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.

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.

On-board mass monitoring of heavy vehicles : results of testing program

The Transport Certification Australia on-board mass feasibility project is testing various on-board mass devices in a range of heavy vehicles (HVs). Extensive field tests of on-board mass measurement systems for HVs have been conducted during 2008. These tests were of accuracy, robustness and tamper-evidence of heavy vehicle on-board mass telematics. All the systems tested showed accuracies within approximately +/- 500 kg of gross combination mass or approximately +/- 2% of the attendant weighbridge reading. Analysis of the dynamic data also showed encouraging results and has raised the possibility of use of such dynamic information in tamper evidence in two areas. This analysis was to determine if the use of averaged dynamic data could identify potential tampering or incorrect operating procedures as well as the possibility of dynamic measurements flagging a tamper event by the use of metrics including a tampering index (TIX). Technical and business options to detect tamper events will now be developed during implementation of regulatory OBM system application to Australian heavy vehicles (HVs).

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.

A regulatory on-board mass monitoring application for heavy vehicles in Australia

This paper reports on the development of specifications for an on-board mass monitoring (OBM) application for regulatory requirements in Australia. An earlier paper reported on feasibility study and pilot testing program prior to the specification development [1]. Learnings from the pilot were used to refine this testing process and a full scale testing program was conducted from July to October 2008. The results from the full scale test and evidentiary implications are presented in this report. The draft specification for an evidentiary on-board mass monitoring application is currently under development.

Recognising audio-visual speech in vehicles using the AVICAR database

Interacting with technology within a vehicle environment using a voice interface can greatly reduce the effects of driver distraction. Most current approaches to this problem only utilise the audio signal, making them susceptible to acoustic noise. An obvious approach to circumvent this is to use the visual modality in addition. However, capturing, storing and distributing audio-visual data in a vehicle environment is very costly and difficult. One current dataset available for such research is the AVICAR [1] database. Unfortunately this database is largely unusable due to timing mismatch between the two streams and in addition, no protocol is available. We have overcome this problem by re-synchronising the streams on the phone-number portion of the dataset and established a protocol for further research. This paper presents the first audio-visual results on this dataset for speaker-independent speech recognition. We hope this will serve as a catalyst for future research in this area.

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.

Planning and implementing trajectories for autonomous underwater vehicles to track evolving ocean processes based on predictions from a regional ocean model

Path planning and trajectory design for autonomous underwater vehicles (AUVs) is of great importance to the oceanographic research community because automated data collection is becoming more prevalent. Intelligent planning is required to maneuver a vehicle to high-valued locations to perform data collection. In this paper, we present algorithms that determine paths for AUVs to track evolving features of interest in the ocean by considering the output of predictive ocean models. While traversing the computed path, the vehicle provides near-real-time, in situ measurements back to the model, with the intent to increase the skill of future predictions in the local region. The results presented here extend prelim- inary developments of the path planning portion of an end-to-end autonomous prediction and tasking system for aquatic, mobile sensor networks. This extension is the incorporation of multiple vehicles to track the centroid and the boundary of the extent of a feature of interest. Similar algorithms to those presented here are under development to consider additional locations for multiple types of features. The primary focus here is on algorithm development utilizing model predictions to assist in solving the motion planning problem of steering an AUV to high-valued locations, with respect to the data desired. We discuss the design technique to generate the paths, present simulation results and provide experimental data from field deployments for tracking dynamic features by use of an AUV in the Southern California coastal ocean.

A geometrical analysis of trajectory design for underwater vehicles

Designing trajectories for a submerged rigid body motivates this paper. Two approaches are addressed: the time optimal approach and the motion planning ap- proach using concatenation of kinematic motions. We focus on the structure of singular extremals and their relation to the existence of rank-one kinematic reduc- tions; thereby linking the optimization problem to the inherent geometric frame- work. Using these kinematic reductions, we provide a solution to the motion plan- ning problem in the under-actuated scenario, or equivalently, in the case of actuator failures. We finish the paper comparing a time optimal trajectory to one formed by concatenation of pure motions.

Robust tracking control of autonomous underwater vehicles in the presence of disturbance inputs

An autonomous underwater vehicle (AUV) is expected to operate in an ocean in the presence of poorly known disturbance forces and moments. The uncertainties of the environment makes it difficult to apply open-loop control scheme for the motion planning of the vehicle. The objective of this paper is to develop a robust feedback trajectory tracking control scheme for an AUV that can track a prescribed trajectory amidst such disturbances. We solve a general problem of feedback trajectory tracking of an AUV in SE(3). The feedback control scheme is derived using Lyapunov-type analysis. The results obtained from numerical simulations confirm the asymptotic tracking properties of the feedback control law. We apply the feedback control scheme to different mission scenarios, with the disturbances being initial errors in the state of the AUV.

Trajectory design for autonomous underwater vehicles based on ocean model predictions for feature tracking

Trajectory design for Autonomous Underwater Vehicles (AUVs) is of great importance to the oceanographic research community. Intelligent planning is required to maneuver a vehicle to high-valued locations for data collection. We consider the use of ocean model predictions to determine the locations to be visited by an AUV, which then provides near-real time, in situ measurements back to the model to increase the skill of future predictions. The motion planning problem of steering the vehicle between the computed waypoints is not considered here. Our focus is on the algorithm to determine relevant points of interest for a chosen oceanographic feature. This represents a first approach to an end to end autonomous prediction and tasking system for aquatic, mobile sensor networks. We design a sampling plan and present experimental results with AUV retasking in the Southern California Bight (SCB) off the coast of Los Angeles.