We summarize our recent contributions to the development of macroscopic transport equations for rarefied gas flows. A combination of the ChapmanEnskog expansion and Grad’s moment method, termed as the order of magnitude method, yields the regularized 13 moment equations (R13 equations) which are of super-Burnett order. A complete set of boundary conditions is derived from the boundary condition...

How should we model evolution in spatially structured populations? Here, I review an evolutionary ecology approach based on the technique of spatial moment equations. I first provide a mathematical underpinning to the derivation of equations for the densities of various spatial configurations in network-based models. I then show how this spatial ecological framework can be coupled with an adapt...

This paper investigates the pth moment globally uniformly exponential stability of a class of impulsive stabilization of stochastic delay differential equations,and the pth moment exponential stability criteria is established by using theLyapunov–Razumikhin method. Keywords—Stochastic delay differential equations; Exponential stability ; Lyapunov-Razumikhin method ; Impulsive control

The one-dimensional stationary PSTF moment equations for radiative transfer in relativistically differentially moving media are examined. It is found that the equations can have two different types of critical points. In regions of strong velocity gradients, solutions might have pathological behavior around such critical points. The moment method may therefore yield unphysical solutions for the...

Partially Encased Composite (PEC) column is one of the recent achievements in the field of composite columns. This paper presents a combined experimental and theoretical study on the mechanical performances of six octagonal PEC columns subjected to axial compressive and bending moment loading. The major different between them was the concrete reinforcement details. The parameters studied in the...

We examine whether a causal interpretation can be given to the function identified by the conditional moment restriction (CMR). It is shown that in a general nonseparable triangular system the CMR does not identify the average structural function (ASF) nor any other structural object. This implies that the CMR identifies a causal relation only if the model is structurally separable in observabl...

In this paper, we are interested in the derivation of macroscopic equations from kinetic ones using a moment method in a relativistic framework. More precisely, we establish the general form of moments that are compatible with the Lorentz invariance and derive a hierarchy of relativistic moment systems from a Boltzmann kinetic equation. The proof is based on the representation theory of Lie alg...

Continuous-time birth-death Markov processes serve as useful models in population biology. When the birth-death rates are nonlinear, the time evolution of the first n order moments of the population is not closed, in the sense that it depends on moments of order higher than n. For analysis purpose, the time evolution of the first n order moments is often made to be closed by approximating these...

In this study, a first-order, nonstationary stochastic model of transient flow is developed which is applicable to the entire domain of a bounded vadose zone in the presence of sink/source. We derive general equations governing the statistical moments of the flow quantities by perturbation expansions. Owing to the mathematical complexity of the equations, in general we need to solve them numeri...