Nonlinear laminates where the effective conductivity is integer valued

We condsider laminates with a power-law relation between the temperature gradient and the heat flux characterized by some constant r > 1. In particular, we discuss the problem of determining what positive integer combination of the local conductivities and the power -r = 1/(t-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.

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