Conductivity and magnetoresistance of a periodic composite by network discretization

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 percolation argument.