We consider the approach to self-similarity (or dynamical scaling) in Smoluchowski’s coagulation equations for the solvable kernels K(x, y) = 2, x+ y and xy. We prove the uniform convergence of densities to the self-similar solution with exponential tails under the regularity hypothesis that a suitable moment have an integrable Fourier transform. For the discrete equations we prove uniform conv...

in this research, numerical simulation of a symmetric impact of a 2-d wedge, considering dynamic equations in two-phase flow is taken into account. the two-phase flow around the wedge is solved based on finite volume method and volume of fluid (vof) scheme. the dynamic mesh model is used to simulate dynamic motion of the wedge, thereby the effects of different dynamic meshes in both structured ...

3.1 Overview The proposed equations in the AISC Guide (Murray et al. 1997) for the effective moment of inertia of a steel joist-concrete slab system, Equations (1.7) and (1.8), are based on research from Kitterman (1994) and Band (1996), and a theoretical derivation. The modeling techniques developed in Chapter 2 were used to verify the validity of Equation (1.7) as described in the following s...

Cluster distribution kinetics is adopted to explore the kinetics of polymer crystallization. Population balance equations based on crystal size distribution and concentration of amorphous polymer segments are solved numerically and the related dynamic moment equations are also solved. The model accounts for heterogeneous or homogeneous nucleation and crystal growth. Homogeneous nucleation rates...

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...

The message passing approach of Karrer and Newman [Phys. Rev. E 82, 016101 (2010)] is an exact and practicable representation of susceptible-infected-recovered dynamics on finite trees. Here we show that, assuming Poisson contact processes, a pair-based moment-closure representation [Sharkey, J. Math. Biol. 57, 311 (2008)] can be derived from their equations. We extend the applicability of both...

We present numerical calculations of spherically symmetric radiative transport using a two-moment (P-1) method with a two-dimensional non-linear closure on the Eddington factor. The stationary state solutions contain a critical point. We demonstrate that the two-moment equations with a non-linear closure are well behaved. The solutions are physically acceptable , regular and accurate.

Absorption and fluorescence spectra of quinine sulphate (QSD) have been recorded at room temperature in wide range of solvents of different polarities. The ground-state dipole moment of QSD was obtained from quantum mechanical calculations and the excited state dipole moment of QSD was estimated from Bakhshiev’s and Kawski-Chamma-Viallet’s equations by means of solvatochromic shift method. High...

The present article focuses on the evaluation of a first-moment closure model applicable to film cooling flow and heat transfer computations. The present first-moment closure model consists of a higher level of turbulent heat flux modeling in which two additional transport equations for temperature variance kθ and its dissipation rate εθ are ...

The Vlasov equation of kinetic theory is introduced and the Hamiltonian structure of its moments is presented. Then we focus on the geodesic evolution of the Vlasov moments. As a first step, these moment equations generalize the Camassa-Holm equation to its multicomponent version. Subsequently, adding electrostatic forces to the geodesic moment equations relates them to the Benney equations and...