Nonlinear laminates where the effective conductivity is integer valued

We consider laminates with a power-law relation between the temperature gradient and the heat flux characterized by some constant τ>1τ>1. In particular, we discuss the problem of determining what positive integer combinations of the local conductivities and the power −r=1/(τ−1)−r=1/(τ−1) which make the effective conductivity integer valued. The problem is settled for the case when the number of layers, kk, equals 2. For k>2k>2 the problem is settled for the case r=−1r=−1, but for lower values, we can only identify certain classes of solutions.