CONDUCTIVITY AND MAGNETORESISTANCE OF A PERIODIC COMPOSITE BY NETWORKDISCRETIZATION

We describe a simple approach for calculating the effective conductivi ty, dielectric constant, and magnetoresistance of periodic composites, by reducing the composite to an effective impedance network. The meth od is used to calculate the effective conductance of periodic two-dime nsional 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 magne tic field perpendicular to the cylinders. We find a striking anisotrop y, depending on the angle between the magnetic field and an axis of th e square lattice. The anisotropy is explained by means of a percolatio n argument.