On the low-temperature lattice thermal transport in nanowires
  We propose a theory of low temperature thermal transport in nano-wires in the regime where a competition between phonon and flexural modes governs the relaxation processes. Starting with the standard kinetic equations for two different types of quasiparticles we derive a general expression for the coefficient of thermal conductivity. The underlying physics of thermal conductance is completely determined by the corresponding relaxation times, which can be calculated directly for any dispersion of quasiparticles depending on the size of a system. We show that if the considered relaxation mechanism is dominant, then at small wire diameters the temperature dependence of thermal conductivity experiences a crossover from $T^{1/2}$ to $T^3$-dependence. Quantitative analysis shows reasonable agreement with resent experimental results. 
Alexander V. Zhukov, Shilong Yang, and Jianshu Cao