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 > 1 . In particular, we discuss the problem of determining what positive integer combinations of the local conductivities and the power − r = 1 / ( τ − 1 ) which make the effective conductivity integer valued. The problem is settled for the case when the number of layers, k , equals 2. For k > 2 the problem is settled for the case r = − 1 , but for lower values, we can only identify certain classes of solutions.