Analytical and numerical solutions of the space and time fractional bloch-torrey equation

Fractional order dynamics in physics, particularly when applied to diffusion, leads to an extension of the concept of Brown-ian motion through a generalization of the Gaussian probability function to what is termed anomalous diffusion. As MRI is applied with increasing temporal and spatial resolution, the spin dynamics are being examined more closely; such examinations extend our knowledge of biological materials through a detailed analysis of relaxation time distribution and water diffusion heterogeneity. Here the dynamic models become more complex as they attempt to correlate new data with a multiplicity of tissue compartments where processes are often anisotropic. Anomalous diffusion in the human brain using fractional order calculus has been investigated. Recently, a new diffusion model was proposed by solving the Bloch-Torrey equation using fractional order calculus with respect to time and space (see R.L. Magin et al., J. Magnetic Resonance, 190 (2008) 255-270). However effective numerical methods and supporting error analyses for the fractional Bloch-Torrey equation are still limited. In this paper, the space and time fractional Bloch-Torrey equation (ST-FBTE) is considered. The time and space derivatives in the ST-FBTE are replaced by the Caputo and the sequential Riesz fractional derivatives, respectively. Firstly, we derive an analytical solution for the ST-FBTE with initial and boundary conditions on a finite domain. Secondly, we propose an implicit numerical method (INM) for the ST-FBTE, and the stability and convergence of the INM are investigated. We prove that the implicit numerical method for the ST-FBTE is unconditionally stable and convergent. Finally, we present some numerical results that support our theoretical analysis.

Stability and convergence of implicit numerical methods for a class of fractional advection-dispersion models

In this paper, a class of fractional advection-dispersion models (FADM) is investigated. These models include five fractional advection-dispersion models: the immobile, mobile/immobile time FADM with a temporal fractional derivative 0 < γ < 1, the space FADM with skewness, both the time and space FADM and the time fractional advection-diffusion-wave model with damping with index 1 < γ < 2. They describe nonlocal dependence on either time or space, or both, to explain the development of anomalous dispersion. These equations can be used to simulate regional-scale anomalous dispersion with heavy tails, for example, the solute transport in watershed catchments and rivers. We propose computationally effective implicit numerical methods for these FADM. The stability and convergence of the implicit numerical methods are analyzed and compared systematically. Finally, some results are given to demonstrate the effectiveness of our theoretical analysis.

First international workshop on theory and applications of process visualization

The representation of business process models has been a continuing research topic for many years now. However, many process model representations have not developed beyond minimally interactive 2D icon-based representations of directed graphs and networks, with little or no annotation for information over- lays. With the rise of desktop computers and commodity mobile devices capable of supporting rich interactive 3D environments, we believe that much of the research performed in computer human interaction, virtual reality, games and interactive entertainment has much potential in areas of BPM; to engage, pro- vide insight, and to promote collaboration amongst analysts and stakeholders alike. This initial visualization workshop seeks to initiate the development of a high quality international forum to present and discuss research in this field. Via this workshop, we intend to create a community to unify and nurture the development of process visualization topics as a continuing research area.

Networked reading : using AustLit to assist reading and understanding of texts from the past

In response to a focus on reading, this paper examines the notion of reading online; as such it uses the term ‘networked reading’ to describe any act of reading in an online or digital environment. In accordance with this notion of ‘networked’ reading, the paper provides a broad introduction to AustLit: the Australian Literature Resource. This is followed by an examination of a suite of services and digital tools (LORE) developed by the Aus-e-Lit project that extends the scope of AustLit records and facilitates links to external resources. The focus of the final section of the paper is on a collection of Full Text resources located within the AustLit subset Children’s Literature Digital Resources (CLDR). It proposes a number of ways in which these texts, and an accompanying anthology of critical articles, can be utilised in classrooms across the Primary, Middle and Senior School spectrum.

Debating literacy in Australia : a documentary history, 1945 - 1994

A documentary history of 'literacy' as an issue, topic and problem in the Australia print media, 1945-1994. The accompanying critical analysis makes the case that 'literacy crises' in Australia have arisen during periods of major socioeconomic, cultural and geopolitical upheaval and change, with schools and teachers, youth and families the object of 'blame' for such changes.

Defining critical literacy

This article traces the lineage of critical literacy from Freire through critical pedagogies and discourse analysis. The author discusses the need for a contingent definition of critical literacy, as a situated and contextual response to political economies, institutional and cultural relations of power.

Pedagogy and paradox : teaching interpretation in a religious community

A qualitative, discourse analytic study of literate practices in a small religious community in a northern Australian city. The chapter documents how this community constructs religious reading and writing, affiliated ideologies and theologies, and how readers/hearers/learners are positions vis a vis the authority of sacred text.

Literacy for a sustainable world

This chapter describes the ways in which primary school teachers design curriculum to develop children's knowledge about sustainability. Such a curriculum is highly engaging and provides enhanced motivation for children to engage with complex reading and writing as they attempt to represent what they have learned and communicate this to the wider community. The chapter introduces key terms including place-based pedagogy, sustainability and critical literacy and shows how these ideas can be brought together in classrooms.

Creativity is as important as literacy : making a film trailer responding to literature

The first part of the title is from Sir Ken Robinson (Robinson, 2009), the esteemed educator and champion of creativity in schools. Sometimes in the face of meeting the demands of time, timetabling, demanding administration tasks and teaching for high stakes testing accountability, we can find ourselves desperate for time to remember that English has always been one of the places in schools where creativity can flourish. English is a place for the play of the imagination. English teachers are the purveyors of narrative; the keepers and teachers of stories. The new Australian Curriculum: English, (Australian Curriculum and Assessment Reporting Authority (ACARA), 2012) asks us to be using ICT technologies in creative ways to tell those stories. The curriculum asks students to access texts receptively and to then speak about, write and create texts productively. There are so many interesting things to do with texts beyond word processing of print based resources. Responding to literature through media is always an alternative option to writing or simply speaking about it. In this paper my QUT pre-service student Chrystal Armitage describes how she made a mini story via a film trailer in response to a short story, ‘Turned’ (Gilman, 1987) in the unit, Literature in Secondary Teaching.

Thinking Critically in the Land of Princesses and Giants : The Affordances and Challenges of Critical Approaches in the Early Years

During the last four decades, educators have created a range of critical literacy approaches for different contexts, including compulsory schooling (Luke & Woods, 2009) and second language education (Luke & Dooley, 2011). Despite inspirational examples of critical work with young students (e.g., O’Brien, 1994; Vasquez, 1994), Comber (2012) laments the persistent myth that critical literacy is not viable in the early years. Assumptions about childhood innocence and the priorities of the back-to-basics movement seem to limit the possibilities for early years literacy teaching and learning. Yet, teachers of young students need not face an either/or choice between the basic and critical dimensions of literacy. Systematic ways of treating literacy in all its complexity exist. We argue that the integrative imperative is especially important in schools that are under pressure to improve technical literacy outcomes. In this chapter, we document how critical literacy was addressed in a fairytales unit taught to 4.5 - 5.5 year olds in a high diversity, high poverty Australian school. We analyze the affordances and challenges of different approaches to critical literacy, concluding they are complementary rather than competing sources of possibility. Furthermore, we make the case for turning familiar classroom activities to critical ends.

Basic cognitive experiences and definitions in the Longman Dictionary of Contemporary English

This study applies theories of cognitive linguistics to the compilation of English learners’ dictionaries. Specifically, it employs the concepts of basic level categories and image schemas, two basic cognitive experiences, to examine the ‘definition proper’ of English dictionaries for foreign learners. In the study, the definition proper refers to the constituent part of a reference work that provides an explanation of the meanings of a word, phrase or term. This rationalization mainly consists of defining vocabulary, sense division and arrangement, as well as the means of defining (i.e. paraphrase, true definition, functional definition, and pictorial illustration). The aim of the study is to suggest ways of aligning the consultation and learning of definitions with dictionary users’ cognitive experiences. For this purpose, an analysis of the definition proper of the fourth edition of the Longman Dictionary of Contemporary English (LDOCE4) from the perspective of basic cognitive experiences has been undertaken. The study found that, generally, the lexicographic practices of LDOCE4 are consistent with theories of cognitive linguistics. However, there exist shortcomings that result from disregarding basic cognitive experiences.

Schools as meeting places : critical and inclusive literacies in changing local environments

Schools bring people together. Yet for many children there are major discontinuities between their lives in and out of school and such differences impact on literacy teaching and learning in both predictable and unpredictable ways. However if schools were reconceptualised as meeting places, where different people are thrown together (Massey, 2005) curriculum and pedagogy could be designed to take into account students’ and teachers’ different experiences and histories and to make those differences a resource for literacy learning. This paper draws on a long-term project with administrators and teachers working in a school situated in a site of urban regeneration and significant demographic shifts. It draws particularly on the ways in which one teacher re-positioned her grade 4/5 students as researchers, designers and journalists exploring student and staff memories of a school. It argues that place, and people’s relationships with places, can be a rich resource for literacy learning when teachers make it the object of study.

The legacy of Ian Hunter's work on literature education and the history of reading practices : some preliminary remarks

Ian Hunter's early work on the history of literature education and the emergence of English as school subject issued a bold challenge to traditional accounts that have in the main focused on English either as knowledge of a particular field or as ideology. The alternative proposal put forward by Hunter and supported by detailed historical analysis is that English exists as a series of historically contingent techniques and practices for shaping the self-managing capacities of children. The challenge for the field is to advance this historical work and to examine possible implications for English teaching.