TY - JOUR

T1 - Exact relations between critical exponents for elastic stiffness and electrical conductivity of two-dimensional percolating networks

AU - Bergman, David J.

PY - 2002

Y1 - 2002

N2 - It has long been known that the critical exponent T of the elastic stiffness [formula presented] of a d-dimensional percolating network [formula presented] measures the closeness of the network to its percolation threshold [formula presented] satisfies the following inequalities: [formula presented] where t is the critical exponent of the electrical conductivity [formula presented] of the same network and [formula presented] is the critical exponent of the percolation correlation length [formula presented] Similarly, the critical exponents that characterize the divergences [formula presented] [formula presented] of a rigid or normal and a superconducting or normal random mixture [formula presented] now measures the closeness of the rigid or superconducting constituent to its percolation threshold [formula presented] have long been known to satisfy [formula presented] We now show that, when [formula presented] T is in fact exactly equal to [formula presented] and S is exactly equal to s.

AB - It has long been known that the critical exponent T of the elastic stiffness [formula presented] of a d-dimensional percolating network [formula presented] measures the closeness of the network to its percolation threshold [formula presented] satisfies the following inequalities: [formula presented] where t is the critical exponent of the electrical conductivity [formula presented] of the same network and [formula presented] is the critical exponent of the percolation correlation length [formula presented] Similarly, the critical exponents that characterize the divergences [formula presented] [formula presented] of a rigid or normal and a superconducting or normal random mixture [formula presented] now measures the closeness of the rigid or superconducting constituent to its percolation threshold [formula presented] have long been known to satisfy [formula presented] We now show that, when [formula presented] T is in fact exactly equal to [formula presented] and S is exactly equal to s.

UR - http://www.scopus.com/inward/record.url?scp=45849154526&partnerID=8YFLogxK

U2 - 10.1103/PhysRevE.65.026124

DO - 10.1103/PhysRevE.65.026124

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AN - SCOPUS:45849154526

SN - 1063-651X

VL - 65

JO - Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics

JF - Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics

IS - 2

ER -