Magnetoresistance of normal conductor/insulator/perfect conductor composites with a columnar microstructure

The in-plane magnetoresistance of columnar composites is studied for a class of three-constituent mixtures of normal conductor, perfect insulator, and perfect conductor, where the magnetic field B is applied in the plane perpendicular to the columnar axis. Exact relations are found between the bulk effective resistivity tensor ρ̂_e of such a medium and that of a medium where the perfect insulator and perfect conductor have exchanged their spatial locations. Exact expressions are found in some cases for the leading order large B behavior of ρ̂_e for periodic microstructures and certain directions and ranges of directions of B. Numerical calculations are used to compute ρ̂_e in those microstructures for all directions of B, and for various magnitudes of B. The different results are compared and their significance is discussed.