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.     

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     

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.     

Magnetosonic shock waves in dense astrophysical electron–positron–ion plasmas

Multifluid quantum magnetohydrodynamic model (QMHD) is used to investigate small but finite amplitude magnetosonic shock waves in dense) electron–positron–ion (e–p–i) plasmas. The Korteweg–de Vries–Burgers (KdVB) equation is derived by using reductive perturbation method. It is noticed that variations in the positron density modify the profile of magnetosonic shocks in dense e–p–i plasmas significantly. The numerical results are also presented by taking into account the dense plasma parameters from published literature of astrophysical conditions, in compact stars.     

Nonlinear Analysis of an Electromagnetically Levitated Droplet

In this paper, a nonlinear dynamics analysis of the experimental data was considered to study the time evolution of an electromagnetically levitated droplet. The main goals of this work are to decide whether the motion of the droplet is deterministic and to investigate its stability. Quantities characterizing time series data such as attractor dimension or largest Lyapunov exponent were computed. The number of degrees of freedom in the system was also assessed. Data acquired from a levitation instrument developed by Space Power Institute at Auburn University was used to perform the analysis.     

An exponential time differencing method of lines for the Burgers and the modified Burgers equations

A second–order exponential time differencing scheme using the method of lines is developed in this article for the numerical solution of the Burgers and the modified Burgers equations. For each case, the resulting nonlinear system is solved explicitly using a modified predictor‐corrector method. The efficiency of the method introduced is tested by comparing experimental results with others selected from the available literature.     

Gravitational lensing and <Emphasis Type="Italic">f</Emphasis> (<Emphasis Type="Italic">R</Emphasis>) theories in the Palatini approach

We investigate gravitational lensing in the Palatini approach to the f (R) extended theories of gravity. Starting from an exact solution of the f (R) field equations, which corresponds to the Schwarzschild–de Sitter metric and, on the basis of recent studies on this metric, we focus on some lensing observables, in order to evaluate the effects of the nonlinearity of the gravity Lagrangian. We give estimates for some astrophysical events, and show that these effects are tiny for galactic lenses, but become interesting for extragalactic ones.