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.

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.

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. ...

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.

Their space, my space, our space? Report of the 2009 Redland City Council Youth and Public Space Survey

This report analyses data collected through the Redland City Council’s Young People and Public Space Survey of 2148 high school students aged 12-19. The survey conducted in 2009 explored their sense of safety and experiences in public spaces across the City, and views on what Council could do to improve these. It is apparent they base their assessment of a space as ‘public’ on their ‘use’ of a space alone or with friends, and where strangers may be present, rather than on a type of ownership of a space (public/ private). The findings of the survey are summarised according to the themes of safety, community attitudes towards young people being in public spaces, young people and authorities, young people’s views of what is needed, and understanding different young people’s experiences of public space.

Whe' yu' from?

"Whe' yu' from?" The question was put to me as I wandered, camera in hand, in the old square of Spanish Town, Jamaica's former capital. The local man, lounging in the shade of one of the colonial Georgian buildings that enclose the square, was mildly curious about what he took to be a typical white tourish photgraphing the sights of the decayed historic town. At that time, my home was in Kingston where i lived with my wife and baby son. I was then working in the Jamaican Government Town Planning Department in a job that took me all over the island. Turning to my questioner, I replied, "Kingston". There was a brief pause, and then the man spoke again: "No Man! Whe' yu' really from?" I still have difficulties when asked this question. Where am I from? What does this question mean? Does it refer to where I was born, where I spent my previous life or where I live now? Does it have a broader meaning, an enquiry about my origins in terms of background and previous experience? The following chapters are my attempt to answer these questions for my own satisfaction and, I hope, for the amusement of others who may be interested in the life of an ordinary English boy whose dream to travel and see the world was realized in ways he could not possibly have imagined. Finding an appropriate title for this book was difficult. Thursday's Child, North and South and War and Peace all came to mind but, unfortunately for me, those titles had been appropriated by other writers. Thursdays's Child is quite a popular book title, presumably because people who were born on that day and, in the words of the nursery rhyme, had 'far to go', are especially likely to have travellers' tales to tell or life stories of the rags-to-riches variety. Born on a Thursday, I have travelled a lot and I suppose that I have gone far in life. Coming from a working class family, I 'got on' by 'getting a good education' and a 'good job'. I decided against adding to the list of Thursday's Children. North and South would have reflected my life in Britain, spent in both the North and South of England, and my later years, divided between the Northern and Southern Hemispheres of the globe, as well as in countries commonly referred to as the 'advanced' North and the 'underdeveloped' South. North and South has already been appropriated by Mrs Gaskell, something that did not deter one popular American writer from using the title for a book of his. My memories of World War Two and the years afterwards made War and Peace a possible candidate, but readers expectnig an epic tale of Tolstoyan proportions may have been disappointed. To my knowledge, no other book has the title "Whe' Yu' From?". I am grateful to the Jamaican man whose question lingered in my memory and provided the title of this memoir, written decades later. This book is a word picture. It is, in a sense, a self-portrait, and like all portraits, it captures something of the character, it attempts to tell the truth, but it is not the whole truth. This is because it is not my intention to write my entire life story; rather I wish to tell about some of the things in my experience of life that have seemed important or interesting to me. Unlike a painted portrait, the picture I have created is intended to suggest the passage of time. While, for most of us in Western society, time is linear and unidirectional, like the flight of an arrov or the trajectory of a bullet, memory rearranges things, calling up images of the past in no particular order, making connections that may link events in various patterns, circular, web-like, superimposed. The stream of consciousness is very unlike that of streams we encounter in the physical world. Connections are made in all directions; thoughts hop back and forth in time and space, from topic to topic. My book is a composition drawn from periods, events and thoughts as I remember them. Like life itself, it is made up of patches, some good, some bad, but in my experience, always fascinating. In recording my memories, I have been as accurate as possible. Little of what I have written is about spectacular sights and strange customs. Much of it focuses on my more modest explorations includng observations of everyday things that have attracted my attention. Reading through the chapters, I am struck by my childhood freedom to roam and engage in 'dangerous' activities like climbing trees and playing beside streams, things that many children today are no longer allowed to enjoy. Also noticeable is the survival of traditions and superstitions from the distant past. Obvious too, is my preoccupation with place names, both official ones that appear on maps and sign boards and those used by locals and children, names rarely seen in print. If there is any uniting theme to be found in what I have written, it must be my education in the fields, woods and streets of my English homeland, in the various other countries in which I have lived and travelled, as well as more formally from books and in classrooms. Much of my book is concerned with people and places. Many of the people I mention are among those who have been, and often have remained, important and close to me. Others I remember from only the briefest of encounters, but they remain in my memory because of some specific incident or circumstance that fixed a lasting image in my mind. Some of my closest friends and relatives, however, appear nowhere in these pages or they receive only the slightest mention. This is not because they played an unimportant roles in my life. It is because this book is not the whole story. Among those whe receive little or no mention are some who are especially close to me, with whom I have shared happy and sad times and who have shown me and my family much kindness, giving support when this was needed. Some I have known since childhood and have popped up at various times in my life, often in different parts of the world. Although years may pass without me seeing them, in an important sense they are always with me. These people know who they are. I hope that they know how much I love and appreciate them. When writing my memoir, I consulted a few of the people mentioned in this book, but in the main, I have relied on my own memory, asided by daiary and notebook entries and old correspondence. In the preparation of this manuscript, I benefited greatly from the expert advice and encouragement of Neil Marr of BeWrite Books. My wife Anne, inspiration for this book, also contributed in the valuable role of critic. She has my undying gratitude.

Flight guardian: a common avionics architecture for collision avoidance and safe emergency landing for unmanned aerial systems

This paper presents an approach to derive requirements for an avionics architecture that provides onboard sense-and-avoid and autonomous emergency forced landing capabilities to a UAS. The approach is based on two design paradigms that (1) derive requirements analyzing the common functionality between these two functions to then derive requirements for sensors, computing capability, interfaces, etc. (2) consider the risk and safety mitigation associated with these functions to derive certification requirements for the system design. We propose to use the Aircraft Certification Matrix (ACM) approach to tailor the system Development Assurance Levels (DAL) and architecture requirements in accordance with acceptable risk criteria. This architecture is developed under the name “Flight Guardian”. Flight Guardian is an avionics architecture that integrates common sensory elements that are essential components of any UAS that is required to be dependable. The Flight Guardian concept is also applicable to conventionally piloted aircraft, where it will serve to reduce cockpit workload.