Mean Square Energy Research Articles

Superballistic characteristics in transient phonon ballistic-diffusive transport

While diffusive, superdiffusive, and ballistic phonon transports have been widely investigated, the superballistic phenomenon, where the time index of the energy mean square displacement with respect to time is greater than 2, has been neither predicted nor observed. In this work, we report on the superballistic characteristics obtained from simulations of transient phonon ballistic-diffusive transport both during and after the input of a heat pulse into a nanoscale film. The superballistic behaviors are well described by a previously proposed model for electron wave packet spreading employing a point source and further explained by the superposition effect of heat pulses. The relative superposition time, a dimensionless parameter, is defined to describe the degree of the heat pulse superposition. The analysis of superballistic characteristics in this work is expected to guide experiments for detecting the phonon superballistic transport. Also, it provides a potential phenomenological description for the superballistic phenomena in more complex systems.

Improving Mesoscale Altimetric Data From a Multitracer Convolutional Processing of Standard Satellite-Derived Products

Multisatellite measurements of altimeter-derived sea surface height (SSH) have provided a wealth of information on the ocean. Yet, horizontal scales below 100 km remain scarcely resolved. Especially, in the Mediterranean Sea, an important fraction of the mesoscale range, characterized by a small Rossby radius of deformation of 15–20 km, is not properly retrieved by altimeter-derived gridded products. Here, we investigate a novel processing of AVISO products with a view to resolving the horizontal scales sensed by current along-track altimeter data. The key feature of our framework is the use of linear convolutional operators to model the fine-scale SSH detail as a function of different sea surface fields, especially optimally interpolated SSH and sea surface temperature (SST). The proposed model embeds the surface quasi-geostrophic SST–SSH synergy as a special case. Using an observing system simulation experiment with simulated SSH data from model outputs in the Western Mediterranean Sea, we show that the proposed approach has the potential for improving current optimal interpolations of gridded altimeter-derived SSH fields by more than 20% in terms of relative SSH and kinetic energy mean square error, as well as in terms of spectral signatures for horizontal scales ranging from 30 to 100 km. Our results also suggest that SST–SSH relationship may only play a secondary role compared with the interscale SSH cascade. We further discuss the relevance of the proposed approach in the context of future altimetric satellite missions.

Thermal wave propagation through nanofilms in ballistic-diffusive regime by Monte Carlo simulations

Investigations on ultrafast heat conduction are of great importance not only for the theoretical understanding of thermal transport, but also the applications of ultra-short pulse laser including the micromachining and the measurements of thermophysical properties of micro/nanomaterials where phonons propagate in ballistic-diffusive regime. In this work, the thermal wave in phonon ballistic-diffusive regime is systematically studied by the Monte Carlo (MC) simulation method. Simulation results show significant influence of the phonon boundary emission conditions, i.e. boundary conditions of phonon Boltzmann transport equation (BTE), on the thermal wave propagation. The MC simulations with phonon Lambert emission (LE) predict a dispersive dissipative thermal wave while the MC simulations with directional emission (DE) predict a non-dispersive dissipative thermal wave. Temperature peak in the MC simulations with LE damps more rapidly than that in DE cases, and heat flux in MC simulations with DE damps exponentially while that in with LE does not. Dispersion relations and wave vector spectrums of thermal waves are determined by the phonon boundary emission, proven by theoretical analyses based on the phonon BTE. The indexes of energy mean square displacement (MSD) relation with respect to time are larger than 1 but less than 2 and decrease as time increases, showing that phonons propagate in ballistic-diffusive regime and evolve from ballistic to diffusive. Effects of the reflection boundary on thermal wave propagation are also investigated and it is found that the temperature overshooting phenomena, due to the wave propagation of heat, is significantly influenced by the properties of both emission and reflection boundaries.

Thermal boundary resistance from mode energy relaxation times: Case study of argon-like crystals by molecular dynamics

We derive the mode spectrum of the thermal boundary resistance between two bodies having a temperature difference ΔT. A general expression of the time τ that defines the resistance is derived as the equilibrium autocorrelation of ΔT integrated over time. A further decomposition of this autocorrelation yields the resistance spectrum as equal to the mode relaxation time weighted by its energy mean square fluctuation. We then perform molecular dynamics simulations of argon like crystals in equilibrium and nonequilibrium regimes to prove the relevance of our model. This general method allows for deriving the resistance spectrum and therefore can yield key rules to control the exchanged heat flux.

Approximate harmonic models for roundness profiles with equivalent energy mean square values

A mathematical formula for the method of equivalent energy mean square values is presented. A method of deriving the approximate model of the roundness profile is given based on a single harmonic or on the harmonics of an odd order plus an even order. This method may be used in practice to minimize roundness error.