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

The field of fractional differential equations provides a means for modelling transport processes within complex media which are governed by anomalous transport. Indeed, the application to anomalous transport has been a significant driving force behind the rapid growth and expansion of the literature in the field of fractional calculus. In this paper, we present a finite volume method to solve the time-space two-sided fractional advection dispersion equation on a one-dimensional domain. Such an equation allows modelling different flow regime impacts from either side. The finite volume formulation provides a natural way to handle fractional advection-dispersion equations written in conservative form. The novel spatial discretisation employs fractionally-shifted Gr¨unwald formulas to discretise the Riemann-Liouville fractional derivatives at control volume faces in terms of function values at the nodes, while the L1-algorithm is used to discretise the Caputo time fractional derivative. Results of numerical experiments are presented to demonstrate the effectiveness of the approach.

A second-order accurate numerical approximation for the Riesz space fractional advection-dispersion equation

In this paper, we consider a space Riesz fractional advection-dispersion equation. The equation is obtained from the standard advection-diffusion equation by replacing the ¯rst-order and second-order space derivatives by the Riesz fractional derivatives of order β 1 Є (0; 1) and β2 Є(1; 2], respectively. Riesz fractional advection and dispersion terms are approximated by using two fractional centered difference schemes, respectively. A new weighted Riesz fractional ¯nite difference approximation scheme is proposed. When the weighting factor Ѳ = 1/2, a second- order accurate numerical approximation scheme for the Riesz fractional advection-dispersion equation is obtained. Stability, consistency and convergence of the numerical approximation scheme are discussed. A numerical example is given to show that the numerical results are in good agreement with our theoretical analysis.

Analytical solutions for the multi-term time-space Caputo-Riesz fractional advection-diffusion equations on a finite domain

Generalized fractional partial differential equations have now found wide application for describing important physical phenomena, such as subdiffusive and superdiffusive processes. However, studies of generalized multi-term time and space fractional partial differential equations are still under development. In this paper, the multi-term time-space Caputo-Riesz fractional advection diffusion equations (MT-TSCR-FADE) with Dirichlet nonhomogeneous boundary conditions are considered. The multi-term time-fractional derivatives are defined in the Caputo sense, whose orders belong to the intervals [0, 1], [1, 2] and [0, 2], respectively. These are called respectively the multi-term time-fractional diffusion terms, the multi-term time-fractional wave terms and the multi-term time-fractional mixed diffusion-wave terms. The space fractional derivatives are defined as Riesz fractional derivatives. Analytical solutions of three types of the MT-TSCR-FADE are derived with Dirichlet boundary conditions. By using Luchko's Theorem (Acta Math. Vietnam., 1999), we proposed some new techniques, such as a spectral representation of the fractional Laplacian operator and the equivalent relationship between fractional Laplacian operator and Riesz fractional derivative, that enabled the derivation of the analytical solutions for the multi-term time-space Caputo-Riesz fractional advection-diffusion equations. © 2012.

Introduction

This introduction examines sixteen authors who have contributed to New Voices, New Visions: Challenging Australian Identities and Legacies. The editors explain that the authors draw on ideas, concepts, and theories about nation, identity, space, place,and power in order to rethink stories or reread large-scale and everyday media, private, or public events in new ways. In many cases, the authors are promoting debate on topics where a single viewpoint currently predominates. These authors are introducing to readers new visions and new voices about Australian society and the Australian identity. The editors also draw on the many books about Captain/Governor William Bligh to exemplify how history is constantly being reinterpreted, with new information aiding the reader’s understanding.

Educational markets in space : gamekeeping professionals across Australian communities

This paper argues that the logic of neoliberal choice policy is typically blind to considerations of space and place, but inevitably impacts on rural and remote locations in the way that middle class professionals view the opportunities available in their local educational markets. The paper considers the value of middle class professionals’ educational capitals in regional communities and their problematic distribution, given that class fraction’s particular investment in choice strategies to ensure their children’s future. It then profiles the educational market in six communities along a transect between a major regional centre and a remote ‘outback’ town, using publicly available data from the Australian government’s ‘My School’ website. Comparison of the local markets shows how educational outcomes are distributed across the local markets and how dimensions of ‘choice’ thin out over the transect. Interview data offers insights into how professional families in these localities engage selectively with these local educational markets, or plan to transcend them. The discussion reflects on the growing importance of educational choices as a marker of place in the competition between localities to attract and retain professionals to staff vital human services in their communities.

School-community engagement : a critical approach to involving young people in an urban planning project

This study examines the participation of a group of high school students in designing a Heritage Journey as part of an urban redevelopment project in their community. School-community engagement offers young people an opportunity to engage in community life and influence decisions that affect them. Forging links between community and school is becoming more important for teachers as they attempt to create new authentic learning opportunities for young people within a changing world. Increasingly, researchers and urban planners are including children and young people as active decision makers and participants in community engagement projects. However, models of participation tend to be adult-focussed, conceive participation in terms of low to high graduated levels and lack a clearly articulated theoretical basis. The research problem in this study focuses on investigating whether the inclusion of young people in school-community engagement results in value adding to urban planning and is an example of genuine participation. The aim of the study is to provide a theoretically informed, empirically rich understanding of the inclusion of young people in a community engagement strategy for an urban planning project. Theories of space developed by Henri Lefebvre and Edward Soja are drawn upon for understanding how space is understood, used, and redeveloped by the students and other stakeholders. The study also draws on David Harvey’s notion of utopia and space to consider the imaginative possibilities of the students’ designs and ideas. The study uses a participatory research approach and documents the opportunities and challenges of this methodology. The thesis argues that school-community engagement within a "Thirdspace" offers many new opportunities for the emergence of authentic learning situations. Key findings from the study show young people’s participation in an urban planning project can achieve successful results when young people are given opportunities for full participation in decision-making processes; multiple pathways for active engagement are incorporated into the research design; opportunities for mentoring are provided; realistic timelines are communicated to all stakeholders and the needs and social practices of the local community are acknowledged. A new spatial model of community engagement is proposed as an outcome of the study. Unlike previous models of participation, this model demonstrates how exclusion and inclusion can be conceived visually, and may prove effective for conceptualising future community engagement projects that involve young people.

Space, place and power : the spatial turn in literacy research

Place matters to literacy because the meanings of our language and actions are always materially and socially placed in the world (Scollon & Scollon, 2003). We cannot interpret signs, whether an icon, symbol, gesture, word, or action, without taking into account their associations with other meanings and objects in places. This chapter maps an emergent strand of literacy research that foregrounds place and space as constitutive, rather than a backdrop for the real action. Space and place are seen as relational and dynamic, not as fixed and unchanging. Space and place are socially produced, and hence, can be contested, re-imagined and re-made. In bringing space and place into the frame of literacy studies we see a subtle shift – a rebalancing of the semiotic with the materiality of lived, embodied, and situated experience. ...