Integration of chaos theory and mathematical models in building simulation: Part I: Literature review

Current mathematical models in building research have been limited in most studies to linear dynamics systems. A literature review of past studies investigating chaos theory approaches in building simulation models suggests that as a basis chaos model is valid and can handle the increasingly complexity of building systems that have dynamic interactions among all the distributed and hierarchical systems on the one hand, and the environment and occupants on the other. The review also identifies the paucity of literature and the need for a suitable methodology of linking chaos theory to mathematical models in building design and management studies. This study is broadly divided into two parts and presented in two companion papers. Part (I) reviews the current state of the chaos theory models as a starting point for establishing theories that can be effectively applied to building simulation models. Part (II) develops conceptual frameworks that approach current model methodologies from the theoretical perspective provided by chaos theory, with a focus on the key concepts and their potential to help to better understand the nonlinear dynamic nature of built environment systems. Case studies are also presented which demonstrate the potential usefulness of chaos theory driven models in a wide variety of leading areas of building research. This study distills the fundamental properties and the most relevant characteristics of chaos theory essential to building simulation scientists, initiates a dialogue and builds bridges between scientists and engineers, and stimulates future research about a wide range of issues on building environmental systems.

Integration of chaos theory and mathematical models in building simulation: Part II: Conceptual frameworks

Current mathematical models in building research have been limited in most studies to linear dynamics systems. A literature review of past studies investigating chaos theory approaches in building simulation models suggests that as a basis chaos model is valid and can handle the increasing complexity of building systems that have dynamic interactions among all the distributed and hierarchical systems on the one hand, and the environment and occupants on the other. The review also identifies the paucity of literature and the need for a suitable methodology of linking chaos theory to mathematical models in building design and management studies. This study is broadly divided into two parts and presented in two companion papers. Part (I), published in the previous issue, reviews the current state of the chaos theory models as a starting point for establishing theories that can be effectively applied to building simulation models. Part (II) develop conceptual frameworks that approach current model methodologies from the theoretical perspective provided by chaos theory, with a focus on the key concepts and their potential to help to better understand the nonlinear dynamic nature of built environment systems. Case studies are also presented which demonstrate the potential usefulness of chaos theory driven models in a wide variety of leading areas of building research. This study distills the fundamental properties and the most relevant characteristics of chaos theory essential to (1) building simulation scientists and designers (2) initiating a dialogue between scientists and engineers, and (3) stimulating future research on a wide range of issues involved in designing and managing building environmental systems.

Quantifying chaos: a tale of two maps

In many applications, there is a desire to determine if the dynamics of interest are chaotic or not. Since positive Lyapunov exponents are a signature for chaos, they are often used to determine this. Reliable estimates of Lyapunov exponents should demonstrate evidence of convergence; but literature abounds in which this evidence lacks. This paper presents two maps through which it highlights the importance of providing evidence of convergence of Lyapunov exponent estimates. The results suggest cautious conclusions when confronted with real data. Moreover, the maps are interesting in their own right.

The chaos machine: analogue computing rediscovered (1)

Analogue computers provide actual rather than virtual representations of model systems. They are powerful and engaging computing machines that are cheap and simple to build. This two-part Retronics article helps you build (and understand!) your own analogue computer to simulate the Lorenz butterfly that's become iconic for Chaos theory.

Chaos in high performance digital robot controllers

Active robot force control requires some form of dynamic inner loop control for stability. The author considers the implementation of position-based inner loop control on an industrial robot fitted with encoders only. It is shown that high gain velocity feedback for such a robot, which is effectively stationary when in contact with a stiff environment, involves problems beyond the usual caveats on the effects of unknown environment stiffness. It is shown that it is possible for the controlled joint to become chaotic at very low velocities if encoder edge timing data are used for velocity measurement. The results obtained indicate that there is a lower limit on controlled velocity when encoders are the only means of joint measurement. This lower limit to speed is determined by the desired amount of loop gain, which is itself determined by the severity of the nonlinearities present in the drive system.

Chaos of Wolbachia Sequences Inside the Compact Fig Syconia of Ficus benjamina (Ficus: Moraceae)

Figs and fig wasps form a peculiar closed community in which the Ficus tree provides a compact syconium (inflorescence) habitat for the lives of a complex assemblage of Chalcidoid insects. These diverse fig wasp species have intimate ecological relationships within the closed world of the fig syconia. Previous surveys of Wolbachia, maternally inherited endosymbiotic bacteria that infect vast numbers of arthropod hosts, showed that fig wasps have some of the highest known incidences of Wolbachia amongst all insects. We ask whether the evolutionary patterns of Wolbachia sequences in this closed syconium community are different from those in the outside world. In the present study, we sampled all 17 fig wasp species living on Ficus benjamina, covering 4 families, 6 subfamilies, and 8 genera of wasps. We made a thorough survey of Wolbachia infection patterns and studied evolutionary patterns in wsp (Wolbachia Surface Protein) sequences. We find evidence for high infection incidences, frequent recombination between Wolbachia strains, and considerable horizontal transfer, suggesting rapid evolution of Wolbachia sequences within the syconium community. Though the fig wasps have relatively limited contact with outside world, Wolbachia may be introduced to the syconium community via horizontal transmission by fig wasps species that have winged males and visit the syconia earlier.

Chaos, culture and fantasy: The television plays of Howard Schuman

The single plays of American ex-pat playwright Howard Schuman produced for British television between 1973 and 1983 have received little critical attention. Written in a distinctly un-British madcap, non-naturalistic and often pulpy 'B movie' style, they centre around caricatured, hysterical and/or camp characters and make frequent references to popular culture. This article provides a general survey of Schuman's plays and analyses his sensibility as a screenwriter, drawing extensively on material from interviews with the writer. The article's particular focus is how and why different cultural forms including music, film and theatre are used and referred to in Schuman's plays, and how this conditions the plays' narrative content and visual and aural form. It also considers the reception of Schuman's plays and their status as non-naturalistic dramas that engage heavily with American pop culture, within the context of British drama. Finally, it explores the writer's relationship to style and aesthetics, and considers how his written works have been enhanced through creative design decisions, comparing his directions (in one of his scripts) with the realized play to reflect on the use of key devices.

Chaos in foreign exchange markets: a sceptical view

This paper tests directly for deterministic chaos in a set of ten daily Sterling-denominated exchange rates by calculating the largest Lyapunov exponent. Although in an earlier paper, strong evidence of nonlinearity has been shown, chaotic tendencies are noticeably absent from all series considered using this state-of-the-art technique. Doubt is cast on many recent papers which claim to have tested for the presence of chaos in economic data sets, based on what are argued here to be inappropriate techniques.

Suppressing grazing chaos in impacting system by structural nonlinearity

In this note we investigate the influence of structural nonlinearity of a simple cantilever beam impacting system on its dynamic responses close to grazing incidence by a means of numerical simulation. To obtain a clear picture of this effect we considered two systems exhibiting impacting motion, where the primary stiffness is either linear (piecewise linear system) or nonlinear (piecewise nonlinear system). Two systems were studied by constructing bifurcation diagrams, basins of attractions, Lyapunov exponents and parameter plots. In our analysis we focused on the grazing transitions from no impact to impact motion. We observed that the dynamic responses of these two similar systems are qualitatively different around the grazing transitions. For the piecewise linear system, we identified on the parameter space a considerable region with chaotic behaviour, while for the piecewise nonlinear system we found just periodic attractors. We postulate that the structural nonlinearity of the cantilever impacting beam suppresses chaos near grazing. (C) 2007 Elsevier Ltd. All rights reserved.

Low-dimensional chaos and wave turbulence in plasmas

We investigated drift-wave turbulence in the plasma edge of a small tokamak by considering solutions of the Hasegawa-Mima equation involving three interacting modes in Fourier space. The resulting low-dimensional dynamics presented periodic as well as chaotic evolution of the Fourier-mode amplitudes, and we performed the control of chaotic behaviour through the application of a fourth resonant wave of small amplitude.

Control and chaos for vibro-impact and non-ideal oscillators

In the paper, we discuss dynamics of two kinds of mechanical systems. Initially, we consider vibro-impact systems which have many implementations in applied mechanics, ranging from drilling machinery and metal cutting processes to gear boxes. Moreover, from the point of view of dynamical systems, vibro-impact systems exhibit a rich variety of phenomena, particularly chaotic motion. In this paper, we review recent works on the dynamics of vibro-impact systems, focusing on chaotic motion and its control. The considered systems are a gear-rattling model and a smart damper to suppress chaotic motion. Furthermore, we investigate systems with non-ideal energy source, represented by a limited power supply. As an example of a non-ideal system, we analyse chaotic dynamics of the damped Duffing oscillator coupled to a rotor. Then, we show how to use a tuned liquid damper to control the attractors of this non-ideal oscillator.

Financial time series analysis : Chaos and neurodynamics approach

This work aims at combining the Chaos theory postulates and Artificial Neural Networks classification and predictive capability, in the field of financial time series prediction. Chaos theory, provides valuable qualitative and quantitative tools to decide on the predictability of a chaotic system. Quantitative measurements based on Chaos theory, are used, to decide a-priori whether a time series, or a portion of a time series is predictable, while Chaos theory based qualitative tools are used to provide further observations and analysis on the predictability, in cases where measurements provide negative answers. Phase space reconstruction is achieved by time delay embedding resulting in multiple embedded vectors. The cognitive approach suggested, is inspired by the capability of some chartists to predict the direction of an index by looking at the price time series. Thus, in this work, the calculation of the embedding dimension and the separation, in Takens‘ embedding theorem for phase space reconstruction, is not limited to False Nearest Neighbor, Differential Entropy or other specific method, rather, this work is interested in all embedding dimensions and separations that are regarded as different ways of looking at a time series by different chartists, based on their expectations. Prior to the prediction, the embedded vectors of the phase space are classified with Fuzzy-ART, then, for each class a back propagation Neural Network is trained to predict the last element of each vector, whereas all previous elements of a vector are used as features.