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.

Measuring motion with kinematically redundant accelerometer arrays: theory, simulation and implementation

This work presents two schemes of measuring the linear and angular kinematics of a rigid body using a kinematically redundant array of triple-axis accelerometers with potential applications in biomechanics. A novel angular velocity estimation algorithm is proposed and evaluated that can compensate for angular velocity errors using measurements of the direction of gravity. Analysis and discussion of optimal sensor array characteristics are provided. A damped 2 axis pendulum was used to excite all 6 DoF of the a suspended accelerometer array through determined complex motion and is the basis of both simulation and experimental studies. The relationship between accuracy and sensor redundancy is investigated for arrays of up to 100 triple axis (300 accelerometer axes) accelerometers in simulation and 10 equivalent sensors (30 accelerometer axes) in the laboratory test rig. The paper also reports on the sensor calibration techniques and hardware implementation.

E-commerce system simulation for construction and demolition waste exchange

This article introduces a quantitative approach to e-commerce system evaluation based on the theory of process simulation. The general concept of e-commerce system simulation is presented based on the considerations of some limitations in e-commerce system development such as the huge amount of initial investments of time and money, and the long period from business planning to system development, then to system test and operation, and finally to exact return; in other words, currently used system analysis and development method cannot tell investors about some keen attentions such as how good their e-commerce system could be, how many investment repayments they could have, and which area they should improve regarding the initial business plan. In order to exam the value and its potential effects of an e-commerce business plan, it is necessary to use a quantitative evaluation approach and the authors of this article believe that process simulation is an appropriate option. The overall objective of this article is to apply the theory of process simulation to e-commerce system evaluation, and the authors will achieve this though an experimental study on a business plan for online construction and demolition waste exchange. The methodologies adopted in this article include literature review, system analysis and development, simulation modelling and analysis, and case study. The results from this article include the concept of e-commerce system simulation, a comprehensive review of simulation methods adopted in e-commerce system evaluation, and a real case study of applying simulation to e-commerce system evaluation. Furthermore, the authors hope that the adoption and implementation of the process simulation approach can effectively support business decision-making, and improve the efficiency of e-commerce systems.

A perspective on chaos theory: Potential applications to intelligent buildings

Mathematical models have been vitally important in the development of technologies in building engineering. A literature review identifies that linear models are the most widely used building simulation models. The advent of intelligent buildings has added new challenges in the application of the existing models as an intelligent building requires learning and self-adjusting capabilities based on environmental and occupants' factors. It is therefore argued that the linearity is an impropriate basis for any model of either complex building systems or occupant behaviours for control or whatever purpose. Chaos and complexity theory reflects nonlinear dynamic properties of the intelligent systems excised by occupants and environment and has been used widely in modelling various engineering, natural and social systems. It is proposed that chaos and complexity theory be applied to study intelligent buildings. This paper gives a brief description of chaos and complexity theory and presents its current positioning, recent developments in building engineering research and future potential applications to intelligent building studies, which provides a bridge between chaos and complexity theory and intelligent building research.

A micro-level simulation for the prediction of intention and behaviour

In this contribution we aim at anchoring Agent-Based Modeling (ABM) simulations in actual models of human psychology. More specifically, we apply unidirectional ABM to social psychological models using low level agents (i.e., intra-individual) to examine whether they generate better predictions, in comparison to standard statistical approaches, concerning the intentions of performing a behavior and the behavior. Moreover, this contribution tests to what extent the predictive validity of models of attitude such as the Theory of Planned Behavior (TPB) or Model of Goal-directed Behavior (MGB) depends on the assumption that peoples’ decisions and actions are purely rational. Simulations were therefore run by considering different deviations from rationality of the agents with a trembling hand method. Two data sets concerning respectively the consumption of soft drinks and physical activity were used. Three key findings emerged from the simulations. First, compared to standard statistical approach the agent-based simulation generally improves the prediction of behavior from intention. Second, the improvement in prediction is inversely proportional to the complexity of the underlying theoretical model. Finally, the introduction of varying degrees of deviation from rationality in agents’ behavior can lead to an improvement in the goodness of fit of the simulations. By demonstrating the potential of ABM as a complementary perspective to evaluating social psychological models, this contribution underlines the necessity of better defining agents in terms of psychological processes before examining higher levels such as the interactions between individuals.

A simple analysis of thermodynamic properties for classical plasmas: I. theory

By eliminating the short range negative divergence of the Debye–Hückel pair distribution function, but retaining the exponential charge screening known to operate at large interparticle separation, the thermodynamic properties of one-component plasmas of point ions or charged hard spheres can be well represented even in the strong coupling regime. Predicted electrostatic free energies agree within 5% of simulation data for typical Coulomb interactions up to a factor of 10 times the average kinetic energy. Here, this idea is extended to the general case of a uniform ionic mixture, comprising an arbitrary number of components, embedded in a rigid neutralizing background. The new theory is implemented in two ways: (i) by an unambiguous iterative algorithm that requires numerical methods and breaks the symmetry of cross correlation functions; and (ii) by invoking generalized matrix inverses that maintain symmetry and yield completely analytic solutions, but which are not uniquely determined. The extreme computational simplicity of the theory is attractive when considering applications to complex inhomogeneous fluids of charged particles.

Formal theory building for the avalanche game: explaining counter-intuitive behaviour of a complex system using geometrical and human behavioural/physiological effects

In 'Avalanche', an object is lowered, players staying in contact throughout. Normally the task is easily accomplished. However, with larger groups counter-intuitive behaviours appear. The paper proposes a formal theory for the underlying causal mechanisms. The aim is to not only provide an explicit, testable hypothesis for the source of the observed modes of behaviour-but also to exemplify the contribution that formal theory building can make to understanding complex social phenomena. Mapping reveals the importance of geometry to the Avalanche game; each player has a pair of balancing loops, one involved in lowering the object, the other ensuring contact. For more players, sets of balancing loops interact and these can allow dominance by reinforcing loops, causing the system to chase upwards towards an ever-increasing goal. However, a series of other effects concerning human physiology and behaviour (HPB) is posited as playing a role. The hypothesis is therefore rigorously tested using simulation. For simplicity a 'One Degree of Freedom' case is examined, allowing all of the effects to be included whilst rendering the analysis more transparent. Formulation and experimentation with the model gives insight into the behaviours. Multi-dimensional rate/level analysis indicates that there is only a narrow region in which the system is able to move downwards. Model runs reproduce the single 'desired' mode of behaviour and all three of the observed 'problematic' ones. Sensitivity analysis gives further insight into the system's modes and their causes. Behaviour is seen to arise only when the geometric effects apply (number of players greater than degrees of freedom of object) in combination with a range of HPB effects. An analogy exists between the co-operative behaviour required here and various examples: conflicting strategic objectives in organizations; Prisoners' Dilemma and integrated bargaining situations. Additionally, the game may be relatable in more direct algebraic terms to situations involving companies in which the resulting behaviours are mediated by market regulations. Finally, comment is offered on the inadequacy of some forms of theory building and the case is made for formal theory building involving the use of models, analysis and plausible explanations to create deep understanding of social phenomena.

Chapter 4: Simulation of reaction injection moulding

Reaction Injection Moulding is a technology that enables the rapid production of complex plastic parts directly from a mixture of two reactive materials of low viscosity. The reactants are mixed in specific quantities and injected into a mould. This process allows large complex parts to be produced without the need for high clamping pressures. This chapter explores the simulation of the complex processes involved in reaction injection moulding. The reaction processes mean that the dynamics of the material in the mould are in constant evolution and an effective model which takes full account of these changing dynamics is introduced and incorporated in to finite element procedures, which are able to provide a complete simulation of the cycle of mould filling and subsequent curing.

Multi-agent based modeling and simulation of complex system in hospital

This study puts forward a method to model and simulate the complex system of hospital on the basis of multi-agent technology. The formation of the agents of hospitals with intelligent and coordinative characteristics was designed, the message object was defined, and the model operating mechanism of autonomous activities and coordination mechanism was also designed. In addition, the Ontology library and Norm library etc. were introduced using semiotic method and theory, to enlarge the method of system modelling. Swarm was used to develop the multi-agent based simulation system, which is favorable for making guidelines for hospital's improving it's organization and management, optimizing the working procedure, improving the quality of medical care as well as reducing medical charge costs.

A semiotic approach of multi-agent simulation for policy evaluation

Nowadays the changing environment becomes the main challenge for most of organizations, since they have to evaluate proper policies to adapt to the environment. In this paper, we propose a multi-agent simulation method to evaluate policies based on complex adaptive system theory. Furthermore, we propose a semiotic EDA (Epistemic, Deontic, Axiological) agent model to simulate agent's behavior in the system by incorporating the social norms reflecting the policy. A case study is also provided to validate our approach. Our research present better adaptability and validity than the qualitative analysis and experiment approach and the semiotic agent model provides high creditability to simulate agents' behavior.

DK-1D: a drift-kinetic simulation tool for modelling the shear Alfvén wave and its interaction with collisionless plasma

We present a highly accurate tool for the simulation of shear Alfven waves (SAW) in collisionless plasma. SAW are important in space plasma environments because for small perpendicular scale lengths they can support an electric field parallel to the ambient magnetic field. Electrons can be accelerated by the parallel electric field and these waves have been implicated as the source of vibrant auroral displays. However, the parallel electric field carried by SAW is small in comparison to the perpendicular electric field of the wave, making it difficult to measure directly in the laboratory, or by satellites in the near-Earth plasma environment. In this paper, we present a simulation code that provides a means to study in detail the SAW-particle interaction in both space and laboratory plasma. Using idealised, small-amplitude propagating waves with a single perpendicular wavenumber, the simulation code accurately reproduces the damping rates and parallel electric field amplitudes predicted by linear theory for varying temperatures and perpendicular scale lengths. We present a rigorous kinetic derivation of the parallel electric field strength for small-amplitude SAW and show that commonly-used inertial and kinetic approximations are valid except for where the ratio of thermal to Alfv\'{e}n speed is between 0.7 and 1.0. We also present nonlinear simulations of large-amplitude waves and show that in cases of strong damping, the damping rates and parallel electric field strength deviate from linear predictions when wave energies are greater than only a few percent of the plasma kinetic energy, a situation which is often observed in the magnetosphere. The drift-kinetic code provides reliable, testable predictions of the parallel electric field strength which can be investigated directly in the laboratory, and will help to bridge the gap between studies of SAW in man-made and naturally occuring plasma.

Cobalt incorporation in calcite: Thermochemistry of (Ca,Co)CO3 solid solutions from density functional theory simulations

The incorporation of cobalt in mixed metal carbonates is a possible route to the immobilization of this toxic element in the environment. However, the thermodynamics of (Ca,Co)CO3 solid solutions are still unclear due to conflicting data from experiment and from the observation of natural ocurrences. We report here the results of a computer simulation study of the mixing of calcite (CaCO3) and spherocobaltite (CoCO3), using density functional theory calculations. Our simulations suggest that previously proposed thermodynamic models, based only on the range of observed compositions, significantly overestimate the solubility between the two solids and therefore underestimate the extension of the miscibility gap under ambient conditions. The enthalpy of mixing of the disordered solid solution is strongly positive and moderately asymmetric: calcium incorporation in spherocobaltite is more endothermic than cobalt incorporation in calcite. Ordering of the impurities in (0001) layers is energetically favourable with respect to the disordered solid solution at low temperatures and intermediate compositions, but the ordered phase is still unstable to demixing. We calculate the solvus and spinodal lines in the phase diagram using a sub-regular solution model, and conclude that many Ca1-xCoxCO3 mineral solid solutions (with observed compositions of up to x=0.027, and above x=0.93) are metastable with respect to phase separation. We also calculate solid/aqueous distribution coefficients to evaluate the effect of the strong non-ideality of mixing on the equilibrium with aqueous solution, showing that the thermodynamically-driven incorporation of cobalt in calcite (and of calcium in spherocobaltite) is always very low, regardless of the Co/Ca ratio of the aqueous environment.