In recent years, there has been increasing interest in understanding thermal phenomena at the sub-micron scale. Applications have included the thermal performance of microelectronic devices, thermo-electric energy conversion, ultra-fast laser machining and many others. More recently, understanding sub-micron thermal transport has become important in the design of micro- and nano-electromechanical systems, both in terms of controlling thermal fluctuations, and in utilizing thermal gradients effectively. It is now accepted that Fourier's law for heat conduction is invalid at small length and time scales. The talk reviews alternative models for phonon transport, including the Boltzman transport equation and molecular dynamical models. The talk focuses on numerical techniques for the solution of the BTE, the development of phonon transport models which include phonon dispersion, and the application of these models to steady and unsteady sub-micron thermal transport.
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