A Framework on Moment Model Reduction for Kinetic Equation

By a further investigation on the structure of the coefficient matrix of the globally hyperbolic regularized moment equations for Boltzmann equation in [Z. Cai, Y. Fan and R. Li, Comm. Math. Sci., 11 (2013), pp. 547-571], we propose a uniform framework to carry out model reduction to general kinetic equations, to achieve certain moment system. With this framework, the underlying reason why the globally hyperbolic regularization in [Z. Cai, Y. Fan and R. Li, Comm. Math. Sci., 11 (2013), pp. 547-571] works is revealed. The even fascinating point is, with only routine calculation, existing models are represented and brand new models are discovered. Even if the study is restricted in the scope of the classical Grad's 13-moment system, new model with global hyperbolicity can be deduced.Comment: 22 page

13-Moment System with Global Hyperbolicity for Quantum Gas

We point out that the quantum Grad's 13-moment system [R. Yano, Physica A: Statistical Mechanics and its Applications, 416:231-241, 2014] is lack of global hyperbolicity, and even worse, the thermodynamic equilibrium is not an interior point of the hyperbolicity region of the system. To remedy this problem, by fully considering Grad's expansion, we split the expansion into the equilibrium part and the non-equilibrium part, and propose a regularization for the system with the help of the new theory developed in [Z. Cai et al., SIAM J. Appl. Math., 75(5):2001-2023, 2015, Y. Fan, J. Stat. Phys., 161(4), 2015]. This provides us a new model which is hyperbolic for all admissible thermodynamic states, and meanwhile preserves the approximate accuracy of the original system. It should be noted that this procedure is not a trivial application of the theory in [Z. Cai et al., SIAM J. Appl. Math., 75(5):2001-2023, 2015, Y. Fan, J. Stat. Phys., 161(4), 2015].Comment: 23 pages and 12 figure

Time-Resolved Studies and Nanostructure Formation in Sb2Te3 Films Using Femtosecond Lasers.

Antimony telluride (Sb2Te3) is an important material with a wide range of applications in thermoelectrics, data storage devices and topological insulator research. Our work on femtosecond laser studies of Sb2Te3 films has significance for insights into femtosecond laser interaction with Sb2Te3 above the damage threshold, as well as providing a new pathway for novel fabrication of highly-ordered nanostructured Sb2Te3. These new developments are made possible by careful control of the laser scanning conditions, opening the way to future nanoscale studies and materials applications. The pump-probe scheme for the time-resolved studies employed a novel asynchronous optical sampling (ASOPS) technique, which has distinctive advantages over the traditional mechanical-delay scheme including superior stability of beam alignment during scans, faster data acquisition rates, and the ability to monitor a much wider range of dynamics up to ten nanoseconds. With ASOPS, it is shown that a sequence of connected processes can be studied in Sb2Te3 films, from coherent optical phonons and acoustic echoes at picosecond timescale, through thermal transport at nanosecond timescale. In particular, the coherent phonons were used, for the first time, to monitor the element segregation in Sb2Te3 films under high-fluence pump laser irradiation conditions. These results are important for the ultrafast spectroscopy research community: they highlight the need for careful interpretation of coherent phonon spectra in tellurides, which are susceptible to fs laser damage. Femtosecond laser irradiation of Sb2Te3 above ~6 mJ/cm2 was also found to produce highly-ordered nanotracks with a periodicity an order of magnitude below the laser wavelength. A variety of characterization techniques identified these nanotracks as single crystalline Sb2Te3 nanowires separated by polycrystalline phases including a large amount of the insulating Sb2O3. Laser irradiation in different gas environments revealed the sensitivity of the Sb2Te3 surface morphology to the surrounding gas species, especially O2, highlighting the critical role of the ambient environment interactions with Sb2Te3 for nanostructure formation in the thin films. These results provide valuable experimental input for the future analysis of the generation mechanism of these nanostructures. Additionally, the results open up new opportunities for fabrication of in-plane Sb2Te3 nanowires for planar applications.PhDPhysicsUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttps://deepblue.lib.umich.edu/bitstream/2027.42/108790/1/yuweili_1.pd

Model Reduction of Kinetic Equations by Operator Projection

By a further study of the mechanism of the hyperbolic regularization of the moment system for Boltzmann equation proposed in [Z. Cai, Y. Fan, R. Li, Comm. Math. Sci. 11(2): 547-571, 2013], we point out that the key point is treating the time and space derivative in the same way. Based on this understanding, a uniform framework to derive globally hyperbolic moment systems from kinetic equations using an operator projection method is proposed. The framework is so concise and clear that it can be treated as an algorithm with four inputs to derive hyperbolic moment system by routine calculations. Almost all existing globally hyperbolic moment system can be included in the framework, as well as some new moment system including globally hyperbolic regularized versions of Grad ordered moment system and a multidimensional extension of the quadrature-based moment system.Comment: 32 pages, 2 figure