Comments on “Embedded pair of extended Runge–Kutta–Nyström type methods for perturbed oscillators”

In a recent paper Fang [Embedded pair of extended Runge–Kutta–Nyström type methods for perturbed oscillators, Appl. Math. Modell. (2009), doi:10.1016/j.apm.2009.12.004] considered the embedded pair of extended Runge–Kutta–Nyström type methods for perturbed oscillators and analyzed numerical stability and phase properties of the methods. The authors claimed that their methods are based on the order conditions of extended Runge–Kutta–Nyström type methods presented by Yang et al. [Extended RKN-type methods for numerical integration of perturbed oscillators, Comput. Phys. Commun. 180 (2009) 1777–1794]. However, some careless mistakes have been made in that paper. For this reason we will make some comments on that paper.     

Isobaric vapor–liquid equilibria for water + n-propanol + n-butanol ternary system at atmospheric pressure

Isobaric vapor–liquid equilibrium (VLE) data for water + n-propanol + n-butanol ternary system have been extensively measured at 99.2 kPa using a recirculating still. The experimental data were then correlated using the extended UNIQUAC model, in which the binary interaction energy parameters between the three components were obtained through a simplex fitting method. The results showed that the calculated data by the extended UNIQUAC model using the same interaction energy parameters agree well with both the experimental data and the literature data. It demonstrated that the experimental data are very consistent with the literature data; and the extended UNIQUAC model is reliable to predict the VLE of the ternary system using the obtained interaction energy parameters.     

Sliding mode control of the forced generalized Burgers equation

^** Email: smaoui{at}mcs.sci.kuniv.edu.kw This paper deals with the sliding mode control (SMC) of theforced generalized Burgers equation via the Karhunen-Loève(K-L) Galerkin method. The decomposition procedure of the K-Lmethod is presented to illustrate the use of this method inanalysing the numerical simulations data which represent thesolutions of the forced generalized Burgers equation for viscosityranging from 1 to 100. The K-L Galerkin projection is used asa model reduction technique for non-linear systems to derivea system of ordinary differential equations (ODEs) that mimicsthe dynamics of the forced generalized Burgers equation. Thedata coefficients derived from the ODE system are then usedto approximate the solutions of the forced Burgers equation.Finally, static and dynamic SMC schemes with the objective ofenhancing the stability of the forced generalized Burgers equationare proposed. Simulations of the controlled system are givento illustrate the developed theory.     

New explicit traveling wave solutions for three nonlinear evolution equations

In this paper, using the extended tanh-function method, new explicit traveling wave solutions including rational solutions for three nonlinear evolution equations are obtained with the aid of Mathematica.     

EXISTENCE OF WEAK SOLUTIONS FOR A DEGENERATE GENERALIZED BURGERS EQUATION WITH LARGE INITIAL DATA

11MroduCtlonIn this paper we will investigate the global exlstence ofwe欢 solutions to a de欧nerate辟nerajlzed Bur驴d equatllJll in the formut ＋(。侧。＝t。。。,x E R‘,t＞0(1．1)with the initial data刚,x)一。。卜 卜)(1．1)is not only a means to study hxPerbolic conser、nonl。s[1,2]but also the mathematicalmodel of*the*、 propapatlon offinlt。。plltude sound w。es in、i劝l。area ofduct(see[3;4]),where u is an roustlc vrable,with the linear effects of chang6s!n the duct area taken out;andt I…     

Modeling quasi-static crack growth with the extended finite element method Part II: Numerical applications

In Part I [Int. J. Solids Struct., 2003], we described the implementation of the extended finite element method (X-FEM) within Dynaflow™, a standard finite element package. In our implementation, we focused on two-dimensional crack modeling in linear elasticity. For crack modeling in the X-FEM, a discontinuous function and the near-tip asymptotic functions are added to the finite element approximation using the framework of partition of unity. This permits the crack to be represented without explicitly meshing the crack surfaces and crack propagation simulations can be carried out without the need for any remeshing. In this paper, we present numerical solutions for the stress intensity factor for crack problems, and also conduct crack growth simulations with the X-FEM. Numerical examples are presented with a two-fold objective: first to show the efficacy of the X-FEM implementation in Dynaflow™; and second to demonstrate the accuracy and versatility of the method to solve challenging problems in computational failure mechanics.     

A boundary value problem in extended thermodynamics - one-dimensional steady flows with heat conduction

Abstract. One-dimensional steady flows with heat conduction, treated by the 13-moment theory of extended thermodynamics are considered. The usual well-posed boundary conditions for the corresponding problems in the Navier-Stokes-Fourier (NSF) theory are insufficient to give unique solutions. In order to have unique physically sensible solutions, minimization of the deviation of iterative approximations from the exact solutions, proposed in [1], is used as a criterion. Moreover, the solutions are shown to be invariant with respect to change of consistent boundary conditions - a requirement abide by our physical intuition. In the problems of plane shearing flow and Couette flow, the minimization with respect to two uncontrollable parameters is involved. The examples are carried out numerically, and the results are compared with the classical results of NSF theory.Received: 16 August 2002, Accepted: 20 April 2003, Published online: 5 December 2003PACS: 83.20.Lr, 83.50.Ax Correspondence to: I-S. Liu Dedicated to Professor Ingo Müller on the occasion of his 65th birthday     

Extended Affine Weyl Groups: Presentation by Conjugation via Integral Collection

We give several necessary and sufficient conditions for the existence of the presentation by conjugation for a non-simply laced extended affine Weyl group. We invent a computational tool by which one can determine simply the existence of the presentation by conjugation for an extended affine Weyl group. As an application, we determine the existence of the presentation by conjugation for a large class of extended affine Weyl groups.     

The effect of extended conjugation on electrocatalytic CO2 reduction by molecular catalysts and macromolecular structures

Homogenous molecular catalysts have shown significant promise for the selective reduction of CO₂ to single products. However, their practical application in emerging CO₂ reduction technologies is hindered by their limited solubility and stability in aqueous solutions, their diffusion-dependent kinetics, and their poor recyclability. Incorporating discrete molecular catalysts into macromolecular architectures such as covalent organic frameworks is one solution to these limitations that allows for the synthesis of heterogeneous materials with increased activity and stability but that still maintain the selectivity and active-site tunability of discrete molecular catalysts. Forming such macromolecular materials necessarily extends the ligand π-conjugated network, which can have important effects on the electrocatalytic activity. In this review, we discuss recent studies on the effect of extended π-conjugation on the catalytic activity of molecular catalyst and extended macromolecular architectures, with an emphasis on how activity is influenced by charge delocalization, electrostatic effects, and electronic coupling between active sites.     

Algebraic Rossby Solitary Waves Excited by Non-Stationary External Source

The paper deals with the effects of non-stationary external source forcing and dissipation on algebraic Rossby solitary waves.From quasi-geostrophic potential vorticity equation,basing on the multiple-scale method,an inhomogeneous Korteweg-de Vries-Benjamin-Ono-Burgers(KdV-B-O-Burgers) equation is obtained.This equation has not been previously derived for Rossby waves.By analysis and calculation,four conservation laws associated with the above equation are first obtained.With the help of pseudo-spectral method,the waterfall plots are obtained and the evolutional characters of algebraic Rossby solitary waves are studied.The results show that non-stationary external source and dissipation have great effect on the generation and evolution of algebraic solitary Rossby waves.