We derive a series of moment equations describing the motion and flavor transformation of neutrinos in supernova. We find a particular series of moments of neutrino density matrix in supernova. The emission angle distribution of neutrinos is described by this series of moments. We expand the equation of neutrinos using these moments and obtain moment equations. We find that these moments have v...

The challenge of modeling low-speed rarefied gas flow in the transition regime is well known. In this paper, we propose a numerical solution procedure for the regularized 13 moment equations within a finite-volume framework. The stress and heat flux equations arising in the method of moments are transformed into the governing equations for the stress and heat flux deviators based on their first...

In the stochastic formulation of chemical kinetics, the stationary moments of the population count of species can be described via a set of linear equations. However, except for some specific cases such as systems with linear reaction propensities, the moment equations are underdetermined as a lower order moment might depend upon a higher order moment. Here, we propose a method to find lower, a...

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...

We provide methods of computing multivalued solutions to the Euler-Poisson system and test them in the context of a klystron amplifier. An Eulerian formulation capable of computing multivalued solutions is derived from a kinetic description of the Euler-Poisson system and a moment closure. The system of the moment equations may be closed due to the special structure of the solution in phase spa...

In this paper, we investigate almost-sure and moment stabilization of continuous time jump linear systems with a finite-state Markov jump form process. We first clarify the concepts of -moment stabilizability, exponential -moment stabilizability, and stochastic -moment stabilizability. We then present results on the relationships among these concepts. Coupled Riccati equations that provide nece...

In this paper, we apply projective integration methods to hyperbolic moment models of the Boltzmann equation and BGK equation, investigate numerical properties resulting scheme. Projective is an explicit scheme that tailored problems with large spectral gaps between slow (one or many) fast eigenvalue clusters model. The analysis a linearized model clearly shows reveals multi-scale nature for wh...