Induced Thermal Transport in the Toda Lattice Using Localized Passive Control

Thermal behavior at the nanoscale presents both formidable challenges and tremendous opportunities. Theoretical treatment at this scale differs fundamentally from macroscopic analysis, because thermal energy may take a variety of forms at the crystal lattice level, with distinctly different consequences for dissipation. These dynamical behaviors have the potential to greatly enhance control of heat transport and, for example, mitigate the effects of local heating. To a surprising degree, simple lattice models display many of the salient phenomena observed in epitaxial crystal layers. The Toda lattice is a completely integrable, anharmonic, discrete particle model, incorporating only nearest-neighbor interactions. In this paper, we employ the Toda lattice, originally developed as a model of thermal transport in crystals, to develop ideas for applying control theory to such systems. As a first result, we show that localized feedback of a small number of integrals of motion can be used to convert slow phonon modes, associated with limited heat transfer, into fast phonons modes, thereby reducing local heating. We present simulations to validate the approach