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.

A simplified mathematical model for urban microclimate simulation

Techniques for modelling urban microclimates and urban block surfaces temperatures are desired by urban planners and architects for strategic urban designs at the early design stages. This paper introduces a simplified mathematical model for urban simulations (UMsim) including urban surfaces temperatures and microclimates. The nodal network model has been developed by integrating coupled thermal and airflow model. Direct solar radiation, diffuse radiation, reflected radiation, long-wave radiation, heat convection in air and heat transfer in the exterior walls and ground within the complex have been taken into account. The relevant equations have been solved using the finite difference method under the Matlab platform. Comparisons have been conducted between the data produced from the simulation and that from an urban experimental study carried out in a real architectural complex on the campus of Chongqing University, China in July 2005 and January 2006. The results show a satisfactory agreement between the two sets of data. The UMsim can be used to simulate the microclimates, in particular the surface temperatures of urban blocks, therefore it can be used to assess the impact of urban surfaces properties on urban microclimates. The UMsim will be able to produce robust data and images of urban environments for sustainable urban design.

A novel scheme for human-friendly and time-delays robust neuropredictive teleoperation

A novel Neuropredictive Teleoperation (NPT) Scheme is presented. The design results from two key ideas: the exploitation of the measured or estimated neural input to the human arm or its electromyograph (EMG) as the system input and the employment of a predictor of the arm movement, based on this neural signal and an arm model, to compensate for time delays in the system. Although a multitude of such models, as well as measuring devices for the neural signals and the EMG, have been proposed, current telemanipulator research has only been considering highly simplified arm models. In the present design, the bilateral constraint that the master and slave are simultaneously compliant to each other's state (equal positions and forces) is abandoned, thus obtaining a simple to analyzesuccession of only locally controlled modules, and a robustness to time delays of up to 500 ms. The proposed designs were inspired by well established physiological evidence that the brain, rather than controlling the movement on-line, programs the arm with an action plan of a complete movement, which is then executed largely in open loop, regulated only by local reflex loops. As a model of the human arm the well-established Stark model is employed, whose mathematical representation is modified to make it suitable for an engineering application. The proposed scheme is however valid for any arm model. BIBO-stability and passivity results for a variety of local control laws are reported. Simulation results and comparisons with traditional designs also highlight the advantages of the proposed design.

Making the least active pay: a simulation of rewards and penalties under Demand Side Participation programs

The orthodox approach for incentivising Demand Side Participation (DSP) programs is that utility losses from capital, installation and planning costs should be recovered under financial incentive mechanisms which aim to ensure that utilities have the right incentives to implement DSP activities. The recent national smart metering roll-out in the UK implies that this approach needs to be reassessed since utilities will recover the capital costs associated with DSP technology through bills. This paper introduces a reward and penalty mechanism focusing on residential users. DSP planning costs are recovered through payments from those consumers who do not react to peak signals. Those consumers who do react are rewarded by paying lower bills. Because real-time incentives to residential consumers tend to fail due to the negligible amounts associated with net gains (and losses) or individual users, in the proposed mechanism the regulator determines benchmarks which are matched against responses to signals and caps the level of rewards/penalties to avoid market distortions. The paper presents an overview of existing financial incentive mechanisms for DSP; introduces the reward/penalty mechanism aimed at fostering DSP under the hypothesis of smart metering roll-out; considers the costs faced by utilities for DSP programs; assesses linear rate effects and value changes; introduces compensatory weights for those consumers who have physical or financial impediments; and shows findings based on simulation runs on three discrete levels of elasticity.

A mathematical approach to chemical equilibrium theory for gaseous systems—I: theory

Equilibrium theory occupies an important position in chemistry and it is traditionally based on thermodynamics. A novel mathematical approach to chemical equilibrium theory for gaseous systems at constant temperature and pressure is developed. Six theorems are presented logically which illustrate the power of mathematics to explain chemical observations and these are combined logically to create a coherent system. This mathematical treatment provides more insight into chemical equilibrium and creates more tools that can be used to investigate complex situations. Although some of the issues covered have previously been given in the literature, new mathematical representations are provided. Compared to traditional treatments, the new approach relies on straightforward mathematics and less on thermodynamics, thus, giving a new and complementary perspective on equilibrium theory. It provides a new theoretical basis for a thorough and deep presentation of traditional chemical equilibrium. This work demonstrates that new research in a traditional field such as equilibrium theory, generally thought to have been completed many years ago, can still offer new insights and that more efficient ways to present the contents can be established. The work presented here can be considered appropriate as part of a mathematical chemistry course at University level.

A mathematical approach to chemical equilibrium theory for gaseous systems—II: extensions and applications

Straightforward mathematical techniques are used innovatively to form a coherent theoretical system to deal with chemical equilibrium problems. For a systematic theory it is necessary to establish a system to connect different concepts. This paper shows the usefulness and consistence of the system by applications of the theorems introduced previously. Some theorems are shown somewhat unexpectedly to be mathematically correlated and relationships are obtained in a coherent manner. It has been shown that theorem 1 plays an important part in interconnecting most of the theorems. The usefulness of theorem 2 is illustrated by proving it to be consistent with theorem 3. A set of uniform mathematical expressions are associated with theorem 3. A variety of mathematical techniques based on theorems 1–3 are shown to establish the direction of equilibrium shift. The equilibrium properties expressed in initial and equilibrium conditions are shown to be connected via theorem 5. Theorem 6 is connected with theorem 4 through the mathematical representation of theorem 1.

The contributions of domain-general and numerical factors to third-grade arithmetic skills and mathematical learning disability

Explanations of the marked individual differences in elementary school mathematical achievement and mathematical learning disability (MLD or dyscalculia) have involved domain-general factors (working memory, reasoning, processing speed and oral language) and numerical factors that include single-digit processing efficiency and multi-digit skills such as number system knowledge and estimation. This study of third graders (N = 258) finds both domain-general and numerical factors contribute independently to explaining variation in three significant arithmetic skills: basic calculation fluency, written multi-digit computation, and arithmetic word problems. Estimation accuracy and number system knowledge show the strongest associations with every skill and their contributions are both independent of each other and other factors. Different domain-general factors independently account for variation in each skill. Numeral comparison, a single digit processing skill, uniquely accounts for variation in basic calculation. Subsamples of children with MLD (at or below 10th percentile, n = 29) are compared with low achievement (LA, 11th to 25th percentiles, n = 42) and typical achievement (above 25th percentile, n = 187). Examination of these and subsets with persistent difficulties supports a multiple deficits view of number difficulties: most children with number difficulties exhibit deficits in both domain-general and numerical factors. The only factor deficit common to all persistent MLD children is in multi-digit skills. These findings indicate that many factors matter but multi-digit skills matter most in third grade mathematical achievement.

Nutrient-limited toxin production and the dynamics of two phytoplankton in culture media: a mathematical model

In this paper we have proposed and analyzed a simple mathematical model consisting of four variables, viz., nutrient concentration, toxin producing phytoplankton (TPP), non-toxic phytoplankton (NTP), and toxin concentration. Limitation in the concentration of the extracellular nutrient has been incorporated as an environmental stress condition for the plankton population, and the liberation of toxic chemicals has been described by a monotonic function of extracellular nutrient. The model is analyzed and simulated to reproduce the experimental findings of Graneli and Johansson [Graneli, E., Johansson, N., 2003. Increase in the production of allelopathic Prymnesium parvum cells grown under N- or P-deficient conditions. Harmful Algae 2, 135–145]. The robustness of the numerical experiments are tested by a formal parameter sensitivity analysis. As the first theoretical model consistent with the experiment of Graneli and Johansson (2003), our results demonstrate that, when nutrient-deficient conditions are favorable for the TPP population to release toxic chemicals, the TPP species control the bloom of other phytoplankton species which are non-toxic. Consistent with the observations made by Graneli and Johansson (2003), our model overcomes the limitation of not incorporating the effect of nutrient-limited toxic production in several other models developed on plankton dynamics.

Do IMF and World Bank programs induce government crises? an empirical analysis

We examine whether and under what circumstances World Bank and International Monetary Fund (IMF) programs affect the likelihood of major government crises. We find that crises are, on average, more likely as a consequence of World Bank programs. We also find that governments face an increasing risk of entering a crisis when they remain under an IMF or World Bank arrangement once the economy's performance improves. The international financial institution's (IFI) scapegoat function thus seems to lose its value when the need for financial support is less urgent. While the probability of a crisis increases when a government turns to the IFIs, programs inherited by preceding governments do not affect the probability of a crisis. This is in line with two interpretations. First, the conclusion of IFI programs can signal the government's incompetence, and second, governments that inherit programs might be less likely to implement program conditions agreed to by their predecessors.

A mathematical model of crystallization in an emulsion

A mathematical model incorporating many of the important processes at work in the crystallization of emulsions is presented. The model describes nucleation within the discontinuous domain of an emulsion, precipitation in the continuous domain, transport of monomers between the two domains, and formation and subsequent growth of crystals in both domains. The model is formulated as an autonomous system of nonlinear, coupled ordinary differential equations. The description of nucleation and precipitation is based upon the Becker–Döring equations of classical nucleation theory. A particular feature of the model is that the number of particles of all species present is explicitly conserved; this differs from work that employs Arrhenius descriptions of nucleation rate. Since the model includes many physical effects, it is analyzed in stages so that the role of each process may be understood. When precipitation occurs in the continuous domain, the concentration of monomers falls below the equilibrium concentration at the surface of the drops of the discontinuous domain. This leads to a transport of monomers from the drops into the continuous domain that are then incorporated into crystals and nuclei. Since the formation of crystals is irreversible and their subsequent growth inevitable, crystals forming in the continuous domain effectively act as a sink for monomers “sucking” monomers from the drops. In this case, numerical calculations are presented which are consistent with experimental observations. In the case in which critical crystal formation does not occur, the stationary solution is found and a linear stability analysis is performed. Bifurcation diagrams describing the loci of stationary solutions, which may be multiple, are numerically calculated.