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...

concrete beams reinforced with glass fiber reinforced polymer (gfrp) bars exhibit large deflections and crack widths as compared with steel reinforced concrete beams due to the low modulus of elasticity of gfrp bars. different studies show that aci 318 equation for the effective moment of inertia ie does not predict deflection well for frp reinforced concrete beams. the purpose of this paper is...

The goal of this research is developing a unified numerical method for simulating continuum and transitional flow. To achieve our ultimate goal, first, hyperbolic-relaxation equations are introduced, then a new discretization method is developed. The method is based on Huynh’s upwind moment scheme, with implicit treatment of the source term. Our previous linear method is generalized to 1-D nonl...

A wide range of econometric and statistical models are specified through moment conditions. Efficient estimation of such models essentially employs two distinct ideas: optimally combining estimation equations (e.g., the optimal estimating equations of Godambe (1976), the generalized method of moments of Hansen (1982) and the empirical likelihood of Qin and Lawless (1994)), and optimally combini...

A linear kinetic equation for heat transfer is solved by means of the method of moments. The moment equations are solved with Maxwelltype boundary conditions for steady state energy transport. The results exhibit marked Knudsen boundary layers. The accuracy of the description is examined, and it is shown that already a relatively small number of moments can give satisfactory resolution of Knuds...

The \closure problem" is a well known and widely discussed problem in transport theory. From the full transport equation one can derive a (innnite) sequence of hyperbolic subsystems for the moments. The question arises how to close the system for the rst n moments. In case of Boltzmann equations it can be answered in the theory of extended thermodynamics. Here we consider transport equations wh...

In this paper, the continuous optimal control theory is used to model and solve the maximum entropy problem for a continuous random variable. The maximum entropy principle provides a method to obtain least-biased probability density function (Pdf) estimation. In this paper, to find a closed form solution for the maximum entropy problem with any number of moment constraints, the entropy is consi...

As stochastic simulations become increasingly common in biological research, tools for analysis of such systems are in demand. The deterministic analogue to stochastic models, a set of probability moment equations equivalent to the Chemical Master Equation (CME), offers the possibility of a priori analysis of systems without the need for computationally costly Monte Carlo simulations. Despite t...