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.

A computationally effective alternating direction method for the space and time fractional Bloch–Torrey equation in 3-D

The space and time fractional Bloch–Torrey equation (ST-FBTE) has been used to study anomalous diffusion in the human brain. Numerical methods for solving ST-FBTE in three-dimensions are computationally demanding. In this paper, we propose a computationally effective fractional alternating direction method (FADM) to overcome this problem. We consider ST-FBTE on a finite domain where the time and space derivatives are replaced by the Caputo–Djrbashian and the sequential Riesz fractional derivatives, respectively. The stability and convergence properties of the FADM are discussed. Finally, some numerical results for ST-FBTE are given to confirm our theoretical findings.

The Cube : a very large-scale interactive engagement space

“The Cube” is a unique facility that combines 48 large multi-touch screens and very large-scale projection surfaces to form one of the world’s largest interactive learning and engagement spaces. The Cube facility is part of the Queensland University of Technology’s (QUT) newly established Science and Engineering Centre, designed to showcase QUT’s teaching and research capabilities in the STEM (Science, Technology, Engineering, and Mathematics) disciplines. In this application paper we describe, the Cube, its technical capabilities, design rationale and practical day-to-day operations, supporting up to 70,000 visitors per week. Essential to the Cube’s operation are five interactive applications designed and developed in tandem with the Cube’s technical infrastructure. Each of the Cube’s launch applications was designed and delivered by an independent team, while the overall vision of the Cube was shepherded by a small executive team. The diversity of design, implementation and integration approaches pursued by these five teams provides some insight into the challenges, and opportunities, presented when working with large distributed interaction technologies. We describe each of these applications in order to discuss the different challenges and user needs they address, which types of interactions they support and how they utilise the capabilities of the Cube facility.

Time and space in biogeography : response to Parenti & Ebach (2013)

A recent Guest Editorial by Parenti & Ebach (2013, Journal of Biogeography, 40, 813–820) disagrees with the methods or interpretations in two of our recent papers. In addition, the authors open a debate on biogeographical concepts, and present an alternative philosophy for biogeographical research in the context of their recently described biogeographical subregion called ‘Pandora’. We disagree with their approach and conclusions, and comment on several issues related to our differing conceptual approaches for biogeographical research; namely, our use of molecular phylogenetic analyses, including time estimates; and Parenti & Ebach's reliance on taxon/general area cladograms. Finally, we re-examine their ‘tests’ supporting the existence of ‘Pandora’.

Sense-making across space and time : implications for the organization and findability of information

This paper presents the results from a study of information behaviors, with specific focus on information organisation-related behaviours conducted as part of a larger daily diary study with 34 participants. The findings indicate that organization of information in everyday life is a problematic area due to various factors. The self-evident one is the inter-subjectivity between the person who may have organized the information and the person looking for that same information (Berlin et. al., 1993). Increasingly though, we are not just looking for information within collections that have been designed by someone else, but within our own personal collections of information, which frequently include books, electronic files, photos, records, documents, desktops, web bookmarks, and portable devices. The passage of time between when we categorized or classified the information, and the time when we look for the same information, poses several problems of intra-subjectivity, or the difference between our own past and present perceptions of the same information. Information searching, and hence the retrieval of information from one's own collection of information in everyday life involved a spatial and temporal coordination with one's own past selves in a sort of cognitive and affective time travel, just as organizing information is a form of anticipatory coordination with one's future information needs. This has implications for finding information and also on personal information management.

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.

Time-domain hydroelastic analysis of a flexible marine structure using state-space models

This article deals with time-domain hydroelastic analysis of a marine structure. The convolution terms associated with fluid memory effects are replaced by an alternative state-space representation, the parameters of which are obtained by using realization theory. The mathematical model established is validated by comparison to experimental results of a very flexible barge. Two types of time-domain simulations are performed: dynamic response of the initially inert structure to incident regular waves and transient response of the structure after it is released from a displaced condition in still water. The accuracy and the efficiency of the simulations based on the state-space model representations are compared to those that integrate the convolutions.

Exploring Bodies in Time and Space

While the body, time and space are fundamental to human experience, comparatively little attention has been given to the connections between them. Here scholars from a wide range of disciplines explore important themes of embodied life in time and space across cultures, activities and bodymind states. Motivated by a common desire to deepen and extend our comprehension of these phenomena and the connections and conversations between them, this book emerged from intense inter-disciplinary dialogue during the 1st Global Conferences on Time, Space and the Body and Body Horror. A plenitude of theoretical approaches and media are deployed to investigate assumptions and pose problems, to creatively deconstruct and reconstruct the terms through which experience is rendered meaningful, pleasurable, and functional. These investigations, pursued through various research methods in fields of the arts, social and psychological sciences and humanities, invite readers into a genuinely pluralistic conversation around the most basic and profound aspects of being.

Introduction : Understanding Connections between Time, Space and the Body

The experiences and constructs of time, space and bodies saturate human discourse—naturally enough, since they are fundamental to existence—yet there has long been a tendency for the terms to be approached somewhat independently, belying the depth of their interconnections. It was a desire to address that apparent shortcoming that inspired this book, and the interdisciplinary meetings from which it was born, the 1st Global Conferences on ‘Time, Space and the Body’ and ‘Body Horror’ held in Sydney in February 2013. Following the lively, often provocative, exchange of ideas throughout those meetings, the writing here crosses conventional boundaries inhabiting everyday life and liminal experiences, across cultures, life circumstances, and bodily states. Through numerous theoretical frameworks and with reference to a variety of media, the authors problematize or deconstruct commonplace assumptions to reveal challenging new perspectives on the diverse cultures and communities which make our world. If there is an overarching theme of this collection it is diversity itself. The writers here come from numerous academic fields, but a good number of them also draw on first-hand cultural production in the arts: photography, sculpture and fine art instillation, for example. Of course, however laudable it might be, there is a potential problem in such diversity: does it produce fruitful dialogue moving toward creative, workable syntheses or simply a cacophony of competing, incomprehensible, barely comprehending voices? To a large degree this depends upon the intellectual, existential ambitions as well as the old-fashioned goodnatured tolerance of both writers and readers. But we hope three unifying characteristics are discernable in the following chapters viewed as a whole: firstly, a genuine concern for the world humans inhabit and the communities they form as bodies in space and time; secondly, an emphasis upon the experience of the human subject, exemplified perhaps by the number of chapters drawing on phenomenology; thirdly, an adventurous, explorative impulse associated with an underlying sense that being, since it is inseparable from the body’s temporality, is always becoming, and here the presence of poststructuralist influences is unmistakable, often explicit. Our challenge as editors has been to present the enormous variety of subjects and views in a way that would render the book coherent and at the same time encourage readers to make explorations themselves into realms they might usually consider beyond their field of interest. To that end we have divided the book into six sections around loosely defined themes, each offering different angles on how time and/or space unfold in and around bodies.

Time, space, and text in the elementary school digital writing classroom

Theorists of multiliteracies, social semiotics, and the New Literacy Studies have drawn attention to the potential changing nature of writing and literacy in the context of networked communications. This article reports findings from a design-based research project in Year 4 classrooms (students aged 8.5-10 years) in a low socioeconomic status school. A new writing program taught students how to design multimodal and digital texts across a range of genres and text types, such as web pages, online comics, video documentaries, and blogs. The authors use Bernstein’s theory of the pedagogic device to theorize the pedagogic struggles and resolutions in remaking English through the specialization of time, space, and text. The changes created an ideological struggle as new writing practices were adapted from broader societal fields to meet the instructional and regulative discourses of a conventional writing curriculum.

Genetic bottlenecks in time and space: reconstructing invasions from contemporary and historical collections

Herbarium accession data offer a useful historical botanical perspective and have been used to track the spread of plant invasions through time and space. Nevertheless, few studies have utilised this resource for genetic analysis to reconstruct a more complete picture of historical invasion dynamics, including the occurrence of separate introduction events. In this study, we combined nuclear and chloroplast microsatellite analyses of contemporary and historical collections of Senecio madagascariensis, a globally invasive weed first introduced to Australia c. 1918 from its native South Africa. Analysis of nuclear microsatellites, together with temporal spread data and simulations of herbarium voucher sampling, revealed distinct introductions to south-eastern Australia and mid-eastern Australia. Genetic diversity of the south-eastern invasive population was lower than in the native range, but higher than in the mid-eastern invasion. In the invasive range, despite its low resolution, our chloroplast microsatellite data revealed the occurrence of new haplotypes over time, probably as the result of subsequent introduction(s) to Australia from the native range during the latter half of the 20th century. Our work demonstrates how molecular studies of contemporary and historical field collections can be combined to reconstruct a more complete picture of the invasion history of introduced taxa. Further, our study indicates that a survey of contemporary samples only (as undertaken for the majority of invasive species studies) would be insufficient to identify potential source populations and occurrence of multiple introductions.