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.

The constrained compartmentalized knapsack problem: mathematical models and solution methods

The constrained compartmentalized knapsack problem can be seen as an extension of the constrained knapsack problem. However, the items are grouped into different classes so that the overall knapsack has to be divided into compartments, and each compartment is loaded with items from the same class. Moreover, building a compartment incurs a fixed cost and a fixed loss of the capacity in the original knapsack, and the compartments are lower and upper bounded. The objective is to maximize the total value of the items loaded in the overall knapsack minus the cost of the compartments. This problem has been formulated as an integer non-linear program, and in this paper, we reformulate the non-linear model as an integer linear master problem with a large number of variables. Some heuristics based on the solution of the restricted master problem are investigated. A new and more compact integer linear model is also presented, which can be solved by a branch-and-bound commercial solver that found most of the optimal solutions for the constrained compartmentalized knapsack problem. On the other hand, heuristics provide good solutions with low computational effort. (C) 2011 Elsevier BM. All rights reserved.

Quantitative microbial risk assessment models for consumption of raw vegetables irrigated with reclaimed water

Quantitative microbial risk assessment models for estimating the annual risk of enteric virus infection associated with consuming raw vegetables that have been overhead irrigated with nondisinfected secondary treated reclaimed water were constructed. We ran models for several different scenarios of crop type, viral concentration in effluent, and time since last irrigation event. The mean annual risk of infection was always less for cucumber than for broccoli, cabbage, or lettuce. Across the various crops, effluent qualities, and viral decay rates considered, the annual risk of infection ranged from 10–3 to 10–1 when reclaimed-water irrigation ceased 1 day before harvest and from 10–9 to 10–3 when it ceased 2 weeks before harvest. Two previously published decay coefficients were used to describe the die-off of viruses in the environment. For all combinations of crop type and effluent quality, application of the more aggressive decay coefficient led to annual risks of infection that satisfied the commonly propounded benchmark of ≤10–4, i.e., one infection or less per 10,000 people per year, providing that 14 days had elapsed since irrigation with reclaimed water. Conversely, this benchmark was not attained for any combination of crop and water quality when this withholding period was 1 day. The lower decay rate conferred markedly less protection, with broccoli and cucumber being the only crops satisfying the 10–4 standard for all water qualities after a 14-day withholding period. Sensitivity analyses on the models revealed that in nearly all cases, variation in the amount of produce consumed had the most significant effect on the total uncertainty surrounding the estimate of annual infection risk. The models presented cover what would generally be considered to be worst-case scenarios: overhead irrigation and consumption of vegetables raw. Practices such as subsurface, furrow, or drip irrigation and postharvest washing/disinfection and food preparation could substantially lower risks and need to be considered in future models, particularly for developed nations where these extra risk reduction measures are more common.

The conceptualisation of operational risk management models

Operational risk is evolving as a specialist field of risk management that must be practiced within all organisations, but currently has a particular relevance to banks. The Basel Committee on Banking Supervision has circulated a consultative paper which, if adopted by nation-state bank supervisors, will impose an operational risk capital charge on banks as part of a new Capital Accord. The definition of operational risk is wide-ranging and creates some unique issues related to the development of appropriate risk management models. This paper conceptualises two distinct operational risk management models; being a predictive model that will result in a known outcome upon its implementation, and a pre-emptive operational risk management model which prepares an organisation in the event that a future risk occurrence results in a disruption to critical business operations.

The conceptualisation of operational risk management models

Operational risk is evolving as a specialist field of risk management that must be practiced within all organisations, but currently has a particular relevance to banks. The Basel Committee on Banking Supervision has circulated a consultative paper which, if adopted by nation-state bank supervisors, will impose an operational risk capital charge on banks as part of a new Capital Accord. The definition of operational risk is wide-ranging and creates some unique issues related to the development of appropriate risk management models. This paper conceptualises two distinct operational risk management models; being a predictive model that will result in a known outcome upon its implementation, and a pre-emptive operational risk management model which prepares an organisation in the event that a future risk occurrence results in a disruption to critical business operations.

Deterministic versus stochastic quantitative microbial Risk Assessment models for wastewater irrigation of food crops

Reuse of wastewater to irrigate food crops is being practiced in many parts of the world and is becoming more commonplace as the competition for, and stresses on, freshwater resources intensify. But there are risks associated with wastewater irrigation, including the possibility of transmission of pathogens causing infectious disease, to both workers in the field and to consumers buying and eating produce irrigated with wastewater. To manage these risks appropriately we need objective and quantitative estimates of them. This is typically achieved through one of two modelling approaches: deterministic or stochastic. Each parameter in a deterministic model is represented by a single value, whereas in stochastic models probability functions are used. Stochastic models are theoretically superior because they account for variability and uncertainty, but they are computationally demanding and not readily accessible to water resource and public health managers. We constructed models to estimate risk of enteric virus infection arising from the consumption of wastewater-irrigated horticultural crops (broccoli, cucumber and lettuce), and compared the resultant levels of risk between the deterministic and stochastic approaches. Several scenarios were tested for each crop, accounting for different concentrations of enteric viruses and different lengths of environmental exposure (i.e. the time between the last irrigation event and harvest, when the viruses are liable to decay or inactivation). In most situations modelled the two approaches yielded similar estimates of risk (within 1 order-of-magnitude). The two methods diverged most markedly, up to around 2 orders-of-magnitude, when there was large uncertainty associated with the estimate of virus concentration and the exposure period was short (1 day). Therefore, in some circumstances deterministic modelling may offer water resource managers a pragmatic alternative to stochastic modelling, but its usefulness as a surrogate will depend upon the level of uncertainty in the model parameters.

Overview of risk prediction models in cardiovascular disease research

Many risk prediction models have been developed for cardiovascular diseases in different countries during the past three decades. However, there has not been consistent agreement regarding how to appropriately assess a risk prediction model, especially when new markers are added to an established risk prediction model. Researchers often use the area under the receiver operating characteristic curve (ROC) to assess the discriminatory ability of a risk prediction model. However, recent studies suggest that this method has serious limitations and cannot be the sole approach to evaluate the usefulness of a new marker in clinical and epidemiological studies. To overcome the shortcomings of this traditional method, new assessment methods have been proposed. The aim of this article is to overview various risk prediction models for cardiovascular diseases, to describe the receiver operating characteristic curve method and discuss some new assessment methods proposed recently. Some of the methods were illustrated with figures from a cardiovascular disease study in Australia.

Laboratory and non-laboratory-based risk prevention models for secondary prevention of cardiovascular disease : the LIPID study

Aims : The aims of this study were to examine whether risk prediction models for recurrent cardiovascular disease (CVD) events have prognostic value, and to particularly examine the performance of those models based on non-laboratory data. We also aimed to construct a risk chart based on the risk factors that showed the strongest relationship with CVD.

Methods and results : Cox proportional hazards models were used to calculate a risk score for each recurrent event in a CVD patient who was enrolled in a very large randomized controlled clinical trial. Patients were then classified into groups according to quintiles of their risk score. These risk models were validated by calibration and discrimination analyses based on data from patients recruited in New Zealand for the same study. Non-laboratory-based risk factors, such as age, sex, body mass index, smoking status, angina grade, history of myocardial infarction, revascularization, stroke, diabetes or hypertension and treatment with pravastatin, were found to be significantly associated with the risk of developing a recurrent CVD event. Patients who were classified into the medium and high-risk groups had two-fold and four-fold the risk of developing a CVD event compared with those in the low-risk group, respectively. The risk prediction models also fitted New Zealand data well after recalibration.

Conclusion : A simpler non-laboratory-based risk prediction model performed equally as well as the more comprehensive laboratory-based risk prediction models. The risk chart based on the further simplified Score Model may provide a useful tool for clinical cardiologists to assess an individual patient's risk for recurrent CVD events.

Deep bed filtration : mathematical models and observations

Numerous mathematical models have been developed to evaluate both initial and transient stage removal efficiency of deep bed filters. Microscopic models either using trajectory analysis or convective diffusion equations were used to compute the initial removal efficiency. These models predicted the removal efficiency under favorable filtration conditions quantitatively, but failed to predict the removal efficiency under unfavorable conditions. They underestimated the removal efficiency under unfavorable conditions. Thus, semi-empirical formulations were developed to compute initial removal efficiencies under unfavorable conditions. Also, correction for the adhesion of particles onto filter grains improved the results obtained for removal efficiency from the trajectory analysis. Macroscopic models were used to predict the transient stage removal efficiency of deep bed filters. The O’Melia and Ali1 model assumed that the particle removal is due to filter grains as well as the particles that are already deposited onto the filter grain. Thus, semi-empirical models were used to predict the ripening of filtration. Several modifications were made to the model developed by O’Melia and Ali to predict the deterioration of particle removal during the transient stages of filtration. Models considering the removal of particles under favorable conditions and the accumulation of charges on the filter grains during the transient stages were also developed. This article evaluates those models and their applicability under different operating conditions of filtration.

High rate filtration using buoyant medium : experiments and mathematical models

In this study, the high rate filtration system using buoyant medium of polypropylene or polystyrene was introduced with the study on its performance evaluation via: (i) specific surface coverage, (ii) ultimate specific deposit, (iii) blocking effect and (iv) particle detachment. The filter system was arranged in the downflow mode with an in-line flocculation. Experimental results obtained were analyzed using filtration models. This study showed that: (i) the specific surface coverage increased with the increase in the velocity; (ii) the ultimate specific deposit changed slightly at different filtration velocities and different flocculants; (iii) the blocking effect was significant in the transient stage removal of flocs; and (iv) the detachment model parameter was found to decrease with the increase in the adhesive force, Fad that acts on the flocs (above-micron size).

Mathematical models of generalized diffusion

We discuss in this paper equations describing processes involving non-linear and higher-order diffusion. We focus on a particular case (u(t) = 2 lambda (2)(uu(x))(x) + lambda (2)u(xxxx)), which is put into analogy with the KdV equation. A balance of nonlinearity and higher-order diffusion enables the existence of self-similar solutions, describing diffusive shocks. These shocks are continuous solutions with a discontinuous higher-order derivative at the shock front. We argue that they play a role analogous to the soliton solutions in the dispersive case. We also discuss several physical instances where such equations are relevant.

Mathematical models for Isoptera (Insecta) mound growth

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Test systems and mathematical models for transmission network expansion planning

The data of four networks that can be used in carrying out comparative studies with methods for transmission network expansion planning are given. These networks are of various types and different levels of complexity. The main mathematical formulations used in transmission expansion studies-transportation models, hybrid models, DC power flow models, and disjunctive models are also summarised and compared. The main algorithm families are reviewed-both analytical, combinatorial and heuristic approaches. Optimal solutions are not yet known for some of the four networks when more accurate models (e.g. The DC model) are used to represent the power flow equations-the state of the art with regard to this is also summarised. This should serve as a challenge to authors searching for new, more efficient methods.