What question did this study set out to answer?

Extend percolation theory to electrical transport and evaluate conductance behavior in disordered resistor networks both near and far from the percolation threshold.

October 1, 1973Reviews of Modern Physics

Percolation and Conduction

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Authors

SKScott KirkpatrickHebrew University of Jerusalem

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Implication

Numerical modeling demonstrates dimension-dependent conductance in random resistor networks, indicating that effective medium theory accurately models transport away from percolation thresholds.

Key Points

Extend percolation theory to electrical transport and evaluate conductance behavior in disordered resistor networks both near and far from the percolation threshold.
Modeled bond percolation by randomly removing resistors from families of two-dimensional and three-dimensional lattice resistor networks to compute normalized conductance.
Developed a Green's function derivation of effective medium theory analogous to methods used for disordered alloys to test its quantitative accuracy against network simulations.
Derived a theoretical expression mapping network conductance to the spin-stiffness coefficient of a model dilute ferromagnet.
Demonstrated that normalized network conductance has a sharply defined concentration dependence near the percolation threshold that is sensitive primarily to spatial dimensionality.
Observed that effective medium theory accurately predicts the conductance of bond percolation networks across most concentrations, failing only in the immediate vicinity of the threshold.
Established that conducting percolation channels carrying electric current above the threshold behave as three-dimensional structures based on correspondence to dilute ferromagnets.

Cite This Study

Scott Kirkpatrick (1973) studied this question.

synapsesocial.com/papers/69d8752ed2f7327e70ae3364 https://doi.org/10.1103/revmodphys.45.574

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October 1, 1973Reviews of Modern Physics

Percolation and Conduction

View Full Paper

Ask AI

Bookmark

Authors

SKScott KirkpatrickHebrew University of Jerusalem

Discussion

Member takes

Implication

Numerical modeling demonstrates dimension-dependent conductance in random resistor networks, indicating that effective medium theory accurately models transport away from percolation thresholds.

Key Points

Extend percolation theory to electrical transport and evaluate conductance behavior in disordered resistor networks both near and far from the percolation threshold.
Modeled bond percolation by randomly removing resistors from families of two-dimensional and three-dimensional lattice resistor networks to compute normalized conductance.
Developed a Green's function derivation of effective medium theory analogous to methods used for disordered alloys to test its quantitative accuracy against network simulations.
Derived a theoretical expression mapping network conductance to the spin-stiffness coefficient of a model dilute ferromagnet.
Demonstrated that normalized network conductance has a sharply defined concentration dependence near the percolation threshold that is sensitive primarily to spatial dimensionality.
Observed that effective medium theory accurately predicts the conductance of bond percolation networks across most concentrations, failing only in the immediate vicinity of the threshold.
Established that conducting percolation channels carrying electric current above the threshold behave as three-dimensional structures based on correspondence to dilute ferromagnets.

Cite This Study

Scott Kirkpatrick (1973) studied this question.

synapsesocial.com/papers/69d8752ed2f7327e70ae3364 https://doi.org/10.1103/revmodphys.45.574

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