Design of fixed order robust power oscillation damper for TCSC

This paper illustrates robust fixed order power oscillation damper design for mitigating power systems oscillations. From implementation and tuning point of view, such low and fixed structure is common practice for most practical applications, including power systems. However, conventional techniques of optimal and robust control theory cannot handle the constraint of fixed-order as it is, in general, impossible to ensure a target closed-loop transfer function by a controller of any given order. This paper deals with the problem of synthesizing or designing a feedback controller of dynamic order for a linear time-invariant plant for a fixed plant, as well as for an uncertain family of plants containing parameter uncertainty, so that stability, robust stability and robust performance are attained. The desired closed-loop specifications considered here are given in terms of a target performance vector representing a desired closed-loop design. The performance of the designed controller is validated through non-linear simulations for a range of contingencies.

Computationally efficient methods for solving time-variable-order time-space fractional reaction-diffusion equation

Fractional differential equations are becoming more widely accepted as a powerful tool in modelling anomalous diffusion, which is exhibited by various materials and processes. Recently, researchers have suggested that rather than using constant order fractional operators, some processes are more accurately modelled using fractional orders that vary with time and/or space. In this paper we develop computationally efficient techniques for solving time-variable-order time-space fractional reaction-diffusion equations (tsfrde) using the finite difference scheme. We adopt the Coimbra variable order time fractional operator and variable order fractional Laplacian operator in space where both orders are functions of time. Because the fractional operator is nonlocal, it is challenging to efficiently deal with its long range dependence when using classical numerical techniques to solve such equations. The novelty of our method is that the numerical solution of the time-variable-order tsfrde is written in terms of a matrix function vector product at each time step. This product is approximated efficiently by the Lanczos method, which is a powerful iterative technique for approximating the action of a matrix function by projecting onto a Krylov subspace. Furthermore an adaptive preconditioner is constructed that dramatically reduces the size of the required Krylov subspaces and hence the overall computational cost. Numerical examples, including the variable-order fractional Fisher equation, are presented to demonstrate the accuracy and efficiency of the approach.

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.

Semantic service discovery in the service ecosystem

Electronic services are a leitmotif in ‘hot’ topics like Software as a Service, Service Oriented Architecture (SOA), Service oriented Computing, Cloud Computing, application markets and smart devices. We propose to consider these in what has been termed the Service Ecosystem (SES). The SES encompasses all levels of electronic services and their interaction, with human consumption and initiation on its periphery in much the same way the ‘Web’ describes a plethora of technologies that eventuate to connect information and expose it to humans. Presently, the SES is heterogeneous, fragmented and confined to semi-closed systems. A key issue hampering the emergence of an integrated SES is Service Discovery (SD). A SES will be dynamic with areas of structured and unstructured information within which service providers and ‘lay’ human consumers interact; until now the two are disjointed, e.g., SOA-enabled organisations, industries and domains are choreographed by domain experts or ‘hard-wired’ to smart device application markets and web applications. In a SES, services are accessible, comparable and exchangeable to human consumers closing the gap to the providers. This requires a new SD with which humans can discover services transparently and effectively without special knowledge or training. We propose two modes of discovery, directed search following an agenda and explorative search, which speculatively expands knowledge of an area of interest by means of categories. Inspired by conceptual space theory from cognitive science, we propose to implement the modes of discovery using concepts to map a lay consumer’s service need to terminologically sophisticated descriptions of services. To this end, we reframe SD as an information retrieval task on the information attached to services, such as, descriptions, reviews, documentation and web sites - the Service Information Shadow. The Semantic Space model transforms the shadow's unstructured semantic information into a geometric, concept-like representation. We introduce an improved and extended Semantic Space including categorization calling it the Semantic Service Discovery model. We evaluate our model with a highly relevant, service related corpus simulating a Service Information Shadow including manually constructed complex service agendas, as well as manual groupings of services. We compare our model against state-of-the-art information retrieval systems and clustering algorithms. By means of an extensive series of empirical evaluations, we establish optimal parameter settings for the semantic space model. The evaluations demonstrate the model’s effectiveness for SD in terms of retrieval precision over state-of-the-art information retrieval models (directed search) and the meaningful, automatic categorization of service related information, which shows potential to form the basis of a useful, cognitively motivated map of the SES for exploratory search.

State convergence and keyspace reduction of the mixer stream cipher

This paper presents an analysis of the stream cipher Mixer, a bit-based cipher with structural components similar to the well-known Grain cipher and the LILI family of keystream generators. Mixer uses a 128-bit key and 64-bit IV to initialise a 217-bit internal state. The analysis is focused on the initialisation function of Mixer and shows that there exist multiple key-IV pairs which, after initialisation, produce the same initial state, and consequently will generate the same keystream. Furthermore, if the number of iterations of the state update function performed during initialisation is increased, then the number of distinct initial states that can be obtained decreases. It is also shown that there exist some distinct initial states which produce the same keystream, resulting in a further reduction of the effective key space

Negative space and positive environment : mapping opportunities for urban resilience

Cities have long held a fascination for people – as they grow and develop, there is a desire to know and understand the intricate interplay of elements that makes cities ‘live’. In part, this is a need for even greater efficiency in urban centres, yet the underlying quest is for a sustainable urban form. In order to make sense of the complex entities that we recognise cities to be, they have been compared to buildings, organisms and more recently machines. However the search for better and more elegant urban centres is hardly new, healthier and more efficient settlements were the aim of Modernism’s rational sub-division of functions, which has been translated into horizontal distribution through zoning, or vertical organisation thought highrise developments. However both of these approaches have been found to be unsustainable, as too many resources are required to maintain this kind or urbanisation and social consequences of either horizontal or vertical isolation must also be considered. From being absolute consumers of resources, of energy and of technology, cities need to change, to become sustainable in order to be more resilient and more efficient in supporting culture, society as well as economy. Our urban centres need to be re-imagined, re-conceptualised and re-defined, to match our changing society. One approach is to re-examine the compartmentalised, mono-functional approach of urban Modernism and to begin to investigate cities like ecologies, where every element supports and incorporates another, fulfilling more than just one function. This manner of seeing the city suggests a framework to guide the re-mixing of urban settlements. Beginning to understand the relationships between supporting elements and the nature of the connecting ‘web’ offers an invitation to investigate the often ignored, remnant spaces of cities. This ‘negative space’ is the residual from which space and place are carved out in the Contemporary city, providing the link between elements of urban settlement. Like all successful ecosystems, cities need to evolve and change over time in order to effectively respond to different lifestyles, development in culture and society as well as to meet environmental challenges. This paper seeks to investigate the role that negative space could have in the reorganisation of the re-mixed city. The space ‘in-between’ is analysed as an opportunity for infill development or re-development which provides to the urban settlement the variety that is a pre-requisite for ecosystem resilience. An analysis of the urban form is suggested as an empirical tool to map the opportunities already present in the urban environment and negative space is evaluated as a key element in achieving a positive development able to distribute diverse environmental and social facilities in the city.

Alternating direction implicit numerical method for the space and time fractional Bloch-Torrey equation in 3-D

Recently, some authors have considered a new diffusion model–space and time fractional Bloch-Torrey equation (ST-FBTE). Magin et al. (2008) have derived analytical solutions with fractional order dynamics in space (i.e., _ = 1, β an arbitrary real number, 1 < β ≤ 2) and time (i.e., 0 < α < 1, and β = 2), respectively. Yu et al. (2011) have derived an analytical solution and an effective implicit numerical method for solving ST-FBTEs, and also discussed the stability and convergence of the implicit numerical method. However, due to the computational overheads necessary to perform the simulations for nuclear magnetic resonance (NMR) in three dimensions, they present a study based on a two-dimensional example to confirm their theoretical analysis. Alternating direction implicit (ADI) schemes have been proposed for the numerical simulations of classic differential equations. The ADI schemes will reduce a multidimensional problem to a series of independent one-dimensional problems and are thus computationally efficient. In this paper, we consider the numerical solution of a ST-FBTE on a finite domain. The time and space derivatives in the ST-FBTE are replaced by the Caputo and the sequential Riesz fractional derivatives, respectively. A fractional alternating direction implicit scheme (FADIS) for the ST-FBTE in 3-D is proposed. Stability and convergence properties of the FADIS are discussed. Finally, some numerical results for ST-FBTE are given.

A new implicit numerical method for the space and time fractional Bloch-Torrey equation

In recent years, it has been found that many phenomena in engineering, physics, chemistry and other sciences can be described very successfully by models using mathematical tools from fractional calculus. Recently, noted a new space and time fractional Bloch-Torrey equation (ST-FBTE) has been proposed (see Magin et al. (2008)), and successfully applied to analyse diffusion images of human brain tissues to provide new insights for further investigations of tissue structures. In this paper, we consider the ST-FBTE on a finite domain. The time and space derivatives in the ST-FBTE are replaced by the Caputo and the sequential Riesz fractional derivatives, respectively. Firstly, we propose a new effective implicit numerical method (INM) for the STFBTE whereby we discretize the Riesz fractional derivative using a fractional centered difference. Secondly, we prove that the implicit numerical method for the ST-FBTE is unconditionally stable and convergent, and the order of convergence of the implicit numerical method is ( T2 - α + h2 x + h2 y + h2 z ). Finally, some numerical results are presented to support our theoretical analysis.

Analytical solutions of the multi-term modified power law wave equations in a finite domain

Fractional partial differential equations with more than one fractional derivative term in time, such as the Szabo wave equation, or the power law wave equation, describe important physical phenomena. However, studies of these multi-term time-space or time fractional wave equations are still under development. In this paper, multi-term modified power law wave equations in a finite domain are considered. The multi-term time fractional derivatives are defined in the Caputo sense, whose orders belong to the intervals (1, 2], [2, 3), [2, 4) or (0, n) (n > 2), respectively. Analytical solutions of the multi-term modified power law wave equations are derived. These new techniques are based on Luchko’s Theorem, a spectral representation of the Laplacian operator, a method of separating variables and fractional derivative techniques. Then these general methods are applied to the special cases of the Szabo wave equation and the power law wave equation. These methods and techniques can also be extended to other kinds of the multi term time-space fractional models including fractional Laplacian.

Numerical methods for solving the multi-term time-fractional wave-diffusion equations

In this paper, the multi-term time-fractional wave diffusion equations are considered. The multiterm time fractional derivatives are defined in the Caputo sense, whose orders belong to the intervals [0,1], [1,2), [0,2), [0,3), [2,3) and [2,4), respectively. Some computationally effective numerical methods are proposed for simulating the multi-term time-fractional wave-diffusion equations. The numerical results demonstrate the effectiveness of theoretical analysis. These methods and techniques can also be extended to other kinds of the multi-term fractional time-space models with fractional Laplacian.

A finite volume method for solving the two-sided time-space fractional advection-dispersion equation

The field of fractional differential equations provides a means for modelling transport processes within complex media which are governed by anomalous transport. Indeed, the application to anomalous transport has been a significant driving force behind the rapid growth and expansion of the literature in the field of fractional calculus. In this paper, we present a finite volume method to solve the time-space two-sided fractional advection dispersion equation on a one-dimensional domain. Such an equation allows modelling different flow regime impacts from either side. The finite volume formulation provides a natural way to handle fractional advection-dispersion equations written in conservative form. The novel spatial discretisation employs fractionally-shifted Gr¨unwald formulas to discretise the Riemann-Liouville fractional derivatives at control volume faces in terms of function values at the nodes, while the L1-algorithm is used to discretise the Caputo time fractional derivative. Results of numerical experiments are presented to demonstrate the effectiveness of the approach.