Application of the wavelet transform to nanoscale thermal transport

The continuous wavelet transform is employed to analyze the dynamics and time-dependent energy distribution of phonon wave-packet propagation and scattering in molecular dynamics simulations. The equations of the one-dimensional continuous wavelet transform are presented and then discretized for implementation. Practical aspects and limitations of the transform are discussed, with attention to its application in the analysis of molecular dynamics simulations. The transform is demonstrated using three examples that are relevant to nanoscale thermal transport. First, a system of wave packets that interfere in both the spatial and Fourier domains are separated by the wavelet transform, allowing the measurement of each packet's contribution to the system energy. Second, the wavelet transform is applied to a multiple wave-packet simulation of a silicon, heavy-silicon interface. The wavelet-based calculation of mode-dependent transmission is validated through comparison to literature results and theoretical predictions. Third, the dynamic scattering of a large amplitude wave packet is studied using the wavelet transform. The transform reveals a transition in the structure of the energy distribution. Unlike current techniques, the wavelet transform can be used to determine how the energy of a simulated system is distributed in time, in space, and among wave numbers, simultaneously. The ability to resolve phonon motion and energy from a vibrating ensemble of atoms in a molecular dynamics simulation makes the wavelet transform a promising technique for probing the physical mechanisms of nanoscale thermal transport.