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Conductivity and Magnetoresistance of a Periodic Composite by
Network Discretization

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K. D. Fisher and D. Stroud,
Department of Physics, The Ohio State University, Columbus,
Ohio 43210

We describe a simple approach for calculating the effective
conductivity, dielectric constant, and magnetoresistance of periodic
composites, by reducing the composite to an effective impedance
network. The method is used to calculate the effective conductance of
periodic two-dimensional binary composites on a square lattice, in
good agreement with previous calculations using other methods. We use
the same approach to calculate the magnetoresistivity of a periodic
composite of parallel perfectly conducting cylinders arranged on a
square lattice in a magnetic field perpendicular to the cylinders. We
find a striking anisotropy, depending on the angle between the
magnetic field and an axis of the square lattice. The anisotropy is
explained by means of a novel percolation argument.
PACS Nos: 72.80.Tm, 72.15.Gd,73.61.-r,74.76.Db