• Abstract

Observations are reported on thermoplastic elastomer (ethylene-octene copolymer) melt in small-amplitude shear oscillatory tests and start-up shear tests with various strain rates in the interval of temperatures between 120 and 210 $^{\circ}$C. Based on the concept of heterogeneous non-affine polymer networks, constitutive equations are developed for the thermo-mechanical behavior of a melt at three-dimensional deformations with finite strains. Adjustable parameters in the stress-strain relations are found by fitting the experimental data. The model is applied to the analysis of Poiseuille flow. The effects of temperature and pressure gradient on the steady velocity profile are studied numerically.

• Abstract

In this paper, we describe a residual distribution (RD) method where, contrarily to "standard" this type schemes, the mesh is not necessarily conformal. It also allows using discontinuous elements, contrary to the "standard" case where continuous elements are requested. Moreover, if continuity is forced, the scheme is similar to the standard RD case. Hence, the situation becomes comparable with the Discontinuous Galerkin (DG) method, but it is simpler to implement than DG and has guaranteed $L^∞$ bounds. We focus on the second-order case, but the method can be easily generalized to higher degree polynomials.

• Abstract

In this paper, we formulate a two-way interfacial condition for simulating lattice dynamics in one space dimension. With a time history treatment, the incoming waves are incorporated into the motion of the boundary atoms accurately. This condition reduces to the absorbing boundary condition when there is no incoming wave. Numerical tests validate the effectiveness of the proposed condition in treating simultaneously incoming waves and outgoing waves.

• Abstract

We investigate the superconvergence properties of the constrained quadratic elliptic optimal control problem which is solved by using rectangular mixed finite element methods. We use the lowest order Raviart-Thomas mixed finite element spaces to approximate the state and co-state variables and use piecewise constant functions to approximate the control variable. We obtain the superconvergence of $\mathcal{O}(h^{1+s})$ $(0$<$s\leq$<$1)$ for the control variable. Finally, we present two numerical examples to confirm our superconvergence results.

• Abstract

In this article, natural convection of a magnetic fluid in a cubic cavity with a heat generating object inside and under a uniform magnetic field is simulated by the lattice Boltzmann method. Results obtained from the present simulations are shown to agree well with our experimental measurements, and reveal more of effects of the magnetic field on the flow and heat transfer of the magnetic fluids.

• Abstract

The objectives of the present study are to investigate the effects of heat  and mass transfer on the unsteady flow of a perfect conducting polar fluid over a flat sheet with a linear velocity in the presence of thermal radiation. Successive approximation method developed in Zakaria [Appl. Math. Comput. 10 (2002), Appl. Math. Comput. 155 (2005)] is adopted to solve the problem. The effects of Alfven velocity, mass transfer, various material parameters, Prandtl number, Schmidt number and relaxation time on the velocity, angular velocity, temperature and concentration are discussed and illustrated graphically.

• Abstract

Optimum design of structures is achieved by genetic algorithm. The evolutionary algorithm is employed to design structures. The method improves the computing efficiency of the large-scale optimization problems and enhances the global convergence of the design process. The loads are considered as earthquake loads. A time history analysis is carried out for the dynamic analysis. To decrease the computational work, a wavelet transform is used by which the number of points in the earthquake record is reduced. A reverse wavelet transform is also employed to reconstruct the functions under consideration in the time domain. A number of space structures are designed for minimum weight and the results are compared with exact dynamic analysis.

• Abstract

This paper presents the application of a new method for obtaining new exact solutions of some well-known nonlinear partial differential equations. The Rational Hyperbolic method is used for handling the Zhiber-Shabat equation and the related equations such as Liouville, Sinh-Gordon, Dodd-Bullough-Mikhailov and Tzitzeica-Dodd-Bullough equations. We show power of the Rational Hyperbolic method that is simple and effective for solving nonlinear partial differential equations.