Polymer electrolyte membrane (PEM) fuel cells have increasingly become promising green energy sources for automobile and stationary cogeneration applications but its success in commercialization depends on performance optimization and manufacturing cost. The activation losses, expensive platinum catalyst, and water flooding phenomenon are the key factors currently hindering commercialization of PEM fuel cells. These factors are associated with the cathode catalyst layer (CCL), which is about ten micrometers thick. Given the small scale of this layer, it is extremely difficult to study transport phenomena inside the catalyst layer experimentally, either intrusively or non-intrusively. Therefore, mathematical and numerical models become the only means to provide insight on the physical phenomena occurring inside the CCL and to optimize the CCL designs before building a prototype for engineering application. In this thesis research, a comprehensive two-phase mathematical model for the CCL has been derived from the fundamental conservation equations using a volume-averaging method. The model also considers several water transport and physical processes that are involved in the CCL. The processes are: (a) electro-osmotic transport from the membrane to the CCL, (b) back-diffusion of water from the CCL to the membrane, (c) condensation and evaporation of water, and (d) removal of liquid water to the gas flow channel through the gas diffusion layer (GDL). A simple analytical model for the activation overpotential in the CCL has also been developed and an optimization study has been carried out using the analytical activation overpotential formulation. Further, the mathematical model has been simplified for the CCL and an analytical approach has been provided for the liquid water transport in the catalyst layer. The volume-averaged mathematical model of the CCL is finally implemented numerically along with an investigation how the physical structure of a catalyst layer affects fuel cell performance. Since the numerical model requires various effective transport properties, a set of mathematical expressions has been developed for estimating the effective transport properties in the CCL and GDL of a PEM fuel cell. The two-dimensional (2D) numerical model has been compared with the analytical model to validate the numerical results. Subsequently, using this validated model, 2D numerical studies have been carried out to investigate the effect of various physical and wetting properties of CCL and GDL on the performance of a PEM fuel cell. It has been observed that the wetting properties of a CCL control the flooding behavior, and hydrophilic characteristics of the CCL play a significant role on the cell performance. To investigate the effect of concentration variation in the flow channel, a three-dimensional numerical simulation is also presented.

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Drug active transport into milk is a major concern for breastfeeding mothers and healthcare providers. Studies from the literature indicated that breast cancer resistance protein (ABCG2) plays an important role in drug transfer into milk. There has been limited study on stereoselective interactions with ABCG2. A mechanistic analysis of flux across cell monolayer model is a critical first step toward extrapolating in vitro results for predicting in vivo disposition (including distribution into milk), drug disposition or drug-drug interactions. The objectives of this thesis were (1) to establish a “Chemical knockout model” in rat for studying drug accumulation into milk, (2) to investigate the impact of stereoselective interaction between ABCG2/Abcg2 and pantoprazole on drug transport in milk, (3) to understand in vitro monolayer flux model using experimental data and a mechanistic mathematical model. Quantitive PCR, Western blotting and immunohistochemistry results indicated that Abcg2 was up-regulated during lactation and localized on apical side of epithelial cells in mammary gland. In vitro and in vivo experiments confirmed that Abcg2 is responsible for nitrofurantoin active transport in rat milk and GF120918 was established as a chemical knockout model. Abcg2 interacts stereoselectively with pantoprazole isomers. A significant different apical flux between two pantoprazole isomers was observed in Abcg2-MDCKII cell line. The milk to serum (M/S) ratio of (-)-pantoprazole was almost 3 times as that of (+)-pantoprazole in lactating rats. Administration GF120918 decreased M/S of (-)-pantoprazole (p<0.001) but not (+)-pantoprazole (p>0.05). A stably transfected ABCG2/Abcg2 overexpressing MDCKII cell line was successfully created and used to explore the theoretical relationships in a monolayer flux model. Based on the profiles of pantoprazole isomer transport, a simple three compartment model for drug transfer into breast milk incorporating the permeability-surface area products for passive diffusion (PSD), paracellular flux (PSPC) and apically efflux ABCG2 (PSA,E) transfection was developed. The mathematical model was developed to more fully understand the interplay of paracellular, passive diffusion, active transport, and flux kinetic parameters (Km, Vmax, IC50 and Ki). This model provided useful insights into the meaning and limitation of parameters obtained from monolayer flux.

Naltrexone (NTX) is a drug used primarily in the management of alcohol dependence and opioid dependence. Based on several drawbacks associated with the oral and injectable intramuscular dosage forms of naltrexone currently available on the market, there is substantial interest in delivering naltrexone transdermally. Although naltrexone does not permeate skin at the rate sufficient to reach therapeutic plasma concentrations in humans, novel flux enhancement methods such as microneedles help address this challenge. Earlier work in humans has demonstrated that the use of microneedles achieves plasma concentrations in the lower end of expected therapeutic values. Further flux enhancement is desired to decrease the patch area while increasing drug transport rates. In the present work, several strategies aiming at in vitro flux maximization were employed including: formulation optimization, naltrexone salt screening, and naltrexone prodrug design. While naltrexone prodrugs did not reveal any improved permeation characteristics formulation optimization through decrease in vehicle microviscosity allowed a 5-fold increase in the percutaneous transport rates, and naltrexone glycolate salt selection provided an additional 1.5-fold enhancement in flux. One of the key observations was a good correlation (R2 = 0.99) between vehicle microviscosity and drug transport rates across the microchannel pathway. This finding alone allowed for formulation optimization and, at the same time, provided a potential explanation for the low permeation of high-concentration naltrexone salts and prodrugs. In vivo studies were carried out in Yucatan minipigs using a “poke and patch” microneedle method to deliver NTX•HCl. These studies demonstrated that initial plasma concentrations spiked to 2.5 ng/ml but rapidly dropped to a plateau of below 1 ng/ml. This pharmacokinetic profile could be explained by the use of a mathematical model which identified the importance of microchannel closure kinetics on drug transport. Also, an estimate of diffusional resistance of the viable tissue associated with percutaneous NTX•HCl delivery through microchannels was obtained. Its relatively large value suggests that the effect of diffusional resistance of the dermis in vivo should not be ignored and must be accounted for in order to obtain a good in vitro-in vivo correlation.

Recent literature has established that breast cancer resistance protein (ABCG2) is upregulated during lactation and is responsible for the greater than predicted accumulation of many drugs in breast milk. The objectives of this project were (1) to investigate the role of this transporter in the reported apically-directed nitrofurantoin flux in the CIT3 cell culture model of lactation, (2) to develop a mathematical model for drug transfer into breast milk to relate initial flux rates, steady-state concentrations, efflux ratios, and in vivo milk to serum ratios (M/S) and (3) to identify xenobiotic transporters that are highly expressed, and therefore potentially important for drug accumulation during lactation in mice and humans. Expression, localization, and functional assays confirmed that Abcg2 is the molecular mechanism for the apically-directed nitrofurantoin flux in CIT3 cells despite an unchanged expression level following lactogenic hormone stimulation in this model. A simple three compartment model for drug transfer into breast milk incorporating the permeability-surface area products for passive diffusion (PSD), paracellular flux (PSPC), endogenous transporters (PSB,U, PSA,E, PSB,E, and PSA,U), and ABCG2 (PSA,E(ABCG2)) transfection was developed. A stably transfected ABCG2 overexpressing MDCKII cell line was successfully created and used to explore the theoretical relationships of this new model. Derivations and correlations presented herein show the relationships between the calculated efflux ratios, PSA,E(ABCG2), and M/S attributed to ABCG2. Six xenobiotic transporters (Abcg2, Slc22a1, Slc15a2, Slc29a1, Slc16a1, and Abcc5) were identified as upregulated during lactation in murine developmental datasets analyzed by microarray expression profiling. As existing methods were inadequate to obtain pure populations of luminal epithelial cells in sufficient numbers from human breast milk or reduction mammoplasty samples for microarray analysis, a new fluorescence activated cell sorting method was developed and validated. ABCG2, SLC15A2, SLC22A12, SLC6A14, and SLCO4C1 were significantly upregulated 164-, 70-, 41-, 8-, and 2-fold during lactation, respectively. ABCC10, SLC10A1, SLC16A1, SLC22A4, SLC22A5, SLC22A9, SLC28A3, SLC29A1, SLC29A2, and SLCO4A1 had an expression level similar to, or greater than, levels in the kidney or liver. The significant upregulation of SLCO4C1 with ABCG2 is a novel finding that suggests a coordinated vectorial pathway for substrate movement into breast milk.

Smart Grid has emerged a very important concept in modern power systems. The integration of different loads such as residential, commercial and industrial into the smart grid and their optimal operation has a significant effect on the system's reliability, stability, peak power demand and energy price. This work presents the mathematical modeling of a Centralized Temperature Control System (CTCS) of a Multi-Unit Residential Building (MURB) and its optimal operation considering electricity prices and weather variations. The model considers comfort levels, preference settings and activity of residents in different units of the building to determine the optimal operation schedules of the CTCS, minimizing its total energy consumption cost. Multi-objective operation of the MURB is also investigated when residents in different units have conflicting interests, and the impact of such conflicting preferences on the operation of CTCS is analyzed. A case-study on optimal energy management of a single unit house considering net-metering is also presented. The proposed CTCS model is a Mixed Integer Non Linear Programing (MINLP) model, where some of the constraints are linearized to reduce the computational complexity arising from the non-linearity, for real-time applications. The model is studied for various customers' preferences using a realistic MURB model. Simulation results show that significant cost savings can be achieved using the proposed mathematical model.

With the rapid growth of energy demand and consequently growth in supply, increasing energy costs, and environmental concerns, there is a critical need to find new ways to make better use of existing energy systems and resources and decelerate the demand growth towards a sustainable energy system. All of these facts are leading to the proposal of novel approaches to optimize the utilization of energy in different sectors to reduce the customer's total energy costs, demand and greenhouse gas (GHG) emissions while taking into account the end-user preferences. Utilities have implemented Demand Side Management (DSM) and Demand Response (DR) programs to better manage their network, offer better services to their customers, handle the increase in electricity demand, and at the same time increase system reliability and reduce environmental impacts. Smart Grid developments such as information technology, communication infrastructure and smart meters improve the effectiveness and capability of Energy Management Systems (EMSs) and facilitate the development of automated operational decision-making structures for energy systems, thus assisting DSM and DR programs to reach their full potential. The literature review indicates that whereas significant work has been done in DSM and DR in utilities, these works have mostly focused on direct load control of particular loads, and there is a lack of a general framework to consider all types of energy hubs in an integrated Energy Hub Management System (EHMS). In this context, mathematical modeling of energy systems for EMSs, which is the main concern of the present work, plays a critical role. This research proposes mathematical optimization models of energy hubs which can be readily incorporated into EHMS in the context of Smart Grids. The energy hub could be a single or multi-carrier energy system in residential, commercial, agricultural and/or industrial sectors. Therefore, mathematical models for energy hubs in residential, commercial, and agricultural sectors have been developed and are presented and discussed in this thesis. In the residential sector, this research presents mathematical optimization models of residential energy hubs which can be readily incorporated into automated decision making technologies in Smart Grids, and can be solved efficiently in a real-time frame to optimally control all major residential energy loads, storage and production components while properly considering the customer preferences and comfort levels. Mathematical models for major household demand, i.e., fridge, freezer, dishwasher, washer and dryer, stove, water heater, hot tub, and pool pumps, are formulated. Also, mathematical models of other components of a residential energy system including lighting, heating, and air-conditioning are developed, and generic models for solar PV panels and energy storage/generation devices are proposed. The developed mathematical models result in a Mixed Integer Linear Programming (MILP) optimization problem, whose objective is to minimize demand, total costs of electricity and gas, emissions and peak load over the scheduling horizon while considering end-user preferences. The application of this model to a real household are shown to result in savings of up to 20% on energy costs and 50% on peak demand, while maintaining the household owner's desired comfort levels. In the commercial sector, mathematical optimization models of produce storage facilities to optimize the operation of their energy systems are proposed. In the storage facilities, climate control of the storage rooms consumes considerable energy; thus, a mathematical model of storage facilities appropriate for their optimal operation is developed, so that it can be implemented as a supervisory control in existing climate controllers. The proposed model incorporates weather forecasts, electricity price information, and the end-user preferences to optimally operate existing climate control systems in storage facilities. The objective is to minimize total energy costs and demand charges while considering important parameters of storage facilities; in particular, inside temperature and humidity should be kept within acceptable ranges. Effects of uncertainty in electricity price and weather forecast on optimal operation of the storage facilities are studied via Monte-Carlo simulations. The presented simulation results show the effectiveness of the proposed model to reduce total energy costs while maintaining required operational constraints. In the agricultural sector, this work presents mathematical optimization models of greenhouses to optimize the operation of their energy systems. In greenhouses, artificial lighting, CO2 production, and climate control consume considerable energy; thus, a mathematical model of greenhouses appropriate for their optimal operation is developed, so that it can be implemented as a supervisory control in existing greenhouse controllers. The proposed model incorporates weather forecasts, electricity price information, and the end-user preferences to optimally operate existing control systems in greenhouses. The objective is to minimize total energy costs and demand charges while considering important parameters of greenhouses; in particular, inside temperature and humidity, CO2 concentration, and lighting levels should be kept within acceptable ranges. Effects of uncertainty in electricity price and weather forecast on optimal operation of the storage facilities are studied via Monte-Carlo simulations and robust optimization approach. The presented simulation results show the effectiveness of the proposed model to reduce total energy costs while maintaining required operational constraints.

This thesis mainly concerns modeling, approximation and inference of gene regulatory dynamics on the basis of gene expression patterns. The dynamical behavior of gene expressions is represented by a system of ordinary dierential equations. We introduce a gene-interaction matrix with some nonlinear entries, in particular, quadratic polynomials of the expression levels to keep the system solvable. The model parameters are determined by using optimization. Then, we provide the time-discrete approximation of our time-continuous model. We analyze the approximating model under the aspect of stability. Finally, from the considered models we derive gene regulatory networks, discuss their qualitative features of the networks and provide a basis for analyzing networks with nonlinear connections.

A comprehensive model, previously developed and tested for prediction of behavior of continuous fluidized bed combustors is extended to incorporate NOx formation and reduction reactions and applied to the simulation of METU 0.3 MWt Atmospheric Bubbling Fluidized Bed Combustor (ABFBC) burning lignites with high volatile matter in their own ashes. The predictive accuracy of the model was assessed by comparing its predictions with measurements taken previously on the same rig. Favorable comparisons are obtained between the predicted and measured temperatures and concentrations of gaseous species along the combustor. Results show that determination of partitioning of coal nitrogen into char nitrogen and volatile nitrogen, and release of volatile nitrogen along the combustor are found to be the most important parameters that affect NOx formation and reduction in bubbling fluidized bed combustors. The system model proposed in this study proves to be a useful tool in qualitatively and quantitatively simulating the processes taking place in an atmospheric fluidized bed combustor.

Good process control is often critical for the economic viability of large-scale production of several commercial products. In this work, the production of biodiesel from microalgae is investigated. Successful implementation of a model-based control strategy requires the identification of a model that properly captures the biochemical dynamics of microalgae, yet is simple enough to allow its implementation for controller design. For this purpose, two model reparameterization algorithms are proposed that partition the parameter space into estimable and inestimable subspaces. Both algorithms are applied using a first principles ODE model of a microalgal bioreactor, containing 6 states and 12 unknown parameters. Based on initial simulations, the non-linear algorithm achieved better degree of output prediction when compared to the linear one at a greatly decreased computational cost. Using the parameter estimates obtained through implementation of the non-linear algorithm on experimental data from a fed-batch bioreactor, the possible improvement in volumetric productivity was recognized. / Process Control