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We present an analysis of acoustic-phonon propagation through long, free-standing, insulating wires with rough surfaces. Owing to a crossover from ballistic propagation of the lowest-frequency phonon mode at ω<ω₁=πc/W to a diffusive (or even localized) behavior upon the increase of phonon frequency, followed by reentrance into the quasiballistic regime, the heat conductance of a wire acquires an intermediate tendency to saturate within the temperature range T~ω₁/kB.
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Kambili et al. (1999) studied this question.
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