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The author develops a model treatment of the spectral distribution of phonons emitted by a metal heater film into an insulating substrate where the phonons encounter a strong frequency-dependent elastic scattering. The phonon distribution in both the film and the substrate does not reach a steady state and the spectral distortions are similar to those seen in recent experiments at high input power. The basic physical mechanism lies in the frequency-dependent transition from ballistic to diffusive flow for the phonons in the substrate.
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W. L. Schaich (1978) studied this question.
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