What question did this study set out to answer?

Determine and compare the critical exponents for electrical conductivity, elasticity, and permeability near the percolation threshold in continuum versus discrete lattice systems.

June 3, 1985Physical Review Letters

Differences between Lattice and Continuum Percolation Transport Exponents

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Determine and compare the critical exponents for electrical conductivity, elasticity, and permeability near the percolation threshold in continuum versus discrete lattice systems.
Conducted a scaling analysis on disordered continuum systems modeled as 'Swiss-cheese' geometries.
Calculated critical transport exponents in spaces between randomly distributed spherical voids near the percolation threshold.
Critical exponents for electrical conductivity, elastic constants, and fluid permeability are significantly larger in continuum models than in discrete lattice networks.
Two-dimensional electrical conductivity is the only tested scenario where continuum and discrete lattice critical exponents are equal.

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Implication

Scaling analysis reveals larger transport exponents in continuum percolation systems, suggesting distinct critical behavior from discrete lattice networks.

Cite This Study

Halperin et al. (1985) studied this question.

synapsesocial.com/papers/69ff76e22ff633f365778ae8 https://doi.org/10.1103/physrevlett.54.2391

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Implication

Scaling analysis reveals larger transport exponents in continuum percolation systems, suggesting distinct critical behavior from discrete lattice networks.

Differences between Lattice and Continuum Percolation Transport Exponents

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Discussion

Implication

Cite This Study

Differences between Lattice and Continuum Percolation Transport Exponents

Key Points

Discussion

Implication

Cite This Study

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