Efficient preconditioning of the method of lines for solving nonlinear two-sided space-fractional diffusion equations

A standard method for the numerical solution of partial differential equations (PDEs) is the method of lines. In this approach the PDE is discretised in space using �finite di�fferences or similar techniques, and the resulting semidiscrete problem in time is integrated using an initial value problem solver. A significant challenge when applying the method of lines to fractional PDEs is that the non-local nature of the fractional derivatives results in a discretised system where each equation involves contributions from many (possibly every) spatial node(s). This has important consequences for the effi�ciency of the numerical solver. First, since the cost of evaluating the discrete equations is high, it is essential to minimise the number of evaluations required to advance the solution in time. Second, since the Jacobian matrix of the system is dense (partially or fully), methods that avoid the need to form and factorise this matrix are preferred. In this paper, we consider a nonlinear two-sided space-fractional di�ffusion equation in one spatial dimension. A key contribution of this paper is to demonstrate how an eff�ective preconditioner is crucial for improving the effi�ciency of the method of lines for solving this equation. In particular, we show how to construct suitable banded approximations to the system Jacobian for preconditioning purposes that permit high orders and large stepsizes to be used in the temporal integration, without requiring dense matrices to be formed. The results of numerical experiments are presented that demonstrate the effectiveness of this approach.

Discussions in space : interactive urban screens for enhancing citizen engagement

Local governments struggle to engage time poor and seemingly apathetic citizens, as well as the city's young digital natives, the digital locals. Capturing the attention of this digitally literate community who are technology and socially savvy adds a new quality to the challenge of community engagement for urban planning. This project developed and tested a lightweight design intervention towards removing the hierarchy between those who plan the city and those who use it. The aim is to narrow this gap by enhancing people's experience of physical spaces with digital, civic technologies that are directly accessible within that space. The study's research informed the development of a public screen system called Discussions In Space (DIS). It facilitates a feedback platform about specific topics, e.g., a concrete urban planning project, and encourages direct, in-situ, real-time user responses via SMS and Twitter. The thesis presents the findings of deploying and integrating DIS in a wide range of public and urban environments, including the iconic urban screen at Federation Square in Melbourne, to explore the Human-Computer Interaction (HCI) related challenges and implications. It was also deployed in conjunction with a major urban planning project in Brisbane to explore the system's opportunities and challenges of better engaging with Australia's new digital locals. Finally, the merits of the short-texted and ephemeral data generated by the system were evaluated in three focus groups with professional urban planners. DIS offers additional benefits for civic participation as it gives voice to residents who otherwise would not be easily heard. It also promotes a positive attitude towards local governments and gathers complementary information that is different than that captured by more traditional public engagement tools.

White Lines: The Intercultural Politics of Everyday Movement in Local Spaces

This article draws on research into racist vilification experienced by young Arab and Muslim Australians especially since 11 September 2001, to explore the links between public space, movement and national belonging, and the spatial regulation of cultural difference that functions in Australia. The authors analyse the way that the capacity to experience forms of national belonging and cultural citizenship is shaped by inclusion within or exclusion from local as well as nationally significant public spaces. While access to public space and freedom to move are conventionally seen as fundamental to a democratic state, these are often seen in abstract terms. This article emphasises how movement in public space is a very concrete dimension of our experience of freedom, in showing how incivilities directed against Arab and Muslim Australians have operated pedagogically as a spatialised regulation of national belonging. The article concludes by examining how processes associated with the Cronulla riots of December 2005 have retarded the capacities of Muslim and Arab Australians to negotiate within and across spaces, diminishing their opportunities to invest in local and national spaces, shrinking their resources and opportunities for place-making in public space.

Scenes, quarters and clusters : new experiments in the formation and governance of creative places in China

This thesis examines the formation and governance patterns of the social and spatial concentration of creative people and creative business in cities. It develops a typology for creative places, adding the terms 'scene' and 'quarter' to 'clusters', to fill in the literature gap of partial emphasis on the 'creative clusters' model as an organising mechanism for regional and urban policy. In this framework, a cluster is the gathering of firms with a core focus on economic benefits; a quarter is the urban milieu usually driven by a growth coalition consisting of local government, real estate agents and residential communities; and a scene is the spontaneous assembly of artists, performers and fans with distinct cultural forms. The framework is applied to China, specifically to Hangzhou – a second-tier city in central eastern China that is ambitious to become a 'national cultural and creative industries centre'. The thesis selects three cases – Ideal & Silian 166 Creative Industries Park, White-horse Lake Eco-creative City and LOFT49 Creative Industries Park – to represent scene, quarter and cluster respectively. Drawing on in-depth interviews with initiators, managers and creative professionals of these places, together with extensive documentary analysis, the thesis investigates the composition of actors, characteristics of the locality and the diversity of activities. The findings illustrate that, in China, planning and government intervention is the key to the governance of creative space; spontaneous development processes exist, but these need a more tolerant environment, a greater diversity of cultural forms and more time to develop. Moreover, the main business development model is still real estate based: this model needs to incorporate more mature business models and an enhanced IP protection system. The thesis makes a contribution to literature on economic and cultural geography, urban planning and creative industries theory. It advocates greater attention to self-management, collaborative governance mechanisms and business strategies for scenes, quarters and clusters. As intersections exist in the terms discussed, a mixed toolkit of the three models is required to advance the creative city discourse in China.

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.

Anthropogenic landscape change promotes asymmetric dispersal and limits regional patch occupancy in a spatially structured bird population

1. Local extinctions in habitat patches and asymmetric dispersal between patches are key processes structuring animal populations in heterogeneous environments. Effective landscape conservation requires an understanding of how habitat loss and fragmentation influence demographic processes within populations and movement between populations. 2. We used patch occupancy surveys and molecular data for a rainforest bird, the logrunner (Orthonyx temminckii), to determine (i) the effects of landscape change and patch structure on local extinction; (ii) the asymmetry of emigration and immigration rates; (iii) the relative influence of local and between-population landscapes on asymmetric emigration and immigration; and (iv) the relative contributions of habitat loss and habitat fragmentation to asymmetric emigration and immigration. 3. Whether or not a patch was occupied by logrunners was primarily determined by the isolation of that patch. After controlling for patch isolation, patch occupancy declined in landscapes experiencing high levels of rainforest loss over the last 100 years. Habitat loss and fragmentation over the last century was more important than the current pattern of patch isolation alone, which suggested that immigration from neighbouring patches was unable to prevent local extinction in highly modified landscapes. 4. We discovered that dispersal between logrunner populations is highly asymmetric. Emigration rates were 39% lower when local landscapes were fragmented, but emigration was not limited by the structure of the between-population landscapes. In contrast, immigration was 37% greater when local landscapes were fragmented and was lower when the between-population landscapes were fragmented. Rainforest fragmentation influenced asymmetric dispersal to a greater extent than did rainforest loss, and a 60% reduction in mean patch area was capable of switching a population from being a net exporter to a net importer of dispersing logrunners. 5. The synergistic effects of landscape change on species occurrence and asymmetric dispersal have important implications for conservation. Conservation measures that maintain large patch sizes in the landscape may promote asymmetric dispersal from intact to fragmented landscapes and allow rainforest bird populations to persist in fragmented and degraded landscapes. These sink populations could form the kernel of source populations given sufficient habitat restoration. However, the success of this rescue effect will depend on the quality of the between-population landscapes.

Remote, rural, and regional airports in Australia

This paper provides an overview of the challenges faced by remote, rural and regional airports in Australia. The deregulation of airports over the past decades has resulted in local councils owning most of the rural and regional airports across Australia. The paper provides an overview of the international literature on regional airports and research directed at defining the issues faced by regional and rural airports in Australia. A survey of airport managers, regulators and local councils was undertaken across Australia to outline the challenges and stresses that regional airports are facing. Core findings indicate that the operation of rural and regional airports is under stress due to the interrelating factors of infrastructure costs, high cost of maintenance, and security infrastructure upgrades. Small airports often compete with one another to attract airlines and maintain their infrastructure advantage.

Broadband today : the role of Australian local government authorities

The paper seeks to clarify the role of Local Government Authorities in facilitating the Australian digital economy. It does this by analysing responses to the 2012 BTA, NBN and Digital Economy Survey. This reveals the level of recognition by LGAs of relevant issues; their level of use of federal, state and other programs designed to enable end user engagement; and other actions LGAs are undertaking to enable their regional digital economies. The analysis reinforces the significant role of LGAs in the future of Australia’s digital economy and identifies areas where assistance may be required.

Making space for knowledge generation and place for knowledge communities : an analysis of the Australian practice

In the era of global knowledge economy, urban regions—seeking to increase their competitive edge, become destinations for talent and investment, and provide prosperity and quality of life to their inhabitants—have little chance achieving their development goals without forming effective knowledge-based urban development strategies. This paper aims to shed light on the planning and development processes of the knowledge-based urban development phenomenon with respect to the construction of knowledge community precincts aimed at making space for knowledge generation and place for knowledge communities. Following to a thorough review of the literature on knowledge-based urban development and strategic asset-based planning, the paper undertakes policy and best practice analyses to learn from the planning and development processes of internationally renowned knowledge community precincts—from Copenhagen, Eindhoven and Singapore. In the light of the analyses findings, this paper scrutinises major Australian knowledge community precinct initiatives—from Sydney, Melbourne and Brisbane—to better understand the dynamics of national practices, and benchmark them against the international best practice cases. The paper concludes with a discussion on the study findings and recommendations for successfully establishing space and place for both knowledge economy and society in Australian cities.

Importance of a resilient air services network to Australian remote, rural, and regional communities

Rural, regional, and remote settlements in Australia require resilient infrastructure to remain sustainable in a context characterized by frequent large-scale natural disasters, long distances between urban centers, and the pressures of economic change. A critical aspect of this infrastructure is the air services network, a system of airports, aircraft operators, and related industries that enables the high-speed movement of people, goods, and services to remote locations. A process of deregulation during the 1970s and 1980s resulted in many of these airports passing into local government and private ownership, and the rationalization of the industry saw the closure of a number of airlines and airports. This paper examines the impacts of deregulation on the resilience of air services and the contribution that they make to regional and rural communities. In particular, the robustness, redundancy, resourcefulness, and rapidity of the system are examined. The conclusion is that while the air services network has remained resilient in a situation of considerable change, the pressures of commercialization and the tendency to manage aspects of the system in isolation have contributed to a potential decrease in overall resilience.

Information support for health management in regional Sri Lanka : health managers’ perspectives

Good management, supported by accurate, timely and reliable health information, is vital for increasing the effectiveness of Health Information Systems (HIS). When it comes to managing the under resourced health systems of developing countries, information-based decision making is particularly important. This paper reports findings of a self-report survey that investigated perceptions of local health managers (HMs) of their own regional HIS in Sri Lanka. Data were collected through a validated, pre-tested postal questionnaire, and distributed among a selected group of HMs to elicit their perceptions of the current HIS in relation to information generation, acquisition and use, required reforms to the information system and application of information and communication technology (ICT). Results based on descriptive statistics indicated that the regional HIS was poorly organised and in need of reform; that management support for the system was unsatisfactory in terms of relevance, accuracy, timeliness and accessibility; that political pressure and community and donor requests took precedence over vital health information when management decisions were made; and use of ICT was unsatisfactory. HIS strengths included user-friendly paper formats, a centralised planning system and an efficient disease notification system; weaknesses were lack of comprehensiveness, inaccuracy, and lack of a feedback system. Responses of participants indicated that HIS would be improved by adopting an internationally accepted framework and introducing ICT applications. Perceived barriers to such improvements were high initial cost of educating staff to improve computer literacy, introduction of ICTs, and HIS restructure. We concluded that the regional HIS of Central Province, Sri Lanka had failed to provide much needed information support to HMs. These findings are consistent with similar research in other developing countries and reinforce the need for further research to verify causes of poor performance and to design strategic reforms to improve HIS in regional Sri Lanka.

Disaster resilience and local adaptation capacity in coastal Queensland

The 2011 floods illustrated once again Queensland’s vulnerability to flooding and similar disasters. Climate change will increase the frequency and magnitude of such events and will have a variety of other impacts. To deal with these impacts governments at all levels need to be prepared and work together. Like the rest of the nation most of the population of the state is located in the coastal areas and these areas are more vulnerable to the impacts of climate change. This paper examines climate change adaptation efforts in coastal Queensland. The aim is increasing local disaster resilience of people and property through fostering coordination between local and state government planning activities in coastal high hazard areas. By increasing the ability of local governments and state agencies to coordinate planning activities, we can help adapt to impacts of climate change. Towards that end, we will look at the ways that these groups currently interact, especially with regard to issues involving uncertainty related to climate change impacts. Through an examination of climate change related activities by Queensland’s coastal local governments and state level planning agencies and how they coordinate their planning activities at different levels we aim to identify the weaknesses of the current planning system in responding to the challenges of climate change adaptation and opportunities for improving the ways we plan and coordinate planning, and make recommendations to improve resilience in advance of disasters so as to help speed up recovery when they occur.

Efficient solution of two-sided nonlinear space-fractional diffusion equations using fast Poisson preconditioners

We develop a fast Poisson preconditioner for the efficient numerical solution of a class of two-sided nonlinear space fractional diffusion equations in one and two dimensions using the method of lines. Using the shifted Gr¨unwald finite difference formulas to approximate the two-sided(i.e. the left and right Riemann-Liouville) fractional derivatives, the resulting semi-discrete nonlinear systems have dense Jacobian matrices owing to the non-local property of fractional derivatives. We employ a modern initial value problem solver utilising backward differentiation formulas and Jacobian-free Newton-Krylov methods to solve these systems. For efficient performance of the Jacobianfree Newton-Krylov method it is essential to apply an effective preconditioner to accelerate the convergence of the linear iterative solver. The key contribution of our work is to generalise the fast Poisson preconditioner, widely used for integer-order diffusion equations, so that it applies to the two-sided space fractional diffusion equation. A number of numerical experiments are presented to demonstrate the effectiveness of the preconditioner and the overall solution strategy.

A banded preconditioner for the two-sided, nonlinear space-fractional diffusion equation

The method of lines is a standard method for advancing the solution of partial differential equations (PDEs) in time. In one sense, the method applies equally well to space-fractional PDEs as it does to integer-order PDEs. However, there is a significant challenge when solving space-fractional PDEs in this way, owing to the non-local nature of the fractional derivatives. Each equation in the resulting semi-discrete system involves contributions from every spatial node in the domain. This has important consequences for the efficiency of the numerical solver, especially when the system is large. First, the Jacobian matrix of the system is dense, and hence methods that avoid the need to form and factorise this matrix are preferred. Second, since the cost of evaluating the discrete equations is high, it is essential to minimise the number of evaluations required to advance the solution in time. In this paper, we show how an effective preconditioner is essential for improving the efficiency of the method of lines for solving a quite general two-sided, nonlinear space-fractional diffusion equation. A key contribution is to show, how to construct suitable banded approximations to the system Jacobian for preconditioning purposes that permit high orders and large stepsizes to be used in the temporal integration, without requiring dense matrices to be formed. The results of numerical experiments are presented that demonstrate the effectiveness of this approach.