Stability and convergence of an effective numerical method for the time-space fractional Fokker-Planck equation with a nonlinear source term

Fractional Fokker-Planck equations (FFPEs) have gained much interest recently for describing transport dynamics in complex systems that are governed by anomalous diffusion and nonexponential relaxation patterns. However, effective numerical methods and analytic techniques for the FFPE are still in their embryonic state. In this paper, we consider a class of time-space fractional Fokker-Planck equations with a nonlinear source term (TSFFPE-NST), which involve the Caputo time fractional derivative (CTFD) of order α ∈ (0, 1) and the symmetric Riesz space fractional derivative (RSFD) of order μ ∈ (1, 2). Approximating the CTFD and RSFD using the L1-algorithm and shifted Grunwald method, respectively, a computationally effective numerical method is presented to solve the TSFFPE-NST. The stability and convergence of the proposed numerical method are investigated. Finally, numerical experiments are carried out to support the theoretical claims.

Computationally efficient numerical methods for time- and space-fractional Fokker–Planck equations

Fractional Fokker–Planck equations have been used to model several physical situations that present anomalous diffusion. In this paper, a class of time- and space-fractional Fokker–Planck equations (TSFFPE), which involve the Riemann–Liouville time-fractional derivative of order 1-α (α(0, 1)) and the Riesz space-fractional derivative (RSFD) of order μ(1, 2), are considered. The solution of TSFFPE is important for describing the competition between subdiffusion and Lévy flights. However, effective numerical methods for solving TSFFPE are still in their infancy. We present three computationally efficient numerical methods to deal with the RSFD, and approximate the Riemann–Liouville time-fractional derivative using the Grünwald method. The TSFFPE is then transformed into a system of ordinary differential equations (ODE), which is solved by the fractional implicit trapezoidal method (FITM). Finally, numerical results are given to demonstrate the effectiveness of these methods. These techniques can also be applied to solve other types of fractional partial differential equations.

Analytical and numerical solutions for the time and space-symmetric fractional diffusion equation

We consider a time and space-symmetric fractional diffusion equation (TSS-FDE) under homogeneous Dirichlet conditions and homogeneous Neumann conditions. The TSS-FDE is obtained from the standard diffusion equation by replacing the first-order time derivative by the Caputo fractional derivative and the second order space derivative by the symmetric fractional derivative. Firstly, a method of separating variables is used to express the analytical solution of the tss-fde in terms of the Mittag–Leffler function. Secondly, we propose two numerical methods to approximate the Caputo time fractional derivative, namely, the finite difference method and the Laplace transform method. The symmetric space fractional derivative is approximated using the matrix transform method. Finally, numerical results are presented to demonstrate the effectiveness of the numerical methods and to confirm the theoretical claims.

Assessment of the suitability of public mobile data networks for aircraft telemetry and control purposes

This paper provides a review of the state of the art relevant work on the use of public mobile data networks for aircraft telemetry and control proposes. Moreover, it describes the characterisation for airborne uses of the public mobile data communication systems known broadly as 3G. The motivation for this study was the explore how this mature public communication systems could be used for aviation purposes. An experimental system was fitted to a light aircraft to record communication latency, line speed, RF level, packet loss and cell tower identifier. Communications was established using internet protocols and connection was made to a local server. The aircraft was flown in both remote and populous areas at altitudes up to 8500 ft in a region located in South East Queensland, Australia. Results show that the average airborne RF levels are better than those on the ground by 21% and in the order of - 77dbm. Latencies were in the order of 500ms (1/2 the latency of Iridium), an average download speed of 0.48Mb/s, average uplink speed of 0.85Mb/s, a packet of information loss of 6.5%. The maximum communication range was also observed to be 70km from a single cell station. The paper also describes possible limitations and utility of using such communications architecture for both manned and unmanned aircraft systems.

Making space and place for the knowledge economy : knowledge-based development of Australian cities

The impact of what has been broadly labelled the knowledge economy has been such that, even in the absence of precise measurement, it is the undoubted dynamo of today’s global market, and an essential part of any global city. The socio-economic importance of knowledge production in a knowledge economy is clear, and it is an emerging social phenomenon and research agenda in geographical studies. Knowledge production, and where, how and by whom it is produced, is an urban phenomenon that is poorly understood in an era of strong urbanisation. This paper focuses on knowledge community precincts as the catalytic magnet infrastructures impacting on knowledge production in cities. The paper discusses the increasing importance of knowledge-based urban development within the paradigm of the knowledge economy, and the role of knowledge community precincts as instruments to seed the foundation of knowledge production in cities. This paper explores the knowledge based urban development, and particularly knowledge community precinct development, potentials of Sydney, Melbourne and Brisbane, and benchmarks this against that of Boston, Massachusetts.

Making space and place for knowledge production : socio-spatial development of knowledge community precincts

In the knowledge era the importance of making space and place for knowledge production is clearly understood worldwide by many city administrations that are keen on restructuring their cities as highly competitive and creative places. Consequently, knowledge-based urban development and socio-spatial development of knowledge community precincts have taken their places among the emerging agendas of the urban planning and development practice. This chapter explores these emerging issues and scrutinizes the development of knowledge community precincts that have important economic, social and cultural dimensions on the formation of competitive and creative urban regions. The chapter also sheds light on the new challenges for planning discipline, and discusses the need for and some specifics of a new planning paradigm suitable for dealing with 21st Century’s socio-economic development and urbanization problems.

Distributed orthogonal space-time block codes with adaptive diversity gain

In this paper we present a novel distributed coding protocol for multi-user cooperative networks. The proposed distributed coding protocol exploits the existing orthogonal space-time block codes to achieve higher diversity gain by repeating the code across time and space (available relay nodes). The achievable diversity gain depends on the number of relay nodes that can fully decode the signal from the source. These relay nodes then form space-time codes to cooperatively relay to the destination using number of time slots. However, the improved diversity gain is archived at the expense of the transmission rate. The design principles of the proposed space-time distributed code and the issues related to transmission rate and diversity trade off is discussed in detail. We show that the proposed distributed space-time coding protocol out performs existing distributed codes with a variable transmission rate.

The embodied hybrid space : designing ubiquitous computing towards an amplification of situated real world experiences

The emergence of mobile and ubiquitous computing technology has created what is often referred to as the hybrid space – a virtual layer of digital information and interaction opportunities that sit on top of and augment the physical environment. Embodied media materialise digital information as observable and sometimes interactive parts of the physical environment. The aim of this work is to explore ways to enhance people’s situated real world experience, and to find out what the role and impact of embodied media in achieving this goal can be. The Edge, an initiative of the State Library of Queensland in Brisbane, Australia, and case study of this thesis, envisions to be a physical place for people to meet, explore, experience, learn and teach each other creative practices in various areas related to digital technology and arts. Guided by an Action Research approach, this work applies Lefebvre’s triad of space (1991) to investigate the Edge as a social space from a conceived, perceived and lived point of view. Based on its creators’ vision and goals on the conceived level, different embodied media are iteratively designed, implemented and evaluated towards shaping and amplifying the Edge’s visitor experience on the perceived and lived level.

Manifolds, patterns and transitions in a creative life

Using sculpture and drawing as my primary methods of investigation, this research explores ways of shifting the emphasis of my creative visual arts practice from object to process whilst still maintaining a primacy of material outcomes. My motivation was to locate ways of developing a sustained practice shaped as much by new works, as by a creative flow between works. I imagined a practice where a logic of structure within discrete forms and a logic of the broader practice might be developed as mutually informed processes. Using basic structural components of multiple wooden curves and linear modes of deployment – in both sculptures and drawings – I have identified both emergence theory and the image of rhizomic growth (Deleuze and Guattari, 1987) as theoretically integral to this imagining of a creative practice, both in terms of critiquing and developing works. Whilst I adopt a formalist approach for this exegesis, the emergence and rhizome models allow it to work as a critique of movement, of becoming and changing, rather than merely a formalism of static structure. In these models, therefore, I have identified a formal approach that can be applied not only to objects, but to practice over time. The thorough reading and application of these ontological models (emergence and rhizome) to visual arts practice, in terms of processes, objects and changes, is the primary contribution of this thesis. The works that form the major component of the research develop, reflect and embody these notions of movement and change.

Reduction of environmental effects of civil aircraft through multi-objective flight plan optimisation

With rising environmental alarm, the reduction of critical aircraft emissions including carbon dioxides (CO2) and nitrogen oxides (NOx) is one of most important aeronautical problems. There can be many possible attempts to solve such problem by designing new wing/aircraft shape, new efficient engine, etc. The paper rather provides a set of acceptable flight plans as a first step besides replacing current aircrafts. The paper investigates a green aircraft design optimisation in terms of aircraft range, mission fuel weight (CO2) and NOx using advanced Evolutionary Algorithms coupled to flight optimisation system software. Two multi-objective design optimisations are conducted to find the best set of flight plans for current aircrafts considering discretised altitude and Mach numbers without designing aircraft shape and engine types. The objectives of first optimisation are to maximise range of aircraft while minimising NOx with constant mission fuel weight. The second optimisation considers minimisation of mission fuel weight and NOx with fixed aircraft range. Numerical results show that the method is able to capture a set of useful trade-offs that reduce NOx and CO2 (minimum mission fuel weight).

XML documents clustering using tensor space model - A preliminary study

A hierarchical structure is used to represent the content of the semi-structured documents such as XML and XHTML. The traditional Vector Space Model (VSM) is not sufficient to represent both the structure and the content of such web documents. Hence in this paper, we introduce a novel method of representing the XML documents in Tensor Space Model (TSM) and then utilize it for clustering. Empirical analysis shows that the proposed method is scalable for a real-life dataset as well as the factorized matrices produced from the proposed method helps to improve the quality of clusters due to the enriched document representation with both the structure and the content information.

Flagging Spaces : exploring the myth of the Australian beach as an egalitarian space

The Australian beach is now accepted as a significant part of Australian national culture and identity. However, Huntsman (2001) and Booth (2001) both believe that the beach is dying: “intellectuals have failed to apply to the beach the attention they have lavished on the bush…” (Huntsman 2001, 218). Yet the beach remains a prominent image in contemporary literature and film; authors such as Tim Winton and Robert Drewe frequently set their stories in and around the coast. Although initially considered a space of myth (Fiske, Hodge, and Turner 1987), Meaghan Morris labelled the beach as ‘ordinary’ (1998), and as recently as 2001 in the wake of the Sydney Olympic Games, Bonner, McKee, and Mackay termed the beach ‘tacky’ and ‘familiar’. The beach, it appears, defies an easy categorisation. In fact, I believe the beach is more than merely mythic or ordinary, or a combination of the two. Instead it is an imaginative space, seamlessly shifting its metaphorical meanings dependent on readings of the texts. My studies examine the beach through five common beach myths; this paper will explore the myth of the beach as an egalitarian space. Contemporary Australian national texts no longer conform to these mythical representations – (in fact, was the beach ever a space of equality?), instead creating new definitions for the beach space that continually shifts in meaning. Recent texts such as Tim Winton’s Breath (2008) and Stephen Orr’s Time’s Long Ruin (2010) lay a more complex metaphorical meaning upon the beach space. This paper will explore the beach as a space of egalitarianism in conjunction with recent Australian fiction and films in order to discover how the contemporary beach is represented.

Flight testing of an augmented separation management system providing separation protection during failure of the central communication network

Future air traffic management concepts often involve the proposal of automated separation management algorithms that replaces human air traffic controllers. This paper proposes a new type of automated separation management algorithm (based on the satisficing approach) that utilizes inter-aircraft communication and a track file manager (or bank of Kalman filters) that is capable of resolving conflicts during periods of communication failure. The proposed separation management algorithm is tested in a range of flight scenarios involving during periods of communication failure, in both simulation and flight test (flight tests were conducted as part of the Smart Skies project). The intention of the conducted flight tests was to investigate the benefits of using inter-aircraft communication to provide an extra layer of safety protection in support air traffic management during periods of failure of the communication network. These benefits were confirmed.

The smart skies project

This paper describes the Smart Skies project, an ambitious and world-leading research endeavor exploring the development of key enabling technologies, which support the efficient utilization of airspace by manned and unmanned airspace users. This paper provides a programmatic description of the research and development of: an automated separation management system, a mobile aircraft tracking system, and aircraft-based sense-and-act technologies. A summary of the results from a series of real-world flight testing campaigns is also presented.