An analytical method to solve a general class of nonlinear reactive transport models

Three recent papers published in Chemical Engineering Journal studied the solution of a model of diffusion and nonlinear reaction using three different methods. Two of these studies obtained series solutions using specialized mathematical methods, known as the Adomian decomposition method and the homotopy analysis method. Subsequently it was shown that the solution of the same particular model could be written in terms of a transcendental function called Gauss’ hypergeometric function. These three previous approaches focused on one particular reactive transport model. This particular model ignored advective transport and considered one specific reaction term only. Here we generalize these previous approaches and develop an exact analytical solution for a general class of steady state reactive transport models that incorporate (i) combined advective and diffusive transport, and (ii) any sufficiently differentiable reaction term R(C). The new solution is a convergent Maclaurin series. The Maclaurin series solution can be derived without any specialized mathematical methods nor does it necessarily involve the computation of any transcendental function. Applying the Maclaurin series solution to certain case studies shows that the previously published solutions are particular cases of the more general solution outlined here. We also demonstrate the accuracy of the Maclaurin series solution by comparing with numerical solutions for particular cases.

Note on similarity solutions for viscous flow over an impermeable and non-linearly (quadratic) stretching sheet

Similarity solutions for flow over an impermeable, non-linearly (quadratic) stretching sheet were studied recently by Raptis and Perdikis (Int. J. Non-linear Mech. 41 (2006) 527–529) using a stream function of the form ψ=αxf(η)+βx2g(η). A fundamental error in their problem formulation is pointed out. On correction, it is shown that similarity solutions do not exist for this choice of ψ

The synthesis and spectroscopic characterisation of hydrotalcite formed from aluminate solutions

Raman spectroscopy has been used to characterise nine hydrotalcites prepared from aluminate and magnesium solutions (magnesium chloride and seawater). The aluminate hydrotalcites are proposed to have the following formula Mg6Al2(OH)16(CO32-).xH2O, Mg6Al2(OH)16(CO32-,SO42-).xH2O, and Mg6Al2(OH)16(SO42-).xH2O. The synthesis of these hydrotalcites using seawater results in the intercalation of sulfate anions into the hydrotalcite interlayer. The spectra have been used to assess the molecular assembly of the cations and anions in the hydrotalcite structures. The spectra have been conveniently subdivided into spectral features based upon the carbonate anion, the hydroxyl units and water units. This investigation has shown the ideal conditions to form hydrotalcite from aluminate solutions is at pH 14 using magnesium chloride. Changes in synthesis conditions resulted in the formation of impurity products aragonite, thenardite, and gypsum.

Sparseness vs estimating conditional probabilities : some asymptotic results

One of the nice properties of kernel classifiers such as SVMs is that they often produce sparse solutions. However, the decision functions of these classifiers cannot always be used to estimate the conditional probability of the class label. We investigate the relationship between these two properties and show that these are intimately related: sparseness does not occur when the conditional probabilities can be unambiguously estimated. We consider a family of convex loss functions and derive sharp asymptotic results for the fraction of data that becomes support vectors. This enables us to characterize the exact trade-off between sparseness and the ability to estimate conditional probabilities for these loss functions.

Engineering sustainable solutions program : critical literacies for engineers portfolio

Purpose While a number of universities in Australia have embraced concepts such as project/problem‐based learning and design of innovative learning environments for engineering education, there has been a lack of national guidance on including sustainability as a “critical literacy” into all engineering streams. This paper was presented at the 2004 International Conference on Engineering Education in Sustainable Development (EESD) in Barcelona, Spain, outlining a current initiative that is seeking to address the “critical literacy” dilemma. Design/methodology/approach The paper presents the positive steps taken by Australia's peak engineering body, the Institution of Engineers Australia (EA), in considering accreditation requirements for university engineering courses and its responsibility to ensure the inclusion of sustainability education material. It then describes a current initiative called the “Engineering Sustainable Solutions Program – Critical Literacies for Engineers Portfolio” (ESSP‐CL), which is being developed by The Natural Edge Project (TNEP) in partnership with EA and Unesco. Findings Content for the module was gathered from around the world, drawing on research from the publication The Natural Advantage of Nations: Business Opportunities, Innovation, and Governance in the Twenty‐first Century. Parts of the first draft of the ESSP‐CL have been trialled at Griffith University, Queensland, Australia with first year environmental engineering students, in May 2004. Further trials are now proceeding with a number of other universities and organisations nationally and internationally. Practical implications It is intended that ESSP‐CL will be a valuable resource to universities, professional development activities or other education facilities nationally and internationally. Originality/value This paper fulfils an identified information/resources need.

Modelling travelling waves in spatially constrained environment solutions

In this study, we consider how Fractional Differential Equations (FDEs) can be used to study the travelling wave phenomena in parabolic equations. As our method is conducted under intracellular environments that are highly crowded, it was discovered that there is a simple relationship between the travelling wave speed and obstacle density.

Floods, earthquakes and insurance coverage : issues, problems and solutions

The recent floods in Queensland and elsewhere in Australia as well as the recent earthquakes in New Zealand have again given rise to very significant uninsured losses. This article looks at the issue of cover protection against catastrophes such as floods and earthquakes affecting home buildings and contents insurance and the standard cover provisions of the Insurance Contracts Act 1984 (Cth). It points also to the possibility of a national scheme to cover natural disasters including floods.