Higher order spectral analysis of Chua's circuit

Higher order spectral analysis is used to investigate nonlinearities in time series of voltages measured from a realization of Chua's circuit. For period-doubled limit cycles, quadratic and cubic nonlinear interactions result in phase coupling and energy exchange between increasing numbers of triads and quartets of Fourier components as the nonlinearity of the system is increased. For circuit parameters that result in a chaotic Rossler-type attractor, bicoherence and tricoherence spectra indicate that both quadratic and cubic nonlinear interactions are important to the dynamics. When the circuit exhibits a double-scroll chaotic attractor the bispectrum is zero, but the tricoherences are high, consistent with the importance of higher-than-second order nonlinear interactions during chaos associated with the double scroll.

Statistics of tricoherence

Statistics of the estimates of tricoherence are obtained analytically for nonlinear harmonic random processes with known true tricoherence. Expressions are presented for the bias, variance, and probability distributions of estimates of tricoherence as functions of the true tricoherence and the number of realizations averaged in the estimates. The expressions are applicable to arbitrary higher order coherence and arbitrary degree of interaction between modes. Theoretical results are compared with those obtained from numerical simulations of nonlinear harmonic random processes. Estimation of true values of tricoherence given observed values is also discussed

Bispectral and trispectral characterization of transition to chaos in the Duffing oscillator

Higher-order spectral (bispectral and trispectral) analyses of numerical solutions of the Duffing equation with a cubic stiffness are used to isolate the coupling between the triads and quartets, respectively, of nonlinearly interacting Fourier components of the system. The Duffing oscillator follows a period-doubling intermittency catastrophic route to chaos. For period-doubled limit cycles, higher-order spectra indicate that both quadratic and cubic nonlinear interactions are important to the dynamics. However, when the Duffing oscillator becomes chaotic, global behavior of the cubic nonlinearity becomes dominant and quadratic nonlinear interactions are weak, while cubic interactions remain strong. As the nonlinearity of the system is increased, the number of excited Fourier components increases, eventually leading to broad-band power spectra for chaos. The corresponding higher-order spectra indicate that although some individual nonlinear interactions weaken as nonlinearity increases, the number of nonlinearly interacting Fourier modes increases. Trispectra indicate that the cubic interactions gradually evolve from encompassing a few quartets of Fourier components for period-1 motion to encompassing many quartets for chaos. For chaos, all the components within the energetic part of the power spectrum are cubically (but not quadratically) coupled to each other.

Higher-Order spectra of nonlinear polynomial models for Chua's circuit

Polynomial models are shown to simulate accurately the quadratic and cubic nonlinear interactions (e.g. higher-order spectra) of time series of voltages measured in Chua's circuit. For circuit parameters resulting in a spiral attractor, bispectra and trispectra of the polynomial model are similar to those from the measured time series, suggesting that the individual interactions between triads and quartets of Fourier components that govern the process dynamics are modeled accurately. For parameters that produce the double-scroll attractor, both measured and modeled time series have small bispectra, but nonzero trispectra, consistent with higher-than-second order nonlinearities dominating the chaos.

Towards testing the eclectic paradigm on multinational contracting: an approach to reviewing and analysing secondary data

In response to the need to leverage private finance and the lack of competition in some parts of the Australian public sector major infrastructure market, especially in very large economic infrastructure procured using Pubic Private Partnerships, the Australian Federal government has demonstrated its desire to attract new sources of in-bound foreign direct investment (FDI) into the Australian construction market. This paper aims to report on progress towards an investigation into the determinants of multinational contractors’ willingness to bid for Australian public sector major infrastructure projects and which is designed to give an improved understanding of matters surrounding FDI into the Australian construction sector. This research deploys Dunning’s eclectic theory for the first time in terms of in-bound FDI by multinational contractors and as head contractors bidding for Australian major infrastructure public sector projects. Elsewhere, the authors have developed Dunning’s principal hypothesis associated with his eclectic framework in order to suit the context of this research and to address a weakness arising in Dunning’s principal hypothesis that is based on a nominal approach to the factors in the eclectic framework and which fail to speak to the relative explanatory power of these factors. In this paper, an approach to reviewing and analysing secondary data, as part of the first stage investigation in this research, is developed and some illustrations given, vis-à-vis the selected sector (roads, bridges and tunnels) in Australia (as the host location) and using one of the selected home countries (Spain). In conclusion, some tentative thoughts are offered in anticipation of the completion of the first stage investigation - in terms of the extent to which this first stage based on secondary data only might suggest the relative importance of the factors in the eclectic framework. It is noted that more robust conclusions are expected following the future planned stages of the research and these stages including primary data are briefly outlined. Finally, and beyond theoretical contributions expected from the overall approach taken to developing and testing Dunning’s framework, other expected contributions concerning research method and practical implications are mentioned.

A Popperian consilience : modelling mathematical knowledge and understanding

Goldin (2003) and McDonald, Yanchar, and Osguthorpe (2005) have called for mathematics learning theory that reconciles the chasm between ideologies, and which may advance mathematics teaching and learning practice. This paper discusses the theoretical underpinnings of a recently completed PhD study that draws upon Popper’s (1978) three-world model of knowledge as a lens through which to reconsider a variety of learning theories, including Piaget’s reflective abstraction. Based upon this consideration of theories, an alternative theoretical framework and complementary operational model was synthesised, the viability of which was demonstrated by its use to analyse the domain of early-number counting, addition and subtraction.

Young children's understandings about "square" in 3D virtual reality microworlds

This paper reports an investigation of primary school children’s understandings about "square". 12 students participated in a small group teaching experiment session, where they were interviewed and guided to construct a square in a 3D virtual reality learning environment (VRLE). Main findings include mixed levels of "quasi" geometrical understandings, misconceptions about length and angles, and ambiguous uses of geometrical language for location, direction, and movement. These have implications for future teaching and learning about 2D shapes with particular reference to VRLE.

Collision warning dissemination in vehicles strings : an empirical measurement

Inter-Vehicular Communications (IVC) are considered a promising technological approach for enhancing transportation safety and improving highway efficiency. Previous theoretical work has demonstrated the benefits of IVC in vehicles strings. Simulations of partially IVC-equipped vehicles strings showed that only a small equipment ratio is sufficient to drastically reduce the number of head on collisions. However, these results are based on the assumptions that IVC exhibit lossless and instantaneous messages transmission. This paper presents the research design of an empirical measurement of a vehicles string, with the goal of highlighting the constraints introduced by the actual characteristics of communication devices. A warning message diffusion system based on IEEE 802.11 wireless technology was developed for an emergency breaking scenario. Preliminary results are presented as well, showing the latencies introduced by using 802.11a and discussing early findings and experimental limitations

Towards testing a new first-order decision making model for the procurement of public sector major infrastructure

Given global demand for new infrastructure, governments face substantial challenges in funding new infrastructure and simultaneously delivering Value for Money (VfM). As background to this challenge, a brief review is given of current practice in the selection of major public sector infrastructure in Australia, along with a review of the related literature concerning the Multi-Attribute Utility Approach (MAUA) and the effect of MAUA on the role of risk management in procurement selection. To contribute towards addressing the key weaknesses of MAUA, a new first-order procurement decision making model is mentioned. A brief summary is also given of the research method and hypothesis used to test and develop the new procurement model and which uses competition as the dependent variable and as a proxy for VfM. The hypothesis is given as follows: When the actual procurement mode matches the theoretical/predicted procurement mode (informed by the new procurement model), then actual competition is expected to match optimum competition (based on actual prevailing capacity vis-à-vis the theoretical/predicted procurement mode) and subject to efficient tendering. The aim of this paper is to report on progress towards testing this hypothesis in terms of an analysis of two of the four data components in the hypothesis. That is, actual procurement and actual competition across 87 road and health major public sector projects in Australia. In conclusion, it is noted that the Global Financial Crisis (GFC) has seen a significant increase in competition in public sector major road and health infrastructure and if any imperfections in procurement and/or tendering are discernible, then this would create the opportunity, through the deployment of economic principles embedded in the new procurement model and/or adjustments in tendering, to maintain some of this higher level post-GFC competition throughout the next business cycle/upturn in demand including private sector demand. Finally, the paper previews the next steps in the research with regard to collection and analysis of data concerning theoretical/predicted procurement and optimum competition.

An evaluation of the pattern and structure mathematics awareness program in the early school years

This paper reports a 2-year longitudinal study on the effectiveness of the Pattern and Structure Mathematical Awareness Program (PASMAP) on students’ mathematical development. The study involved 316 Kindergarten students in 17 classes from four schools in Sydney and Brisbane. The development of the PASA assessment interview and scale are presented. The intervention program provided explicit instruction in mathematical pattern and structure that enhanced the development of students’ spatial structuring, multiplicative reasoning, and emergent generalisations. This paper presents the initial findings of the impact of the PASMAP and illustrates students’ structural development.

Developing the Pattern and Structure Assessment (PASA) interview to inform early mathematics learning

The Pattern and Structure Mathematical Awareness Program(PASMAP) stems from a 2-year longitudinal study on students’ early mathematical development. The paper outlines the interview assessment the Pattern and Structure Assessment(PASA) designed to describe students’ awareness of mathematical pattern and structure across a range of concepts. An overview of students’ performance across items and descriptions of their structural development are described.

Meaningful engagement with music composition

Musical value cannot be experienced without direct knowledge of music, and engagement with the interactive elements of materials, expressive character and structure. Through these channels something is communicated, something is transmitted, some residue of ‘meaning’ is left with us. When a work of art stirs us it is more than simply sensory stimulation or some kind of emotional indulgence. We are gaining knowledge and expanding our experience... contributing to knowledge of ourselves and of the world.

The promise and possibilities of music, digital media and National Broadband Network

In this article I would like to examine the promise and possibilities of music, digital media and National Broadband Network. I will do this based on concepts that have emerged from a study undertaken by Professor Andrew Brown and I that categorise technologies into what we term representational technologies and technologies with agency

Supply chain sustainability : a relationship management approach moderated by culture and commitment

This paper explores the nature of relationship management on construction projects in Australia and examines the effects of culture, by means of Schwarz’s value survey, on relationships under different contract strategies. The research was based on the view that the development of a sustainable supply chain depends on the transfer of knowledge and capabilities from the larger players in the supply chain through collaboration brought about by relationship management. The research adopted a triangulated approach in which quantitative data were collected by questionnaire, interviews were conducted to explore and enrich the quantitative data and case studies were undertaken in order to illustrate and validate the fi ndings. The aim was to investigate how values and attitudes enhance or reduce the incorporation of the supply chain into the project. From the research it was found that the degree of match and mismatch between values and contract strategy impacts commitment and the engagement and empowerment of the supply chain.

Designerly analysis of a socio-physical design activity

The Making Design and Analysing Interaction track at the Participatory Innovation Conference calls for submissions from ‘Makers’ who will contribute examples of participatory innovation activities documented in video and ‘Analysts’ who will analyse those examples of participatory innovation activity. The aim of this paper is to open up for a discussion within the format of the track of the roles that designers could play in analysing the participatory innovation activities of others and to provide a starting point for this discussion through a concrete example of such ‘designerly analysis’. Designerly analysis opens new analytic frames for understanding participatory innovation and contributes to our understanding of design activities.