The closure problem for the stellar hydrodynamic equations is studied by describing the family of phase space density functions, for which the collisionless Boltzmann equation is strictly equivalent to a finite subset of moment equations. It is proven that the redundancy of the higher-order moment equations and the recurrence of the velocity moments are of similar nature. The method is based on...

The double bracket dissipation approach is applied to the Vlasov kinetic equation. The Vlasov equation is then transformed by a Poisson map to moment dynamics, leading to a nonlocal form of Darcy’s law. Next, kinetic equations for particles with anisotropic interaction are considered and also cast into the double bracket dissipation form. The moment dynamics for these double bracket kinetic equ...

Context. Unlike gas-phase reactions, chemical reactions taking place on interstellar dust grain surfaces cannot always be modeled by rate equations. Due to the small grain sizes and low flux, these reactions may exhibit large fluctuations and thus require stochastic methods such as the moment equations. Aims. We evaluate the formation rates of H2, HD and D2 molecules on dust grain surfaces and ...

Uncertain delay differential equation is a type of differential equations driven by a canonical Liu process. This paper mainly focuses on the stability of uncertain delay differential equations. At first, the concept of stability in measure, stability in mean and stability in moment for uncertain delay differential equations will be presented. In addition, the sufficient condition for uncertain...