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I was looking at an article where the author finds an example of a solotone effect in a heat transfer context of a 1D layered composite rod rather than the usual metal rod made out of one material (solotone effect being existence of oscillatory terms in the distribution of eigenvalues).

Is there any physical or otherwise helpful intuition behind why having a material discontinuity (ie. a discontinuous Sturm-Liouville problem) can change the eigenvalues from the usual $\lambda_n = \pi^2 n^2$ (ie. gap between the eigenvalues increases steadily) to an oscillating distribution?

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