A comparison of finite difference and finite volume methods for solving the space-fractional advection-dispersion equation with variable coefficients

Transport processes within heterogeneous media may exhibit non- classical diffusion or dispersion which is not adequately described by the classical theory of Brownian motion and Fick’s law. We consider a space-fractional advection-dispersion equation based on a fractional Fick’s law. Zhang et al. [Water Resources Research, 43(5)(2007)] considered such an equation with variable coefficients, which they dis- cretised using the finite difference method proposed by Meerschaert and Tadjeran [Journal of Computational and Applied Mathematics, 172(1):65-77 (2004)]. For this method the presence of variable coef- ficients necessitates applying the product rule before discretising the Riemann–Liouville fractional derivatives using standard and shifted Gru ̈nwald formulas, depending on the fractional order. As an alternative, we propose using a finite volume method that deals directly with the equation in conservative form. Fractionally-shifted Gru ̈nwald formulas are used to discretise the Riemann–Liouville fractional derivatives at control volume faces, eliminating the need for product rule expansions. We compare the two methods for several case studies, highlighting the convenience of the finite volume approach.

Spontaneous large volume adipose tissue generation from a vascularized pedicled fat flap inside a chamber space

A novel method of spontaneous generation of new adipose tissue from an existing fat flap is described. A defined volume of fat flap based on the superficial inferior epigastric vascular pedicle in the rat was elevated and inset into a hollow plastic chamber implanted subcutaneously in the groin of the rat. The chamber walls were either perforated or solid and the chambers either contained poly(D,L-lactic-co-glycolic acid) (PLGA) sponge matrix or not. The contents were analyzed after being in situ for 6 weeks. The total volume of the flap tissue in all groups except the control groups, where the flap was not inserted into the chambers, increased significantly, especially in the perforated chambers (0.08 ± 0.007 mL baseline compared to 1.2 ± 0.08 mL in the intact ones). Volume analysis of individual component tissues within the flaps revealed that the adipocyte volume increased and was at a maximum in the chambers without PLGA, where it expanded from 0.04 ± 0.003 mL at insertion to 0.5 ± 0.08 mL (1250% increase) in the perforated chambers and to 0.16 ± 0.03 mL (400% increase) in the intact chambers. Addition of PLGA scaffolds resulted in less fat growth. Histomorphometric analysis rather than simple hypertrophy documented an increased number of adipocytes. The new tissue was highly vascularized and no fat necrosis or atypical changes were observed.

A finite volume scheme with preconditioned Lanczos method for two-dimensional space-fractional reaction–diffusion equations

Fractional differential equations have been increasingly used as a powerful tool to model the non-locality and spatial heterogeneity inherent in many real-world problems. However, a constant challenge faced by researchers in this area is the high computational expense of obtaining numerical solutions of these fractional models, owing to the non-local nature of fractional derivatives. In this paper, we introduce a finite volume scheme with preconditioned Lanczos method as an attractive and high-efficiency approach for solving two-dimensional space-fractional reaction–diffusion equations. The computational heart of this approach is the efficient computation of a matrix-function-vector product f(A)bf(A)b, where A A is the matrix representation of the Laplacian obtained from the finite volume method and is non-symmetric. A key aspect of our proposed approach is that the popular Lanczos method for symmetric matrices is applied to this non-symmetric problem, after a suitable transformation. Furthermore, the convergence of the Lanczos method is greatly improved by incorporating a preconditioner. Our approach is show-cased by solving the fractional Fisher equation including a validation of the solution and an analysis of the behaviour of the model.

Crime, Justice and Social Democracy: Proceedings of the Second International Conference, 2013, volume 2

The refereed papers contained in this volume of conference proceedings were among those presented at the 2nd International Conference on Crime, Justice and Social Democracy, hosted by the Crime and Justice Research Centre, Faculty of Law, QUT, from 8 – 11 July 2013. The conference attracted an impressive list of speakers from Australasia, Europe, North America and Latin America. These seven papers can be viewed at the Crime and Justice Research Centre’s website at http://crimejusticeconference.com/publications/ as can Volume 1 representing another 26 selected papers from the conference. As with the papers contained in the first volume, this set of papers raises important questions about the links between crime, justice and social democracy, and continues the contribution that the Crime and Justice Research Centre makes towards engaging with these topics. We thank all those who submitted papers for review for this second volume of proceedings, as well as the peer reviewers for taking the time to review the papers, often within very tight timelines.

Origins of Australian Football: Victoria's Early History. Volume 2 : A golden era begins : Football in 'Marvellous Melbourne', 1877 to 1885

This is the second volume of a five volume series that describes, assesses, and analyses football in Victoria during the nineteenth century. This volume looks at the cultural contexts of the sport in the late 1870s and early 1880s, describes the important matches played, and provides a full statistical account of this time period. This book is the first comprehensive discussion of the early period in Australian football's development.

Clothing Cultures, Volume 3, Issue 3

Tiziana Ferrero-Regis, guest editor of Vol. 1, issue 3, of Intellect journal Clothing Cultures. "Welcome to the third issue of Clothing Cultures. We are honoured to have served as the guest editors for this issue. The authors in this issue explore three intersecting themes in using various methods: identity, cross-cultural encounters and everyday practices related to designing, branding and wearing clothing. These themes are at the core of fashion and dress: as an everyday individual and social project, and as a system in which people and objects (clothing) globally circulate. The performance of identity (Goffman 1979; Butler 1990), social practices and the movement of people and commodities (Appadurai 1986, 1996) create and transfer cultural meanings..."

Combustion analysis of microalgae methyl ester in a common rail direct injection diesel engine

In this study, the biodiesel properties and effects of blends of oil methyl ester petroleum diesel on a CI direct injection diesel engine is investigated. Blends were obtained from the marine dinoflagellate Crypthecodinium cohnii and waste cooking oil. The experiment was conducted using a four-cylinder, turbo-charged common rail direct injection diesel engine at four loads (25%, 50%, 75% and 100%). Three blends (10%, 20% and 50%) of microalgae oil methyl ester and a 20% blend of waste cooking oil methyl ester were compared to petroleum diesel. To establish suitability of the fuels for a CI engine, the effects of the three microalgae fuel blends at different engine loads were assessed by measuring engine performance, i.e. mean effective pressure (IMEP), brake mean effective pressure (BMEP), in cylinder pressure, maximum pressure rise rate, brake-specific fuel consumption (BSFC), brake thermal efficiency (BTE), heat release rate and gaseous emissions (NO, NOx,and unburned hydrocarbons (UHC)). Results were then compared to engine performance characteristics for operation with a 20% waste cooking oil/petroleum diesel blend and petroleum diesel. In addition, physical and chemical properties of the fuels were measured. Use of microalgae methyl ester reduced the instantaneous cylinder pressure and engine output torque, when compared to that of petroleum diesel, by a maximum of 4.5% at 50% blend at full throttle. The lower calorific value of the microalgae oil methyl ester blends increased the BSFC, which ultimately reduced the BTE by up to 4% at higher loads. Minor reductions of IMEP and BMEP were recorded for both the microalgae and the waste cooking oil methyl ester blends at low loads, with a maximum of 7% reduction at 75% load compared to petroleum diesel. Furthermore, compared to petroleum diesel, gaseous emissions of NO and NOx, increased for operations with biodiesel blends. At full load, NO and NOx emissions increased by 22% when 50% microalgae blends were used. Petroleum diesel and a 20% blend of waste cooking oil methyl ester had emissions of UHC that were similar, but those of microalgae oil methyl ester/petroleum diesel blends were reduced by at least 50% for all blends and engine conditions. The tested microalgae methyl esters contain some long-chain, polyunsaturated fatty acid methyl esters (FAMEs) (C22:5 and C22:6) not commonly found in terrestrial-crop-derived biodiesels yet all fuel properties were satisfied or were very close to the ASTM 6751-12 and EN14214 standards. Therefore, Crypthecodinium cohnii- derived microalgae biodiesel/petroleum blends of up to 50% are projected to meet all fuel property standards and, engine performance and emission results from this study clearly show its suitability for regular use in diesel engines.

Urban Form at the Edge : Proceedings from ISUF 2013 [Volume 1]

Urban morphology as a field of study has developed primarily in Europe and North America, and more recently emerging as a recurrent topic in China and South America. As a counterpoint to this centric view, the ISUF 2013 conference explored aspects of ‘urban form at the edge’. In particular the conference examined ‘off centre areas’ such as India, Africa, Middle East, Central Asia and Australasia which require innovative approaches to the study of traditional, as well as post-colonial and contemporary, morphologies. Broader interpretations of urban form at the edge focus on minor centres and suburbia, with their developing and transilient character; edge cities and regional centres; and new technologies and approaches that are developing alongside established methods, tools and theories of urban morphology...