A hierarchy of diffusive partial differential equations is derived by a moment method and a Chapman-Enskog expansion from the semiconductor Boltzmann equation assuming dominant collisions. The moment equations are closed by employing the entropy maximization principle of Levermore. The new hierarchy contains the well-known drift-diffusion model, the energy-transport equations, and the six-momen...

We develop new probabilistic and deterministic approaches for moment statistics of stochastic partial differential equations with pure jump tempered α-stable (TαS) Lévy processes. With the compound Poisson (CP) approximation or the series representation of the TαS process, we simulate the moment statistics of stochastic reaction-diffusion equations with additive TαS white noises by the probabil...

in this paper, we conduct a comparative study between the homotopy perturbation method (hpm) and adomian’s decomposition method (adm) for analytic treatment of nonlinear volterra integral equations, and we show that the hpm with a specific convex homotopy is equivalent to the adm for these type of equations.

this paper presents a class of theoretical and iterative method for linear partial differential equations. an algorithm and analytical solution with a initial condition is obtained using the reduced differential transform method. in this technique, the solution is calculated in the form of a series with easily computable components. there test modeling problems from mathematical mechanic, physi...

A formulation of the problem of combining data from several sources is discussed in terms of random effects models. The unknown measurement precision is assumed not to be the same for all methods. We investigate maximum likelihood solutions in this model. By representing the likelihood equations as simultaneous polynomial equations, the exact form of the Groebner basis for their stationary poin...

This article is aimed at describing a technique to compensate undesired yaw moment, which is inevitably induced about the support foot during single support phases while a bipedal robot is in motion. The main strategy in this method is to rotate the upper body in a way to exert a secondary moment that counteracts to the factors which create the undesired moment. In order to compute the yaw mome...

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...

The covariant Boltzmann equation for a relativistic gas mixture is used to formulate a theory of relativistic irreversible thermodynamics. The modified moment method is applied to derive various evolution equations for macroscopic variables from the covariant Boltzmann equation. The method rigorously yields the entropy differential which is not an exact differential if

We review some recent developments of Grad’s approach to solving the Boltzmann equation and creating a reduced description. The method of the invariant manifold is put forward as a unified principle to establish corrections to Grad’s equations. A consistent derivation of regularized Grad’s equations in the framework of the method of the invariant manifold is given. A new class of kinetic models...

A novel method is presented for the calculation of weight chain length distribution in free radical polymerization of vinyl monomers. In the proposed method, polymerization kinetic equations and molecular weight moment equations are used in conjunction with a function that defines the weight fraction of polymer in a finite chain length interval. The entire range of molecular weight is divided i...