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.

Coast control for mass rapid transit railways with searching methods

With daily commercial and social activity in cities, regulation of train service in mass rapid transit railways is necessary to maintain service and passenger flow. Dwell-time adjustment at stations is one commonly used approach to regulation of train service, but its control space is very limited. Coasting control is a viable means of meeting the specific run-time in an inter-station run. The current practice is to start coasting at a fixed distance from the departed station. Hence, it is only optimal with respect to a nominal operational condition of the train schedule, but not the current service demand. The advantage of coasting can only be fully secured when coasting points are determined in real-time. However, identifying the necessary starting point(s) for coasting under the constraints of current service conditions is no simple task as train movement is governed by a large number of factors. The feasibility and performance of classical and heuristic searching measures in locating coasting point(s) is studied with the aid of a single train simulator, according to specified inter-station run times.

Non-linear oscillations assessment of the distribution static compensator operating in voltage control mode

This article deals with the non-linear oscillations assessment of a distribution static comensator ooperating in voltage control mode using the bifurcation theory. A mathematical model of the distribution static compensator in the voltage control mode to carry out the bifurcation analysis is derived. The stabiity regions in the Thevein equivalent plane are computed. In addition, the stability regions in the control gains space, as well as the contour lines for different Floquet multipliers are computed. The AC and DC capacitor impacts on the stability are analyzed through the bifurcation theory. The observations are verified through simulaation studies. The computation of the stability region allows the assessment of the stable operating zones for a power system that includes a distribution static compensator operating in the voltage mode.

Simulation and measurement of an electrostatic discharge

Electrostatic discharge is the sudden and brief electric current that flashes between two objects at different voltages. This is a serious issue ranging in application from solid-state electronics to spectacular and dangerous lightning strikes (arc flashes). The research herein presents work on the experimental simulation and measurement of the energy in an electrostatic discharge. The energy released in these discharges has been linked to ignitions and burning in a number of documented disasters and can be enormously hazardous in many other industrial scenarios. Simulations of electrostatic discharges were designed to specifications by IEC standards. This is typically based on the residual voltage/charge on the discharge capacitor, whereas this research examines the voltage and current in the actual spark in order to obtain a more precise comparative measurement of the energy dissipated.

Application of reliability-centred maintenance technology on electric trains

This paper demonstrates the application of the reliability-centred maintenance (RCM) process to analyse and develop preventive maintenance tasks for electric multiple units (EMU) in the East Rail of the Kowloon-Canton Railway Corporation (KCRC). Two systems, the 25 kV electrical power supply and the air-conditioning system of the EMU, have been chosen for the study. RCM approach on the two systems is delineated step by step in the paper. This study confirms the feasibility and effectiveness of RCM applications on the maintenance of electric trains.

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.

Comparing charge transport predictions for a ternary electrolyte using the Maxwell–Stefan and Nernst–Planck equations

In this work, we investigate and compare the Maxwell–Stefan and Nernst–Planck equations for modeling multicomponent charge transport in liquid electrolytes. Specifically, we consider charge transport in the Li+/I−/I3−/ACN ternary electrolyte originally found in dye-sensitized solar cells. We employ molecular dynamics simulations to obtain the Maxwell–Stefan diffusivities for this electrolyte. These simulated diffusion coefficients are used in a multicomponent charge transport model based on the Maxwell– Stefan equations, and this is compared to a Nernst–Planck based model which employs binary diffusion coefficients sourced from the literature. We show that significant differences between the electrolyte concentrations at electrode interfaces, as predicted by the Maxwell–Stefan and Nernst–Planck models, can occur. We find that these differences are driven by a pressure term that appears in the Maxwell–Stefan equations. We also investigate what effects the Maxwell–Stefan diffusivities have on the simulated charge transport. By incorporating binary diffusivities found in the literature into the Maxwell–Stefan framework, we show that the simulated transient concentration profiles depend on the diffusivities; however, the simulated equilibrium profiles remain unaffected.

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.

Who's afraid of the dark? Transpower New Zealand Ltd

On 12 June 2006, the lights went out in New Zealand’s largest city and major commercial centre, Auckland. Business was disrupted and many thousands of people inconvenienced. The unscheduled power cut was the latest in a series of electric power problems in New Zealand over the past decade. Attention turned to state-owned enterprise [SOE] Transpower, which was in charge of maintaining and developing New Zealand’s national electricity grid. The problem of 12 June was traced to two shackles in poor condition, small but essential parts of the electricity grid infrastructure. Closer examination of New Zealand’s electricity sector indicated these shackles were merely the tip of a power supply iceberg. Transpower’s Chief Executive, Ralph Craven, was now answerable to the Prime Minister for the issues creating the problems, and a workable solution to fix them. Transpower Chief Executive Ralph Craven needed to produce answers that went well beyond the problem of the two faulty shackles. The power crisis had brought to the fore wider issues of roles, responsibilities, and expectations in relation to the supply of electric power in New Zealand. Transpower was contending with these issues on a daily basis; however, the incident on 12 June publicly highlighted the urgent need for solutions that served the stakeholders in this critical industry.

Remediation strategies of shaft and common mode voltages in adjustable speed drive systems

AC motors are largely used in a wide range of modern systems, from household appliances to automated industry applications such as: ventilations systems, fans, pumps, conveyors and machine tool drives. Inverters are widely used in industrial and commercial applications due to the growing need for speed control in ASD systems. Fast switching transients and the common mode voltage, in interaction with parasitic capacitive couplings, may cause many unwanted problems in the ASD applications. These include shaft voltage and leakage currents. One of the inherent characteristics of Pulse Width Modulation (PWM) techniques is the generation of the common mode voltage, which is defined as the voltage between the electrical neutral of the inverter output and the ground. Shaft voltage can cause bearing currents when it exceeds the amount of breakdown voltage level of the thin lubricant film between the inner and outer rings of the bearing. This phenomenon is the main reason for early bearing failures. A rapid development in power switches technology has lead to a drastic decrement of switching rise and fall times. Because there is considerable capacitance between the stator windings and the frame, there can be a significant capacitive current (ground current escaping to earth through stray capacitors inside a motor) if the common mode voltage has high frequency components. This current leads to noises and Electromagnetic Interferences (EMI) issues in motor drive systems. These problems have been dealt with using a variety of methods which have been reported in the literature. However, cost and maintenance issues have prevented these methods from being widely accepted. Extra cost or rating of the inverter switches is usually the price to pay for such approaches. Thus, the determination of cost-effective techniques for shaft and common mode voltage reduction in ASD systems, with the focus on the first step of the design process, is the targeted scope of this thesis. An introduction to this research – including a description of the research problem, the literature review and an account of the research progress linking the research papers – is presented in Chapter 1. Electrical power generation from renewable energy sources, such as wind energy systems, has become a crucial issue because of environmental problems and a predicted future shortage of traditional energy sources. Thus, Chapter 2 focuses on the shaft voltage analysis of stator-fed induction generators (IG) and Doubly Fed Induction Generators DFIGs in wind turbine applications. This shaft voltage analysis includes: topologies, high frequency modelling, calculation and mitigation techniques. A back-to-back AC-DC-AC converter is investigated in terms of shaft voltage generation in a DFIG. Different topologies of LC filter placement are analysed in an effort to eliminate the shaft voltage. Different capacitive couplings exist in the motor/generator structure and any change in design parameters affects the capacitive couplings. Thus, an appropriate design for AC motors should lead to the smallest possible shaft voltage. Calculation of the shaft voltage based on different capacitive couplings, and an investigation of the effects of different design parameters are discussed in Chapter 3. This is achieved through 2-D and 3-D finite element simulation and experimental analysis. End-winding parameters of the motor are also effective factors in the calculation of the shaft voltage and have not been taken into account in previous reported studies. Calculation of the end-winding capacitances is rather complex because of the diversity of end winding shapes and the complexity of their geometry. A comprehensive analysis of these capacitances has been carried out with 3-D finite element simulations and experimental studies to determine their effective design parameters. These are documented in Chapter 4. Results of this analysis show that, by choosing appropriate design parameters, it is possible to decrease the shaft voltage and resultant bearing current in the primary stage of generator/motor design without using any additional active and passive filter-based techniques. The common mode voltage is defined by a switching pattern and, by using the appropriate pattern; the common mode voltage level can be controlled. Therefore, any PWM pattern which eliminates or minimizes the common mode voltage will be an effective shaft voltage reduction technique. Thus, common mode voltage reduction of a three-phase AC motor supplied with a single-phase diode rectifier is the focus of Chapter 5. The proposed strategy is mainly based on proper utilization of the zero vectors. Multilevel inverters are also used in ASD systems which have more voltage levels and switching states, and can provide more possibilities to reduce common mode voltage. A description of common mode voltage of multilevel inverters is investigated in Chapter 6. Chapter 7 investigates the elimination techniques of the shaft voltage in a DFIG based on the methods presented in the literature by the use of simulation results. However, it could be shown that every solution to reduce the shaft voltage in DFIG systems has its own characteristics, and these have to be taken into account in determining the most effective strategy. Calculation of the capacitive coupling and electric fields between the outer and inner races and the balls at different motor speeds in symmetrical and asymmetrical shaft and balls positions is discussed in Chapter 8. The analysis is carried out using finite element simulations to determine the conditions which will increase the probability of high rates of bearing failure due to current discharges through the balls and races.

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.