University of Macau / Faculty of Science and Technology / Department of Mathematics

To estimate the propagation of light in tissue-like optical phantoms (fat emulsions), this thesis utilized the diffuse reflectance spectroscopy in combination with Monte Carlo simulations. A method for determining the two-parametric Gegenbauer-kernal phase function was utilized in order to accurately describe the diffuse reflectance from poly-dispersive scattering optical phantoms with small source-detector separations. The method includes the spectral collimated transmission, spatially resolved diffuse reflectance spectra (SRDR) and the inverse technique of matching spectra from Monte Carlo simulations to those measured. An absolute calibration method using polystyrene micro-spheres was utilized to estimate the relation between simulated and measured SRDR intensities. The phase function parameters were comparable with previous studies and were able to model measured spectra with good accuracy. Significant differences between the phase functions for homogenized milk and the nutritive fat emulsions were found.

Microbial growth is a major cause of Indoor Air Quality (IAQ) problems. The implications of mold growth range from unacceptable musty smells and defacement of interior finishes, to structural damage and adverse health effects, not to mention lengthy litigation processes. Mold is likely to occur when a favorable combination of humidity, temperature, and substrate nutrient are maintained long enough. As many modern buildings use products that increase the likelihood of molds (e.g., paper and wood based products), reported cases have increased in recent years. Despite decades of intensive research efforts to prevent mold, modern buildings continue to suffer from mold infestation. The main reason is that current prescriptive regulations focus on the control of relative humidity only. However, recent research has shown that mold occurrences are influenced by a multitude of parameters with complex physical interactions. The set of relevant building parameters includes physical properties of building components, aspects of building usage, certain materials, occupant behavior, cleaning regime, HVAC system components and their operation, and other. Mold occurs mostly as the unexpected result of an unforeseen combination of the uncertain building parameters. Current deterministic mold assessment studies fail to give conclusive results. These simulations are based on idealizations of the building and its use, and therefore unable to capture the effect of the random, situational, and sometimes idiosyncratic nature of building use and operation. The presented research takes a radically different approach, based on the assessment of the uncertainties of all parameters and their propagation through a mixed set of simulations using a Monte Carlo technique. This approach generates a mold risk distribution that reveals the probability of mold occurrence in selected trouble spots in a building. The approach has been tested on three building cases located in Miami and Atlanta. In all cases the new approach was able to show the circumstances under which the mold risk could increase substantially, leading to a set of clear specifications for remediation and, in for new designs, to A/E procurement methods that will significantly reduce any mold risk.

The impedance response of silicon carbide whisker-alumina composites is investigated utilizing novel stereological techniques along with a microstructural simulation. The stereological techniques developed allow for a measurement of the trivariate length, radius and orientation distribution of whiskers in the composite from measurements made on two-dimensional sectioning planes. The measured distributions are then utilized in a Monte Carlo simulation that predicts connectivity in the composite for a given volume fraction. It is assumed in the simulation that connectivity factors dominate the electrical response, not interfacial phenomena. The results of the simulation are compared with impedance spectra taken from real samples, and conclusions are drawn regarding the nature of the impedance response.

This research develops a framework to estimate the effective sample size of Global Positioning System (GPS) based panel surveys in urban travel behavior studies for a variety of planning purposes. Recent advances in GPS monitoring technologies have made it possible to implement panel surveys with lengths of weeks, months or even years. The many advantageous features of GPS-based panel surveys make such surveys attractive for travel behavior studies, but the higher cost of such surveys compared to conventional one-day or two-day paper diary surveys requires scrutiny at the sample size planning stage to ensure cost-effectiveness. The sample size analysis in this dissertation focuses on three major aspects in travel behavior studies: 1) to obtain reliable means for key travel behavior variables, 2) to conduct regression analysis on key travel behavior variables against explanatory variables such as demographic characteristics and seasonal factors, and 3) to examine impacts of a policy measure on travel behavior through before-and-after studies. The sample size analyses in this dissertation are based on the GPS data collected in the multi-year Commute Atlanta study. The sample size analysis with regard to obtaining reliable means for key travel behavior variables utilizes Monte Carlo re-sampling techniques to assess the trend of means against various sample size and survey length combinations. The basis for the framework and methods of sample size estimation related to regression analysis and before-and-after studies are derived from various sample size procedures based on the generalized estimating equation (GEE) method. These sample size procedures have been proposed for longitudinal studies in biomedical research. This dissertation adapts these procedures to the design of panel surveys for urban travel behavior studies with the information made available from the Commute Atlanta study. The findings from this research indicate that the required sample sizes should be much larger than the sample sizes in existing GPS-based panel surveys. This research recommends a desired range of sample sizes based on the objectives and survey lengths of urban travel behavior studies.

Unmanned Aerial Vehicles (UAVs) are the most dynamic growth sector of the aerospace industry today. The need to provide persistent intelligence, surveillance, and reconnaissance for military operations is driving the planned acquisition of over 5,000 UAVs over the next five years. The most pressing need is for quiet, small UAVs with endurance beyond what is capable with advanced batteries or small internal combustion propulsion systems. Fuel cell systems demonstrate high efficiency, high specific energy, low noise, low temperature operation, modularity, and rapid refuelability making them a promising enabler of the small, quiet, and persistent UAVs that military planners are seeking. Despite the perceived benefits, the actual near-term performance of fuel cell powered UAVs is unknown. Until the auto industry began spending billions of dollars in research, fuel cell systems were too heavy for useful flight applications. However, the last decade has seen rapid development with fuel cell gravimetric and volumetric power density nearly doubling every 2-3 years. As a result, a few design studies and demonstrator aircraft have appeared, but overall the design methodology and vehicles are still in their infancy. The design of fuel cell aircraft poses many challenges. Fuel cells differ fundamentally from combustion based propulsion in how they generate power and interact with other aircraft subsystems. As a result, traditional multidisciplinary analysis (MDA) codes are inappropriate. Building new MDAs is difficult since fuel cells are rapidly changing in design, and various competitive architectures exist for balance of plant, hydrogen storage, and all electric aircraft subsystems. In addition, fuel cell design and performance data is closely protected which makes validation difficult and uncertainty significant. Finally, low specific power and high volumes compared to traditional combustion based propulsion result in more highly constrained design spaces that are problematic for design space exploration. To begin addressing the current gaps in fuel cell aircraft development, a methodology has been developed to explore and characterize the near-term performance of fuel cell powered UAVs. The first step of the methodology is the development of a valid MDA. This is accomplished by using propagated uncertainty estimates to guide the decomposition of a MDA into key contributing analyses (CAs) that can be individually refined and validated to increase the overall accuracy of the MDA. To assist in MDA development, a flexible framework for simultaneously solving the CAs is specified. This enables the MDA to be easily adapted to changes in technology and the changes in data that occur throughout a design process. Various CAs that model a polymer electrolyte membrane fuel cell (PEMFC) UAV are developed, validated, and shown to be in agreement with hardware-in-the-loop simulations of a fully developed fuel cell propulsion system. After creating a valid MDA, the final step of the methodology is the synthesis of the MDA with an uncertainty propagation analysis, an optimization routine, and a chance constrained problem formulation. This synthesis allows an efficient calculation of the probabilistic constraint boundaries and Pareto frontiers that will govern the design space and influence design decisions relating to optimization and uncertainty mitigation. A key element of the methodology is uncertainty propagation. The methodology uses Systems Sensitivity Analysis (SSA) to estimate the uncertainty of key performance metrics due to uncertainties in design variables and uncertainties in the accuracy of the CAs. A summary of SSA is provided and key rules for properly decomposing a MDA for use with SSA are provided. Verification of SSA uncertainty estimates via Monte Carlo simulations is provided for both an example problem as well as a detailed MDA of a fuel cell UAV. Implementation of the methodology was performed on a small fuel cell UAV designed to carry a 2.2 kg payload with 24 hours of endurance. Uncertainty distributions for both design variables and the CAs were estimated based on experimental results and were found to dominate the design space. To reduce uncertainty and test the flexibility of the MDA framework, CAs were replaced with either empirical, or semi-empirical relationships during the optimization process. The final design was validated via a hardware-in-the loop simulation. Finally, the fuel cell UAV probabilistic design space was studied. A graphical representation of the design space was generated and the optima due to deterministic and probabilistic constraints were identified. The methodology was used to identify Pareto frontiers of the design space which were shown on contour plots of the design space. Unanticipated discontinuities of the Pareto fronts were observed as different constraints became active providing useful information on which to base design and development decisions.

Polymer chain microstructure, including characteristics such as molecular weight and branch length, can impact the end-use properties of the polymer. The assumptions contained in deterministic models prevent examination of the structure of individual polymer chains, so removal of these assumptions is necessary to gain insight into molecular-level mechanisms that determine chain microstructure. The work presented here uses a combination of stochastic and deterministic models to examine two significant mechanistic issues in free radical polymerization. The zero-one assumption concerning the number of radicals is often made for miniemulsion polymerization using oil-soluble initiators because of accelerated termination due to radical confinement. Although most of the initiator is present inside the particles, opposing viewpoints exist as to whether the locus of radical generation is the particle phase or the aqueous phase. A well-mixed kinetic Monte Carlo (KMC) model is used to simulate the molecular weight distribution and the results are compared to estimated molecular weights for several chain-stopping events, with the finding that the dominant nucleation mechanism varies with reaction temperature and particle size. Intramolecular chain transfer to polymer, or backbiting, is often assumed to produce only short-chain branches. Using a lattice KMC model, a cumulative distribution function (CDF) is obtained for branch lengths produced by backbiting. Implementation of the CDF in both a rate-equation model and the well-mixed KMC model shows that, for the butyl acrylate solution polymerization system used for comparison, backbiting is responsible for most of the branches, including long-chain branches, even though overlap of the polymer coils in the solution is predicted, a condition which would normally be expected to lead to significant intermolecular chain transfer to polymer. The well-mixed KMC model provides a more thorough analysis of chain microstructure while the rate-equation model is more computationally efficient.

Corporate Real Estate (CRE) investors are often confronted with a need for flexibility in buildings. They often embark on costly renovations to accommodate changing use requirements. When new needs arise, landlords and tenants often risk loss due to inability to easily switch to configurations that can meet those needs. The main cause for this problem is lack of a planning model that can allow buildings to easily evolve over time allowing decision-makers to hedge investment positions against risk due to uncertainty. The emergence of Real Options (RO) theory in the 1970's has led to debates in search of a better planning model for real projects. The success of RO application in building construction (BC) hinges on the development of models that can be used to assess economic performance of flexible design options (FDO) in building systems. For building interior spaces, there is currently no model that can value flexibility of partition systems. The purpose of this study is to present a model that can be used to value flexibility in mutually exclusive partition systems over a project's life span. The proposed model uses decision tree representation, stochastic forecasting and random sampling of decision-path scenarios to generate cumulative risk profiles of partition systems' life cycle costs with expected median value, standard deviation and variance to inform decision making under uncertainty. The research processes include: assumptions, decision-making structure for identification of uncertain variable, model representation, spreadsheet programming, Monte Carlo simulation, and validation. The model will enable application of RO "in" BC projects.

The emerging research issues in evidence-based healthcare decision-making and explosion of comparative effectiveness research (CER) are evident proof of the effort to thoroughly incorporate the rich data currently available within the system. The flexibility of Bayesian data mining techniques lends its strength to handle the challenging issues in the biomedical and health care domains. My research focuses primarily on Bayesian data mining techniques for non-traditional data in this domain, which includes, 1. Missing data: Matched-pair studies with fixed marginal totals with application to meta-analysis of dental sealants effectiveness. 2. Data with unusual distribution: Modeling spatial repeated measures with excess zeros and no covariates to estimate U.S. county level natural fluoride concentration. 3. Highly irregular data: Assess overall image regularity in complex wavelet domain to classify mammography image. The goal of my research is to strengthen the link from data to decisions. By using Bayesian data mining techniques including signal and image processing (wavelet analysis), hierarchical Bayesian modeling, clinical trials meta-analyses and spatial statistics, this thesis resolves challenging issues of how to incorporate data to improve the systems of health care and bio fields and ultimately benefit public health.

Achieving an understanding of the nature of monogenetic volcanic fields depends on identification of the spatial and temporal patterns of volcanism in these fields, and their relationships to structures mapped in the shallow crust and inferred in the deep crust and mantle through interpretation of geochemical, radiometric and geophysical data. We investigate the spatial and temporal distributions of volcanism in the Abu Monogenetic Volcano Group, Southwest Japan. E-W elongated volcano distribution, which is identified by a nonparametric kernel method, is found to be consistent with the spatial extent of P-wave velocity anomalies in the lower crust and upper mantle, supporting the idea that the spatial density map of volcanic vents reflects the geometry of a mantle diapir. Estimated basalt supply to the lower crust is constant. This observation and the spatial distribution of volcanic vents suggest stability of magma productivity and essentially constant two-dimensional size of the source mantle diapir. We mapped conduits, dike segments, and sills in the San Rafael sub-volcanic field, Utah, where the shallowest part of a Pliocene magmatic system is exceptionally well exposed. The distribution of conduits matches the major features of dike distribution, including development of clusters and distribution of outliers. The comparison of San Rafael conduit distribution and the distributions of volcanoes in several recently active volcanic fields supports the use of statistical models, such as nonparametric kernel methods, in probabilistic hazard assessment for distributed volcanism. We developed a new recurrence rate calculation method that uses a Monte Carlo procedure to better reflect and understand the impact of uncertainties of radiometric age determinations on uncertainty of recurrence rate estimates for volcanic activity in the Abu, Yucca Mountain Region, and Izu-Tobu volcanic fields. Results suggest that the recurrence rates of volcanic fields can change by more than one order of magnitude on time scales of several hundred thousand to several million years. This suggests that magma generation rate beneath volcanic fields may change over these time scales. Also, recurrence rate varies more than one order of magnitude between these volcanic fields, consistent with the idea that distributed volcanism may be influenced by both the rate of magma generation and the potential for dike interaction during ascent.