A finite volume method with linearisation in time for the solution of advection-reaction-diffusion systems

The numerical solution in one space dimension of advection--reaction--diffusion systems with nonlinear source terms may invoke a high computational cost when the presently available methods are used. Numerous examples of finite volume schemes with high order spatial discretisations together with various techniques for the approximation of the advection term can be found in the literature. Almost all such techniques result in a nonlinear system of equations as a consequence of the finite volume discretisation especially when there are nonlinear source terms in the associated partial differential equation models. This work introduces a new technique that avoids having such nonlinear systems of equations generated by the spatial discretisation process when nonlinear source terms in the model equations can be expanded in positive powers of the dependent function of interest. The basis of this method is a new linearisation technique for the temporal integration of the nonlinear source terms as a supplementation of a more typical finite volume method. The resulting linear system of equations is shown to be both accurate and significantly faster than methods that necessitate the use of solvers for nonlinear system of equations.

A finite volume method for solving the two-sided time-space fractional advection-dispersion equation

We present a finite volume method to solve the time-space two-sided fractional advection-dispersion equation on a one-dimensional domain. The spatial discretisation employs fractionally-shifted Grünwald formulas to discretise the Riemann-Liouville fractional derivatives at control volume faces in terms of function values at the nodes. We demonstrate how the finite volume formulation provides a natural, convenient and accurate means of discretising this equation in conservative form, compared to using a conventional finite difference approach. Results of numerical experiments are presented to demonstrate the effectiveness of the approach.

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..."

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...