Interference of current distortion patterns and magnetoresistance anisotropy in a composite with periodic microstructure

A detailed theoretical and numerical study is presented of the anisotropic magnetotransport which was recently predicted to occur in composite conductors with a periodic microstructure. Contour plots and three-dimensional graphs of the local dissipation rate around an isolated obstacle and around a periodic array of obstacles, as well as vector plots of the distorted current pattern, are produced and used to discuss the details of the anisotropic magnetoresistance. The problem of an isolated spherical or cylindrical inclusion in a homogeneous host has a closed form solution. This is exploited in order to give a perturbation treatment of the problem of multiple inclusions. A good qualitative understanding of many features of the anisotropy can be achieved by considering the interference between the current distortion patterns produced by just two obstacles of either spherical or cylindrical shape. As a result of these discussions, we have now achieved a more complete understanding of how the anisotropic magnetotransport arises in a periodic composite conductor.