Higher order moment equations for rarefied gas mixtures

A Hierarchy of Diffuse Higher-order Moment Equations for Semiconductors

A hierarchy of diffusive partial differential equations is derived by a moment method and a Chapman-Enskog expansion from the semiconductor Boltzmann equation assuming dominant collisions. The moment equations are closed by employing the entropy maximization principle of Levermore. The new hierarchy contains the well-known drift-diffusion model, the energy-transport equations, and the six-momen...

A Hierarchy of Diffusive Higher-Order Moment Equations for Semiconductors

A hierarchy of diffusive partial differential equations is derived by a moment method and a Chapman-Enskog expansion from the semiconductor Boltzmann equation assuming dominant collisions. The moment equations are closed by employing the entropy maximization principle of Levermore. The new hierarchy contains the well-known drift-diffusion model, the energy-transport equations, and the six-momen...

Moment characterization of higher-order risk preferences

Higher Order Bias Correcting Moment Equation for M-Estimation and Its Higher Order Efficiency

This paper studies an alternative bias correction for the M-estimator, which is obtained by correcting the moment equations in the spirit of Firth (1993). In particular, this paper compares the stochastic expansions of the analytically-bias-corrected estimator and the alternative estimator and finds that the third-order stochastic expansions of these two estimators are identical. This implies t...

Unified Solver for Rarefied and Continuum Flows in Multi- Component Gas Mixtures

A Unified Flow Solver (UFS) has been developed for simulations of rarefied, transitional and continuum flows based on direct numerical solution of the Boltzmann equation coupled to kinetic schemes of gas dynamics. The UFS uses dynamically adaptive mesh and automatic domain decomposition into kinetic and continuum domains based on continuum breakdown criteria. This paper describes UFS extensions...