angle between the lines, θ. The fractal dimensions of the cluster mass are independent of w,r, and θ. The slope of the power-law regime of the cluster mass is unaffected by changes in these three variables; however the characteristic mass of the cluster depends upon θ. We propose new scaling functions that reproduce the θ dependence of the characteristic mass found in the simulations.

Original language	English
Pages (from-to)	307-318
Number of pages	12
Journal	Physica A: Statistical Mechanics and its Applications
Volume	318
Issue number	3-4
DOIs	https://doi.org/10.1016/S0378-4371(02)01387-0
State	Published - 15 Feb 2003

Bibliographical note

Funding Information:
We thank L. Braunstein, S.V. Buldyrev, Andre Moreira for helpful discussions, and British Petroleum, CTPETRO/Cenpes/Petrobras, CPNq, the National Science Foundation and NSERC for support.

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title = "Scaling of cluster mass between two lines in 3d percolation",

abstract = "We consider the cluster mass distribution between two lines of arbitrary orientations and lengths in porous media in three dimensions, and model the porous media by bond percolation at the percolation threshold pc. We observe that for many geometrical configurations the mass probability distribution presents power law behavior. We determine how the characteristic mass of the distribution scales with such geometrical parameters as the line length, w, the minimal distance between lines, r, and the angle between the lines, θ. The fractal dimensions of the cluster mass are independent of w,r, and θ. The slope of the power-law regime of the cluster mass is unaffected by changes in these three variables; however the characteristic mass of the cluster depends upon θ. We propose new scaling functions that reproduce the θ dependence of the characteristic mass found in the simulations.",

author = "{Da Silva}, {Luciano R.} and Gerald Paul and Shlomo Havlin and Baker, {Don R.} and Stanley, {H. Eugene}",

note = "Funding Information: We thank L. Braunstein, S.V. Buldyrev, Andre Moreira for helpful discussions, and British Petroleum, CTPETRO/Cenpes/Petrobras, CPNq, the National Science Foundation and NSERC for support.",

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T1 - Scaling of cluster mass between two lines in 3d percolation

AU - Da Silva, Luciano R.

AU - Paul, Gerald

AU - Havlin, Shlomo

AU - Baker, Don R.

AU - Stanley, H. Eugene

N1 - Funding Information: We thank L. Braunstein, S.V. Buldyrev, Andre Moreira for helpful discussions, and British Petroleum, CTPETRO/Cenpes/Petrobras, CPNq, the National Science Foundation and NSERC for support.

PY - 2003/2/15

Y1 - 2003/2/15

N2 - We consider the cluster mass distribution between two lines of arbitrary orientations and lengths in porous media in three dimensions, and model the porous media by bond percolation at the percolation threshold pc. We observe that for many geometrical configurations the mass probability distribution presents power law behavior. We determine how the characteristic mass of the distribution scales with such geometrical parameters as the line length, w, the minimal distance between lines, r, and the angle between the lines, θ. The fractal dimensions of the cluster mass are independent of w,r, and θ. The slope of the power-law regime of the cluster mass is unaffected by changes in these three variables; however the characteristic mass of the cluster depends upon θ. We propose new scaling functions that reproduce the θ dependence of the characteristic mass found in the simulations.

AB - We consider the cluster mass distribution between two lines of arbitrary orientations and lengths in porous media in three dimensions, and model the porous media by bond percolation at the percolation threshold pc. We observe that for many geometrical configurations the mass probability distribution presents power law behavior. We determine how the characteristic mass of the distribution scales with such geometrical parameters as the line length, w, the minimal distance between lines, r, and the angle between the lines, θ. The fractal dimensions of the cluster mass are independent of w,r, and θ. The slope of the power-law regime of the cluster mass is unaffected by changes in these three variables; however the characteristic mass of the cluster depends upon θ. We propose new scaling functions that reproduce the θ dependence of the characteristic mass found in the simulations.

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Scaling of cluster mass between two lines in 3d percolation

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