Application of the wavelet transform to nanoscale thermal transport

Abstract

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.

Enhanced intervalley scattering in artificially stacked double-layer graphene

“…For clarity, L i and L * are redrawn in figure 6(d) as a function of charge carrier density. We found that L ϕ , L i and L * are in line with previous reports for SLG [14,15]. The value of L i (=150 ∼ 210 nm) of the SLG is much larger than that of the artificially stacked double-layer graphene.…”

“…However, a relatively low-cost and feasible approach is chemical vapor deposition (CVD) on metal (Cu, Ni) substrate for largescale growth of graphene [12]. Although a few experiments have been performed on CVDgrown or epitaxially grown graphene [13][14][15], the WL effect is a mesoscopic quantum transport phenomenon that is still a fascinating result from the phase coherence of charge carriers. The interference of electron waves that are scattered by disorder and form closed trajectories leads to an enhancement in resistivity, resulting in the localization of electrons [7][8][9][16][17][18][19].…”

Self-Interfering Wave Packets

“…Such an extension of the Fourier transform is common in signal processing but has found so far little echo to study the dynamics of wavepackets [39]. We show in Fig.…”

Predicting Phonon Properties From Equilibrium Molecular Dynamics Simulations

“…Such simulations allow for direct observations of transport and are discussed in Chapter [Shiomi]. In an unsteady simulation, spatial and temporal temperature variations may exist, allowing for observation of processes such as the propagation of a phonon wave packet [57,58].…”

“…As such, the creation of a phonon wave packet requires a fine resolution of the Brillouin zone. For example, in the non-equilibrium unsteady wave packet technique for studying how phonons interact with interfaces, simulation cells thousands of unit cells long are required to form sufficient localized wave packets [57,58].…”