This paper is concerned with the Navier-Stokes limit of a class globally hyperbolic moment equations from Boltzmann equation. we show that can be formally derived for various different collision mechanisms. Furthermore, formal justified rigorously by using an energy method. It should noted are in non-conservative form and do not have convex entropy function, therefo...

Moment closures of gaskinetic theory offer a method for the prediction of non-equilibrium flows which have a wider range of validity than standard continuum methods, such as solution of the Navier-Stokes equations, and can be much more computationally efficient than particle-based techniques, such as Direct Simulation Monte Carlo (DSMC). Moment methods yield systems of first-order partial diffe...

We present detailed comparisons between high-resolution Monte Carlo simulation (MCS) and low-order numerical solutions of stochastic moment equations (SMEs) for the first and second statistical moments of pressure. The objective is to quantify the difference between the predictions obtained from MCS and SME. Natural formations with high permeability variability and large spatial correlation sca...

The joints between segmental rings can withstand a certain amount of bending moment as well as axial and shear forces. Generally, in the structural analysis of tunnel segmental lining, the joints can be modeled as elastic hinges or rotational springs, and their rigidity should be demonstrated in terms of the rigidity of the joints or their rotational stiffness. Therefore, the bending moment act...

Moment vector equations (MVEs) are presented for use in approximating and analyzing multi-dimensional non-linear discreteand continuous-time equations. A non-linear equation is expanded into simultaneous equations of generalized moments and then reduced to an MVE of a coefficient matrix and a moment vector. The MVE can be used to analyze the statistical properties, such as the mean, variance, c...

Exact moment equations for nonlinear Itô processes are derived. Taylor expansion of the drift and diffusion coefficients around the first conditional moment gives a hierarchy of coupled moment equations which can be closed by truncation or a Gaussian assumption. The state transition density is expanded into a Hermite orthogonal series with leading Gaussian term and the Fourier coefficients are ...

the present article focuses on the evaluation of a first-moment closure model applicable to film cooling flow and heat transfer computations. the present first-moment closure model consists of a higher level of turbulent heat flux modeling in which two additional transport equations for temperature variance kθ and its dissipation rate εθ are considered. it not only employs a time scale that is ...

Using moment equations we analyze collective flavor transformation of supernova neutrinos. We study the convergence of moment equations and find that numerical results using a few moment converge quite fast. We study effects of emission angle distribution of neutrinos on neutrino sphere. We study scaling law of the amplitude of neutrino self-interaction Hamiltonian and find that it depends on m...

Recently developed kinetic theory and related closures for neuronal network dynamics have been demonstrated to be a powerful theoretical framework for investigating coarse-grained dynamical properties of neuronal networks. The moment equations arising from the kinetic theory are a system of (1 + 1)-dimensional nonlinear partial differential equations (PDE) on a bounded domain with nonlinear bou...

3 Magnetic Dipole Moment, Gyromagnetic Ratio, Bohr Magneton, Landeg-Factor and Larmor Precession 8 3.1 Magnetic Dipole Moment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 3.2 Gyromagnetic Ratio, Bohr Magneton and Lande-g-Factor . . . . . . . . . . . 8 3.3 Larmor Velocity, Precession and Magnetic Resonances . . . . . . . . . . . . . 11 3.3.1 Quantum and Classical Pictures . . . . ...