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...

We consider the variance of the reward until absorption in a Markov chain. This variance is usually calculated from the second moment (expectation of the square). We present a direct system of equations for the variance, involving the first moment (expectation) but not the second moment. This method is numerically superior to the calculation from the second moment.

A moment equations method was performed to study the Reversible chain Transfer Catalyzed Polymerization (RTCP) of styrene in 80°C. To do this, a kinetic scheme containing conventional free radical polymerization reactions and equilibrium reactions of RTCP was assumed. After obtaining mass balance equations, three moment equations were defined for free and dormant radicals and dead chains. M...

This paper concerns with numerical approximations of solutions of fully nonlinear second order partial differential equations (PDEs). A new notion of weak solutions, called moment solutions, is introduced for fully nonlinear second order PDEs. Unlike viscosity solutions, moment solutions are defined by a constructive method, called the vanishing moment method, and hence, they can be readily com...

Methods to derive macroscopic transport equations for rarefied gases from the Boltzmann equations are presented. Featured methods include the Chapman-Enskog expansion, Grad’s moment method, and the author’s order of magnitude method. The resulting macroscopic equations are compared and discussed by means of simple problems, including linear stability, shock wave structures, and Couette flow.

Kinetic equations containing terms for spatial transport, gravity, fluid drag and particleparticle collisions can be used to model dilute gas-particle flows. However, the enormity of independent variables makes direct numerical simulation of these equations almost impossible for practical problems. A viable alternative is to reformulate the problem in terms of moments of velocity distribution. ...

In kinetic treatments of hydrodynamics the macroscopic variables such as density and momentum are given by moments of distribution functions. In discrete kinetic theory it is possible to construct a complete set of moments whose evolution provides a complete description of the dynamics of the underlying kinetic equation. Moreover, the collision operator is most easily specified by its action up...