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.

Collective dynamics and control of a 3-D small-world network with time delays

The paper presents a detailed analysis on the collective dynamics and delayed state feedback control of a three-dimensional delayed small-world network. The trivial equilibrium of the model is first investigated, showing that the uncontrolled model exhibits complicated unbounded behavior. Then three control strategies, namely a position feedback control, a velocity feedback control, and a hybrid control combined velocity with acceleration feedback, are then introduced to stabilize this unstable system. It is shown in these three control schemes that only the hybrid control can easily stabilize the 3-D network system. And with properly chosen delay and gain in the delayed feedback path, the hybrid controlled model may have stable equilibrium, or periodic solutions resulting from the Hopf bifurcation, or complex stranger attractor from the period-doubling bifurcation. Moreover, the direction of Hopf bifurcation and stability of the bifurcation periodic solutions are analyzed. The results are further extended to any "d" dimensional network. It shows that to stabilize a "d" dimensional delayed small-world network, at least a "d – 1" order completed differential feedback is needed. This work provides a constructive suggestion for the high dimensional delayed systems.

Discrete phase-locked loop systems and spreadsheets

This paper demonstrates the use of a spreadsheet in exploring non-linear difference equations that describe digital control systems used in radio engineering, communication and computer architecture. These systems, being the focus of intensive studies of mathematicians and engineers over the last 40 years, may exhibit extremely complicated behaviour interpreted in contemporary terms as transition from global asymptotic stability to chaos through period-doubling bifurcations. The authors argue that embedding advanced mathematical ideas in the technological tool enables one to introduce fundamentals of discrete control systems in tertiary curricula without learners having to deal with complex machinery that rigorous mathematical methods of investigation require. In particular, in the appropriately designed spreadsheet environment, one can effectively visualize a qualitative difference in the behviour of systems with different types of non-linear characteristic.

Onset of transition in mixed convection of a lid-driven trapezoidal enclosure filled with water-Al2O3 nanofluid

A numerical study is carried out to investigate the transition from laminar to chaos in mixed convection heat transfer inside a lid-driven trapezoidal enclosure. In this study, the top wall is considered as isothermal cold surface, which is moving in its own plane at a constant speed, and a constant high temperature is provided at the bottom surface. The enclosure is assumed to be filled with water-Al2O3 nanofluid. The governing Navier–Stokes and thermal energy equations are expressed in non-dimensional forms and are solved using Galerkin finite element method. Attention is paid in the present study on the pure mixed convection regime at Richandson number, Ri = 1. The numerical simulations are carried out over a wide range of Reynolds (0.1 ≤ Re ≤ 103) and Grashof (0.01 ≤ Gr ≤ 106) numbers. Effects of the presence of nanofluid on the characteristics of mixed convection heat transfer are also explored. The average Nusselt numbers of the heated wall are computed to demonstrate the influence of flow parameter variations on heat transfer. The corresponding change of flow and thermal fields is visualized from the streamline and the isotherm contour plots.

Controlling chaos? The value and the challenges of applying complexity theory to project management

The literature abounds with descriptions of failures in high-profile projects and a range of initiatives has been generated to enhance project management practice (e.g., Morris, 2006). Estimating from our own research, there are scores of other project failures that are unrecorded. Many of these failures can be explained using existing project management theory; poor risk management, inaccurate estimating, cultures of optimism dominating decision making, stakeholder mismanagement, inadequate timeframes, and so on. Nevertheless, in spite of extensive discussion and analysis of failures and attention to the presumed causes of failure, projects continue to fail in unexpected ways. In the 1990s, three U.S. state departments of motor vehicles (DMV) cancelled major projects due to time and cost overruns and inability to meet project goals (IT-Cortex, 2010). The California DMV failed to revitalize their drivers’ license and registration application process after spending $45 million. The Oregon DMV cancelled their five year, $50 million project to automate their manual, paper-based operation after three years when the estimates grew to $123 million; its duration stretched to eight years or more and the prototype was a complete failure. In 1997, the Washington state DMV cancelled their license application mitigation project because it would have been too big and obsolete by the time it was estimated to be finished. There are countless similar examples of projects that have been abandoned or that have not delivered the requirements.

Finding order in chaos : a problem based collaborative assignment for 1300 students across 19 disciplines

The use of collaborative assignments for assessment is a risky undertaking for students and course designers. Yet the benefits, in terms of core learning outcomes, competencies, collaborative sense making and student involvement, suggest that the effort is worthwhile. Formal descriptions and rules do little to ameliorate the perception of risk and increased anxiety by students. (Ryan, 2007). BEB100 Introducing Professional Learning is a faculty-wide foundation unit with over 1300 students from 19 disciplines across the Faculty of the Built Environment and Engineering (“BEE”) at the Queensland University of Technology (“QUT”), Brisbane, Australia. Finding order in chaos outlines the approach and justification, assessment criteria, learning resources, teamwork tools, tutorial management, communication strategies, 2007-09 Student Learning Experience Survey results, annual improvements, findings and outcomes.

Guided chaos : path planning and control for a UAV-forced landing

In recent years, unmanned aerial vehicles (UAVs) have been widely used in combat, and their potential applications in civil and commercial roles are also receiving considerable attention by industry and the research community. There are numerous published reports of UAVs used in Earth science missions [1], fire-fighting [2], and border security [3] trials, with other speculative deployments, including applications in agriculture, communications, and traffic monitoring. However, none of these UAVs can demonstrate an equivalent level of safety to manned aircraft, particularly in the case of an engine failure, which would require an emergency or forced landing. This may be arguably the main factor that has prevented these UAV trials from becoming full-scale commercial operations, as well as restricted operations of civilian UAVs to only within segregated airspace.

Crossing boundaries to explore sustainable architecture by open system design

This paper argues a model of open system design for sustainable architecture, based on a thermodynamics framework of entropy as an evolutionary paradigm. The framework can be simplified to stating that an open system evolves in a non-linear pattern from a far-from-equilibrium state towards a non-equilibrium state of entropy balance, which is a highly ordered organization of the system when order comes out of chaos. This paper is work in progress on a PhD research project which aims to propose building information modelling for optimization and adaptation of buildings environmental performance as an alternative sustainable design program in architecture. It will be used for efficient distribution and consumption of energy and material resource in life-cycle buildings, with the active involvement of the end-users and the physical constraints of the natural environment.

Natural convection and heat transfer in attics subject to periodic thermal forcing

The heat transfer through the attics of buildings under realistic thermal forcing has been considered in this study. A periodic temperature boundary condition is applied on the sloping walls of the attic to show the basic flow features in the attic space over diurnal cycles. The numerical results reveal that, during the daytime heating stage, the flow in the attic space is stratified; whereas at the night-time cooling stage, the flow becomes unstable. A symmetrical solution is seen for relatively low Rayleigh numbers. However, as the Ra gradually increases, a transition occurs at a critical value of Ra. Above this critical value, an asymmetrical solution exhibiting a pitchfork bifurcation arises at the night-time. It is also found that the calculated heat transfer rate at the night-time cooling stage is much higher than that during the daytime heating stage.

Cultural chaos : Journalism, News and Power in a Globalised World

With examples drawn from media coverage of the War on Terror, the 2003 invasion of Iraq, Hurricane Katrina and the London underground bombings, Cultural Chaos explores the changing relationship between journalism and power in an increasingly globalised news culture. In this new text, Brian McNair examines the processes of cultural, geographic and political dissolution in the post-Cold War era and the rapid evolution of information and communication technologies. He investigates the impact of these trends on domestic and international journalism and on political processes in democratic and authoritarian societies across the world. Written in a lively and accessible style, Cultural Chaos provides students with an overview of the evolution of the sociology of journalism, a critical review of current thinking within media studies and an argument for a revision and renewal of the paradigms that have dominated the field since the early twentieth century. Separate chapters are devoted to new developments such as the rise of the blogosphere and satellite television news and their impact on journalism more generally. Cultural Chaos will be essential reading for all those interested in the emerging globalised news culture of the twenty-first century.

Chaos or complex systems? Identifying factors influencing the success of international and NESB graduate research students in Engineering and Information Technology Fields

The paper explores the results an on-going research project to identify factors influencing the success of international and non-English speaking background (NESB) gradúate students in the fields of Engineering and IT at three Australian universities: the Queensland University of Technology (QUT), the University of Western Australia (UWA), and Curtin University (CU). While the larger study explores the influence of factors from both sides of the supervision equation (e.g., students and supervisors), this paper focusses primarily on the results of an online survey involving 227 international and/or NESB graduate students in the areas of Engineering and IT at the three universities. The study reveals cross-cultural differences in perceptions of student and supervisor roles, as well as differences in the understanding of the requirements of graduate study within the Australian Higher Education context. We argue that in order to assist international and NESB research students to overcome such culturally embedded challenges, it is important to develop a model which recognizes the complex interactions of factors from both sides of the supervision relationship, in order to understand this cohort‟s unique pedagogical needs and develop intercultural sensitivity within postgraduate research supervision.

The uses of satire : unorthodox news, cultural chaos and the interrogation of power

This article focuses on the satirical Australian show The Chaser’s War on Everything, and uses it to critically assess the potential political and social ramifications of what McNair (2006) has called ‘cultural chaos’. Drawing upon and analysing several examples from this particular program, alongside interviews with its production team and qualitative audience research, this article argues that this TV show’s engagement with politicians and political issues, in a way that departs from the conventions of traditional journalism, offers a significant opportunity for the interrogation of power. The program’s use of often bizarre and unexpected comedic confrontation allows it to present a perhaps more authentic image of political agents than is often cultivated in mainstream journalism. This suggests therefore that the shift from homogeneity to heterogeneity in the news media – which McNair (2006) sees as a key feature of cultural chaos – presents a significant challenge to those who wish to retain control over what the public sees and understands about the political world, and is a development which should be viewed in positive terms.

Enlightenment out of chaos : power, politics and The Chaser’s War on Everything

This paper focuses on the satirical Australian television show The Chaser’s War on Everything, and uses it to critically explore the potential ramifications of what McNair (2006) has called ‘cultural chaos’. Through an analysis of several examples from this particular program, alongside interviews with its production team and qualitative audience research, this paper argues that this TV show’s engagement with political issues in a creative, entertaining way that departs from the conventions of traditional journalism, allows it to present a perhaps more authentic image of political agents than is often cultivated in the mainstream news media. This paper therefore provides clear evidence that the shift from homogeneity to heterogeneity in the news media presents a significant challenge to those who wish to heavily control public opinion. It also provides further support for an optimistic re-appraisal of entertainment which emphasises its central (not merely periphery) role in political discourse.