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Grad's moment models for Boltzmann equation were recently regularized to globally hyperbolic systems and thus the regularized models attain local well-posedness for Cauchy data. The hyperbolic regularization is only related to the convection term in Boltzmann equation. We in this paper studied the regularized models with the presentation of collision terms. It is proved that the regularized models are linearly stable at the local equilibrium and satisfy Yong's first stability condition with commonly used approximate collision terms, and particularly with Boltzmann's binary collision model.
We develop the dimension-reduced hyperbolic moment method for the Boltzmann equation, to improve solution efficiency using a numerical regularized moment method for problems with low-dimensional macroscopic variables and high-dimensional microscopic variables. In the present work, we deduce the globally hyperbolic moment equations for the dimension-reduced Boltzmann equation based on the Hermite expansion and a globally hyperbolic regularization. The numbers of Maxwell boundary condition required for well-posedness are studied. The numerical scheme is then developed and an improved projection algorithm between two different Hermite expansion spaces is developed. By solving several benchmark problems, we validate the method developed and demonstrate the significant efficiency improvement by dimension-reduction.
We have modified Sb2Te3 thin film thermoelectric materials by scanning a femtosecond laser across the film surface to create track-like nanostructures. These nanotracks have widths of 50-80 nm and a periodicity of ∼ 130 nm. We show that the nanotrack morphology is highly dependent on laser fluence and scan speed. Moreover, we performed transient thermoreflectance measurements on a laser-irradiated film and found a thermal conductivity reduction of 4.5% in the nanostructured regions compared to that of the unmodified regions. These results suggest the potential use of femtosecond pulsed lasers to create nanostructured thermoelectric materials with improved performance.
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