MODELING FUNCTIONAL DATA WITH SPATIALLY HETEROGENEOUS SHAPE CHARACTERISTICS

We propose a novel class of models for functional data exhibiting skewness or other shape characteristics that vary with spatial or temporal location. We use copulas so that the marginal distributions and the dependence structure can be modeled independently. Dependence is modeled with a Gaussian or t-copula, so that there is an underlying latent Gaussian process. We model the marginal distributions using the skew t family. The mean, variance, and shape parameters are modeled nonparametrically as functions of location. A computationally tractable inferential framework for estimating heterogeneous asymmetric or heavy-tailed marginal distributions is introduced. This framework provides a new set of tools for increasingly complex data collected in medical and public health studies. Our methods were motivated by and are illustrated with a state-of-the-art study of neuronal tracts in multiple sclerosis patients and healthy controls. Using the tools we have developed, we were able to find those locations along the tract most affected by the disease. However, our methods are general and highly relevant to many functional data sets. In addition to the application to one-dimensional tract profiles illustrated here, higher-dimensional extensions of the methodology could have direct applications to other biological data including functional and structural MRI.

A BAYESIAN HIERARCHICAL FRAMEWORK FOR SPATIAL MODELING OF fMRI DATA

Functional neuroimaging techniques enable investigations into the neural basis of human cognition, emotions, and behaviors. In practice, applications of functional magnetic resonance imaging (fMRI) have provided novel insights into the neuropathophysiology of major psychiatric,neurological, and substance abuse disorders, as well as into the neural responses to their treatments. Modern activation studies often compare localized task-induced changes in brain activity between experimental groups. One may also extend voxel-level analyses by simultaneously considering the ensemble of voxels constituting an anatomically defined region of interest (ROI) or by considering means or quantiles of the ROI. In this work we present a Bayesian extension of voxel-level analyses that offers several notable benefits. First, it combines whole-brain voxel-by-voxel modeling and ROI analyses within a unified framework. Secondly, an unstructured variance/covariance for regional mean parameters allows for the study of inter-regional functional connectivity, provided enough subjects are available to allow for accurate estimation. Finally, an exchangeable correlation structure within regions allows for the consideration of intra-regional functional connectivity. We perform estimation for our model using Markov Chain Monte Carlo (MCMC) techniques implemented via Gibbs sampling which, despite the high throughput nature of the data, can be executed quickly (less than 30 minutes). We apply our Bayesian hierarchical model to two novel fMRI data sets: one considering inhibitory control in cocaine-dependent men and the second considering verbal memory in subjects at high risk for Alzheimer’s disease. The unifying hierarchical model presented in this manuscript is shown to enhance the interpretation content of these data sets.

Modeling of electroosmotic and electrophoretic mobilization in capillary and microchip isoelectric focusing

Our dynamic capillary electrophoresis model which uses material specific input data for estimation of electroosmosis was applied to investigate fundamental aspects of isoelectric focusing (IEF) in capillaries or microchannels made from bare fused-silica (FS), FS coated with a sulfonated polymer, polymethylmethacrylate (PMMA) and poly(dimethylsiloxane) (PDMS). Input data were generated via determination of the electroosmotic flow (EOF) using buffers with varying pH and ionic strength. Two models are distinguished, one that neglects changes of ionic strength and one that includes the dependence between electroosmotic mobility and ionic strength. For each configuration, the models provide insight into the magnitude and dynamics of electroosmosis. The contribution of each electrophoretic zone to the net EOF is thereby visualized and the amount of EOF required for the detection of the zone structures at a particular location along the capillary, including at its end for MS detection, is predicted. For bare FS, PDMS and PMMA, simulations reveal that EOF is decreasing with time and that the entire IEF process is characterized by the asymptotic formation of a stationary steady-state zone configuration in which electrophoretic transport and electroosmotic zone displacement are opposite and of equal magnitude. The location of immobilization of the boundary between anolyte and most acidic carrier ampholyte is dependent on EOF, i.e. capillary material and anolyte. Overall time intervals for reaching this state in microchannels produced by PDMS and PMMA are predicted to be similar and about twice as long compared to uncoated FS. Additional mobilization for the detection of the entire pH gradient at the capillary end is required. Using concomitant electrophoretic mobilization with an acid as coanion in the catholyte is shown to provide sufficient additional cathodic transport for that purpose. FS capillaries dynamically double coated with polybrene and poly(vinylsulfonate) are predicted to provide sufficient electroosmotic pumping for detection of the entire IEF gradient at the cathodic column end.

Molecular modeling of EPON 862-DETDA polymer

EPON 862 is an epoxy resin which is cured with the hardening agent DETDA to form a crosslinked epoxy polymer and is used as a component in modern aircraft structures. These crosslinked polymers are often exposed to prolonged periods of temperatures below glass transition range which cause physical aging to occur. Because physical aging can compromise the performance of epoxies and their composites and because experimental techniques cannot provide all of the necessary physical insight that is needed to fully understand physical aging, efficient computational approaches to predict the effects of physical aging on thermo-mechanical properties are needed. In this study, Molecular Dynamics and Molecular Minimization simulations are being used to establish well-equilibrated, validated molecular models of the EPON 862-DETDA epoxy system with a range of crosslink densities using a united-atom force field. These simulations are subsequently used to predict the glass transition temperature, thermal expansion coefficients, and elastic properties of each of the crosslinked systems for validation of the modeling techniques. The results indicate that glass transition temperature and elastic properties increase with increasing levels of crosslink density and the thermal expansion coefficient decreases with crosslink density, both above and below the glass transition temperature. The results also indicate that there may be an upper limit to crosslink density that can be realistically achieved in epoxy systems. After evaluation of the thermo-mechanical properties, a method is developed to efficiently establish molecular models of epoxy resins that represent the corresponding real molecular structure at specific aging times. Although this approach does not model the physical aging process, it is useful in establishing a molecular model that resembles the physically-aged state for further use in predicting thermo-mechanical properties as a function of aging time. An equation has been predicted based on the results which directly correlate aging time to aged volume of the molecular model. This equation can be helpful for modelers who want to study properties of epoxy resins at different levels of aging but have little information about volume shrinkage occurring during physical aging.

Use of manual adaptive remeshing in the mechanical modeling of an intraneural ganglion cyst

Intraneural Ganglion Cysts expand within in a nerve, causing neurological deficits in afflicted patients. Modeling the propagation of these cysts, originating in the articular branch and then expanding radially outward, will help prove articular theory, and ultimately allow for more purposeful treatment of this condition. In Finite Element Analysis, traditional Lagrangian meshing methods fail to model the excessive deformation that occurs in the propagation of these cysts. This report explores the method of manual adaptive remeshing as a method to allow for the use of Lagrangian meshing, while circumventing the severe mesh distortions typical of using a Lagrangian mesh with a large deformation. Manual adaptive remeshing is the process of remeshing a deformed meshed part and then reapplying loads in order to achieve a larger deformation than a single mesh can achieve without excessive distortion. The methods of manual adaptive remeshing described in this Master’s Report are sufficient in modeling large deformations.

EPA's Council for Regulatory Environmental Modeling : a case study of science policy implementation

As environmental problems became more complex, policy and regulatory decisions become far more difficult to make. The use of science has become an important practice in the decision making process of many federal agencies. Many different types of scientific information are used to make decisions within the EPA, with computer models becoming especially important. Environmental models are used throughout the EPA in a variety of contexts and their predictive capacity has become highly valued in decision making. The main focus of this research is to examine the EPA’s Council for Regulatory Modeling (CREM) as a case study in addressing science issues, particularly models, in government agencies. Specifically, the goal was to answer the following questions: What is the history of the CREM and how can this information shed light on the process of science policy implementation? What were the goals of implementing the CREM? Were these goals reached and how have they changed? What have been the impediments that the CREM has faced and why did these impediments occur? The three main sources of information for this research came from observations during summer employment with the CREM, document review and supplemental interviews with CREM participants and other members of the modeling community. Examining a history of modeling at the EPA, as well as a history of the CREM, provides insight into the many challenges that are faced when implementing science policy and science policy programs. After examining the many impediments that the CREM has faced in implementing modeling policies, it was clear that the impediments fall into two separate categories, classic and paradoxical. The classic impediments include the more standard impediments to science policy implementation that might be found in any regulatory environment, such as lack of resources and changes in administration. Paradoxical impediments are cyclical in nature, with no clear solution, such as balancing top-down versus bottom-up initiatives and coping with differing perceptions. These impediments, when not properly addressed, severely hinder the ability for organizations to successfully implement science policy.

Modeling contaminant behavior in Lake Superior : a comparison of PCBs, PBDEs, and mercury

A mass‐balance model for Lake Superior was applied to polychlorinated biphenyls (PCBs), polybrominated diphenyl ethers (PBDEs), and mercury to determine the major routes of entry and the major mechanisms of loss from this ecosystem as well as the time required for each contaminant class to approach steady state. A two‐box model (water column, surface sediments) incorporating seasonally adjusted environmental parameters was used. Both numerical (forward Euler) and analytical solutions were employed and compared. For validation, the model was compared with current and historical concentrations and fluxes in the lake and sediments. Results for PCBs were similar to prior work showing that air‐water exchange is the most rapid input and loss process. The model indicates that mercury behaves similarly to a moderately‐chlorinated PCB, with air‐water exchange being a relatively rapid input and loss process. Modeled accumulation fluxes of PBDEs in sediments agreed with measured values reported in the literature. Wet deposition rates were about three times greater than dry particulate deposition rates for PBDEs. Gas deposition was an important process for tri‐ and tetra‐BDEs (BDEs 28 and 47), but not for higher‐brominated BDEs. Sediment burial was the dominant loss mechanism for most of the PBDE congeners while volatilization was still significant for tri‐ and tetra‐BDEs. Because volatilization is a relatively rapid loss process for both mercury and the most abundant PCBs (tri‐ through penta‐), the model predicts that similar times (from 2 ‐ 10 yr) are required for the compounds to approach steady state in the lake. The model predicts that if inputs of Hg(II) to the lake decrease in the future then concentrations of mercury in the lake will decrease at a rate similar to the historical decline in PCB concentrations following the ban on production and most uses in the U.S. In contrast, PBDEs are likely to respond more slowly if atmospheric concentrations are reduced in the future because loss by volatilization is a much slower process for PBDEs, leading to lesser overall loss rates for PBDEs in comparison to PCBs and mercury. Uncertainties in the chemical degradation rates and partitioning constants of PBDEs are the largest source of uncertainty in the modeled times to steady‐state for this class of chemicals. The modeled organic PBT loading rates are sensitive to uncertainties in scavenging efficiencies by rain and snow, dry deposition velocity, watershed runoff concentrations, and uncertainties in air‐water exchange such as the effect of atmospheric stability.

Numerical modeling of the failure mechanisms in Si thin film anode for Li-ion batteries

In recent times, the demand for the storage of electrical energy has grown rapidly for both static applications and the portable electronics enforcing the substantial improvement in battery systems, and Li-ion batteries have been proven to have maximum energy storage density in all rechargeable batteries. However, major breakthroughs are required to consummate the requirement of higher energy density with lower cost to penetrate new markets. Graphite anode having limited capacity has become a bottle neck in the process of developing next generation batteries and can be replaced by higher capacity metals such as Silicon. In the present study we are focusing on the mechanical behavior of the Si-thin film anode under various operating conditions. A numerical model is developed to simulate the intercalation induced stress and the failure mechanism of the complex anode structure. Effect of the various physical phenomena such as diffusion induced stress, plasticity and the crack propagation are investigated to predict better performance parameters for improved design.

Dynamic modeling of active regeneration in catalyzed and non-catalyzed diesel particulate filters

Particulate matter (PM) emissions standards set by the US Environmental Protection Agency (EPA) have become increasingly stringent over the years. The EPA regulation for PM in heavy duty diesel engines has been reduced to 0.01 g/bhp-hr for the year 2010. Heavy duty diesel engines make use of an aftertreatment filtration device, the Diesel Particulate Filter (DPF). DPFs are highly efficient in filtering PM (known as soot) and are an integral part of 2010 heavy duty diesel aftertreatment system. PM is accumulated in the DPF as the exhaust gas flows through it. This PM needs to be removed by oxidation periodically for the efficient functioning of the filter. This oxidation process is also known as regeneration. There are 2 types of regeneration processes, namely active regeneration (oxidation of PM by external means) and passive oxidation (oxidation of PM by internal means). Active regeneration occurs typically in high temperature regions, about 500 - 600 °C, which is much higher than normal diesel exhaust temperatures. Thus, the exhaust temperature has to be raised with the help of external devices like a Diesel Oxidation Catalyst (DOC) or a fuel burner. The O2 oxidizes PM producing CO2 as oxidation product. In passive oxidation, one way of regeneration is by the use of NO2. NO2 oxidizes the PM producing NO and CO2 as oxidation products. The passive oxidation process occurs at lower temperatures (200 - 400 °C) in comparison to the active regeneration temperatures. Generally, DPF substrate walls are washcoated with catalyst material to speed up the rate of PM oxidation. The catalyst washcoat is observed to increase the rate of PM oxidation. The goal of this research is to develop a simple mathematical model to simulate the PM depletion during the active regeneration process in a DPF (catalyzed and non-catalyzed). A simple, zero-dimensional kinetic model was developed in MATLAB. Experimental data required for calibration was obtained by active regeneration experiments performed on PM loaded mini DPFs in an automated flow reactor. The DPFs were loaded with PM from the exhaust of a commercial heavy duty diesel engine. The model was calibrated to the data obtained from active regeneration experiments. Numerical gradient based optimization techniques were used to estimate the kinetic parameters of the model.

Effect of high order interpolation in the stability and efficiency of the time-integration process in vorticity-velocity CFD algorithms

The numerical solution of the incompressible Navier-Stokes Equations offers an effective alternative to the experimental analysis of Fluid-Structure interaction i.e. dynamical coupling between a fluid and a solid which otherwise is very complex, time consuming and very expensive. To have a method which can accurately model these types of mechanical systems by numerical solutions becomes a great option, since these advantages are even more obvious when considering huge structures like bridges, high rise buildings, or even wind turbine blades with diameters as large as 200 meters. The modeling of such processes, however, involves complex multiphysics problems along with complex geometries. This thesis focuses on a novel vorticity-velocity formulation called the KLE to solve the incompressible Navier-stokes equations for such FSI problems. This scheme allows for the implementation of robust adaptive ODE time integration schemes and thus allows us to tackle the various multiphysics problems as separate modules. The current algorithm for KLE employs a structured or unstructured mesh for spatial discretization and it allows the use of a self-adaptive or fixed time step ODE solver while dealing with unsteady problems. This research deals with the analysis of the effects of the Courant-Friedrichs-Lewy (CFL) condition for KLE when applied to unsteady Stoke’s problem. The objective is to conduct a numerical analysis for stability and, hence, for convergence. Our results confirmthat the time step ∆t is constrained by the CFL-like condition ∆t ≤ const. hα, where h denotes the variable that represents spatial discretization.

ELECTRICITY GENERATION MODELING AND PHOTOVOLTAIC FORECASTS IN CHINA

With the economic development of China, the demand for electricity generation is rapidly increasing. To explain electricity generation, we use gross GDP, the ratio of urban population to rural population, the average per capita income of urban residents, the electricity price for industry in Beijing, and the policy shift that took place in China. Ordinary least squares (OLS) is used to develop a model for the 1979-2009 period. During the process of designing the model, econometric methods are used to test and develop the model. The final model is used to forecast total electricity generation and assess the possible role of photovoltaic generation. Due to the high demand for resources and serious environmental problems, China is pushing to develop the photovoltaic industry. The system price of PV is falling; therefore, photovoltaics may be competitive in the future.

COMBUSTION INITIATION BY ELECTRICAL-DISCHARGE-INDUCED PLASMA IN LEAN AND DILUTE METHANE-AIR MIXTURE: EXPERIMENTAL AND MODELING INVESTIGATION

This dissertation represents experimental and numerical investigations of combustion initiation trigged by electrical-discharge-induced plasma within lean and dilute methane air mixture. This research topic is of interest due to its potential to further promote the understanding and prediction of spark ignition quality in high efficiency gasoline engines, which operate with lean and dilute fuel-air mixture. It is specified in this dissertation that the plasma to flame transition is the key process during the spark ignition event, yet it is also the most complicated and least understood procedure. Therefore the investigation is focused on the overlapped periods when plasma and flame both exists in the system. Experimental study is divided into two parts. Experiments in Part I focuses on the flame kernel resulting from the electrical discharge. A number of external factors are found to affect the growth of the flame kernel, resulting in complex correlations between discharge and flame kernel. Heat loss from the flame kernel to code ambient is found to be a dominant factor that quenches the flame kernel. Another experimental focus is on the plasma channel. Electrical discharges into gases induce intense and highly transient plasma. Detailed observation of the size and contents of the discharge-induced plasma channel is performed. Given the complex correlation and the multi-discipline physical/chemical processes involved in the plasma-flame transition, the modeling principle is taken to reproduce detailed transitions numerically with minimum analytical assumptions. Detailed measurement obtained from experimental work facilitates the more accurate description of initial reaction conditions. The novel and unique spark source considering both energy and species deposition is defined in a justified manner, which is the key feature of this Ignition by Plasma (IBP) model. The results of numerical simulation are intuitive and the potential of numerical simulation to better resolve the complex spark ignition mechanism is presented. Meanwhile, imperfections of the IBP model and numerical simulation have been specified and will address future attentions.

DYNAMICS AND CONTROL OF REACTIVE DISTILLATION PROCESS FOR MONOMER SYNTHESIS OF POLYCARBONATE PLANTS

Polycarbonate (PC) is an important engineering thermoplastic that is currently produced in large industrial scale using bisphenol A and monomers such as phosgene. Since phosgene is highly toxic, a non-phosgene approach using diphenyl carbonate (DPC) as an alternative monomer, as developed by Asahi Corporation of Japan, is a significantly more environmentally friendly alternative. Other advantages include the use of CO2 instead of CO as raw material and the elimination of major waste water production. However, for the production of DPC to be economically viable, reactive-distillation units are needed to obtain the necessary yields by shifting the reaction-equilibrium to the desired products and separating the products at the point where the equilibrium reaction occurs. In the field of chemical reaction engineering, there are many reactions that are suffering from the low equilibrium constant. The main goal of this research is to determine the optimal process needed to shift the reactions by using appropriate control strategies of the reactive distillation system. An extensive dynamic mathematical model has been developed to help us investigate different control and processing strategies of the reactive distillation units to increase the production of DPC. The high-fidelity dynamic models include extensive thermodynamic and reaction-kinetics models while incorporating the necessary mass and energy balance of the various stages of the reactive distillation units. The study presented in this document shows the possibility of producing DPC via one reactive distillation instead of the conventional two-column, with a production rate of 16.75 tons/h corresponding to start reactants materials of 74.69 tons/h of Phenol and 35.75 tons/h of Dimethyl Carbonate. This represents a threefold increase over the projected production rate given in the literature based on a two-column configuration. In addition, the purity of the DPC produced could reach levels as high as 99.5% with the effective use of controls. These studies are based on simulation done using high-fidelity dynamic models.

TanDEM-X High Resolution DEMs and Their Applications to Flow Modeling

Lava flow modeling can be a powerful tool in hazard assessments; however, the ability to produce accurate models is usually limited by a lack of high resolution, up-to-date Digital Elevation Models (DEMs). This is especially obvious in places such as Kilauea Volcano (Hawaii), where active lava flows frequently alter the terrain. In this study, we use a new technique to create high resolution DEMs on Kilauea using synthetic aperture radar (SAR) data from the TanDEM-X (TDX) satellite. We convert raw TDX SAR data into a geocoded DEM using GAMMA software [Werner et al., 2000]. This process can be completed in several hours and permits creation of updated DEMs as soon as new TDX data are available. To test the DEMs, we use the Harris and Rowland [2001] FLOWGO lava flow model combined with the Favalli et al. [2005] DOWNFLOW model to simulate the 3-15 August 2011 eruption on Kilauea's East Rift Zone. Results were compared with simulations using the older, lower resolution 2000 SRTM DEM of Hawaii. Effusion rates used in the model are derived from MODIS thermal infrared satellite imagery. FLOWGO simulations using the TDX DEM produced a single flow line that matched the August 2011 flow almost perfectly, but could not recreate the entire flow field due to the relatively high DEM noise level. The issues with short model flow lengths can be resolved by filtering noise from the DEM. Model simulations using the outdated SRTM DEM produced a flow field that followed a different trajectory to that observed. Numerous lava flows have been emplaced at Kilauea since the creation of the SRTM DEM, leading the model to project flow lines in areas that have since been covered by fresh lava flows. These results show that DEMs can quickly become outdated on active volcanoes, but our new technique offers the potential to produce accurate, updated DEMs for modeling lava flow hazards.

STATE-AND-TRANSITION MODELING AND ADAPTIVE MANAGEMENT: TOOLS FOR FUTURE CO-DEVELOPMENT OF MADAGASCAR’S NATURAL RESOURCES AND PEOPLE

Madagascar’s terrestrial and aquatic ecosystems have long supported a unique set of ecological communities, many of whom are endemic to the tropical island. Those same ecosystems have been a source of valuable natural resources to some of the poorest people in the world. Nevertheless, with pride, ingenuity and resourcefulness, the Malagasy people of the southwest coast, being of Vezo identity, subsist with low development fishing techniques aimed at an increasingly threatened host of aquatic seascapes. Mangroves, sea grass bed, and coral reefs of the region are under increased pressure from the general populace for both food provisions and support of economic opportunity. Besides purveyors and extractors, the coastal waters are also subject to a number of natural stressors, including cyclones and invasive, predator species of both flora and fauna. In addition, the aquatic ecosystems of the region are undergoing increased nutrient and sediment runoff due, in part, to Madagascar’s heavy reliance on land for agricultural purposes (Scales, 2011). Moreover, its coastal waters, like so many throughout the world, have been proven to be warming at an alarming rate over the past few decades. In recognizing the intimate interconnectedness of the both the social and ecological systems, conservation organizations have invoked a host of complimentary conservation and social development efforts with the dual aim of preserving or restoring the health of both the coastal ecosystems and the people of the region. This paper provides a way of thinking more holistically about the social-ecological system within a resiliency frame of understanding. Secondly, it applies a platform known as state-and-transition modeling to give form to the process. State-and-transition modeling is an iterative investigation into the physical makeup of a system of study as well as the boundaries and influences on that state, and has been used in restorative ecology for more than a decade. Lastly, that model is sited within an adaptive management scheme that provides a structured, cyclical, objective-oriented process for testing stakeholders cognitive understanding of the ecosystem through a pragmatic implementation and monitoring a host of small-scale interventions developed as part of the adaptive management process. Throughout, evidence of the application of the theories and frameworks are offered, with every effort made to retool conservation-minded development practitioners with a comprehensive strategy for addressing the increasingly fragile social-ecological systems of southwest Madagascar. It is offered, in conclusion, that the seascapes of the region would be an excellent case study worthy of future application of state-and-transition modeling and adaptive management as frameworks for conservation-minded development practitioners whose multiple projects, each with its own objective, have been implemented with a single goal in mind: preserve and protect the state of the supporting environment while providing for the basic needs of the local Malagasy people.