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A variational approach to predict percolation thresholds of nanomaterials

Study on the properties of inhomogeneous media plays a central role throughout the history of physics, e.g.
Possion’s theory on magnetism of composites, Faraday’s dielectric model of composites, Maxwell’s and later
Rayleigh’s work on conductivity of composites, and Einstein’s thesis on viscosity of fluid-particle media. As
a special branch of this field, percolation research on phase transition and critical phenomena was originated
with lattice percolation theories in 1950s [1]. The idealization of a lattice structure is convenient for analytical

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