The effect of ZnO on the sintering and stabilization of ZrO2 center dot MgO system

The sintering of ZrO2. MgO . ZnO powder has been investigated by TMA (Thermal Mechanical Analyser) and its phases analysed by XRD (X-ray diffraction pattern). The data obtained from sintering was studied by the Bannister equation and its dominant sintering mechanism was calculated. It was observed that the ZnO addition in the ZrO2. MgO solid solution lead to increased zirconia stabilization, According to the vacancies model, the ZnO addition did not lead to zirconia phases stabilization (PSZ). An analysis of the rate control in the initial stage of the sintering (region I) showed a mechanism of volume diffusion type. In other regions (regions II and III), the grain growth did lead to the Bannister equation deviation, which was observed by SEM (Scanning Electron Microscopy). These results were different from those demonstrated by other authors who studied the ZrO2. Y2O3 solid solution and obtained a mechanism of grain boundary diffusion type. (C) 1999 Published by Elsevier B.V. Ltd and Techna S.r.l. All rights reserved.

Sintering mechanisms of ZrO2 center dot MgO with addition of TiO2 and CuO

Substitutions of Ti and Cu in ZrO2.MgO (Z), cause transformation from monoclinic (m) to cubic (c) and tetragonal (t). According to the vacancy model and solid Solution formation models, neither CuO nor TiO2 cause zirconia stabilization, which derives front other phenomena. Data analysis by TMA using the CRH (constant rate of heating) method shows a solid state reaction of ZrO2.MgO.TiO2 (Z.TiO2) demonstrating a dominant mechanism of volume diffusion (n = 1). However, the sintering of ZrO2.MgO.CuO (Z.CuO) shows a viscous flow mechanism (n = 0), a similar phenomena to that of by sintering of glass. Transformations, such as: CuO to Cu2O at 1000 degreesC, ZrO2 (m) to ZrO2 (t) at 1100 degreesC and Cu2O (s) to Cu2O (l) at 1230 degreesC cause successive rearrangements of microstructure inside of region I (sintering process) and lead to interpretation errors when the Bannister equation is used. (C) 2003 Elsevier Ltd and Techna Group S.r.l. All rights reserved.

Detailed analysis of a conservative difference approximation for the time fractional diffusion equation

Diffusion equations that use time fractional derivatives are attractive because they describe a wealth of problems involving non-Markovian Random walks. The time fractional diffusion equation (TFDE) is obtained from the standard diffusion equation by replacing the first-order time derivative with a fractional derivative of order α ∈ (0, 1). Developing numerical methods for solving fractional partial differential equations is a new research field and the theoretical analysis of the numerical methods associated with them is not fully developed. In this paper an explicit conservative difference approximation (ECDA) for TFDE is proposed. We give a detailed analysis for this ECDA and generate discrete models of random walk suitable for simulating random variables whose spatial probability density evolves in time according to this fractional diffusion equation. The stability and convergence of the ECDA for TFDE in a bounded domain are discussed. Finally, some numerical examples are presented to show the application of the present technique.

Exploring first-year academic achievement through structural equation modelling

The purpose of this research was to develop and test a multicausal model of the individual characteristics associated with academic success in first-year Australian university students. This model comprised the constructs of: previous academic performance, achievement motivation, self-regulatory learning strategies, and personality traits, with end-of-semester grades the dependent variable of interest. The study involved the distribution of a questionnaire, which assessed motivation, self-regulatory learning strategies and personality traits, to 1193 students at the start of their first year at university. Students' academic records were accessed at the end of their first year of study to ascertain their first and second semester grades. This study established that previous high academic performance, use of self-regulatory learning strategies, and being introverted and agreeable, were indicators of academic success in the first semester of university study. Achievement motivation and the personality trait of conscientiousness were indirectly related to first semester grades, through the influence they had on the students' use of self-regulatory learning strategies. First semester grades were predictive of second semester grades. This research provides valuable information for both educators and students about the factors intrinsic to the individual that are associated with successful performance in the first year at university.

Implicit difference approximation for the time fractional diffusion equation

In this paper, we consider a time fractional diffusion equation on a finite domain. The equation is obtained from the standard diffusion equation by replacing the first-order time derivative by a fractional derivative (of order $0<\alpha<1$ ). We propose a computationally effective implicit difference approximation to solve the time fractional diffusion equation. Stability and convergence of the method are discussed. We prove that the implicit difference approximation (IDA) is unconditionally stable, and the IDA is convergent with $O(\tau+h^2)$, where $\tau$ and $h$ are time and space steps, respectively. Some numerical examples are presented to show the application of the present technique.

A Petrov-Galerkin method for a singularly perturbed ordinary differential equation with non-smooth data

In this paper, a singularly perturbed ordinary differential equation with non-smooth data is considered. The numerical method is generated by means of a Petrov-Galerkin finite element method with the piecewise-exponential test function and the piecewise-linear trial function. At the discontinuous point of the coefficient, a special technique is used. The method is shown to be first-order accurate and singular perturbation parameter uniform convergence. Finally, numerical results are presented, which are in agreement with theoretical results.

Numerical approximation of a fractional-in-space diffusion equation (II) - with nonhomogeneous boundary conditions

In this paper, a space fractional di®usion equation (SFDE) with non- homogeneous boundary conditions on a bounded domain is considered. A new matrix transfer technique (MTT) for solving the SFDE is proposed. The method is based on a matrix representation of the fractional-in-space operator and the novelty of this approach is that a standard discretisation of the operator leads to a system of linear ODEs with the matrix raised to the same fractional power. Analytic solutions of the SFDE are derived. Finally, some numerical results are given to demonstrate that the MTT is a computationally e±cient and accurate method for solving SFDE.