A New Method for Modeling Free Surface Flows and Fluid-structure Interaction with Ocean Applications

The computational modeling of ocean waves and ocean-faring devices poses numerous challenges. Among these are the need to stably and accurately represent both the fluid-fluid interface between water and air as well as the fluid-structure interfaces arising between solid devices and one or more fluids. As techniques are developed to stably and accurately balance the interactions between fluid and structural solvers at these boundaries, a similarly pressing challenge is the development of algorithms that are massively scalable and capable of performing large-scale three-dimensional simulations on reasonable time scales. This dissertation introduces two separate methods for approaching this problem, with the first focusing on the development of sophisticated fluid-fluid interface representations and the second focusing primarily on scalability and extensibility to higher-order methods.

We begin by introducing the narrow-band gradient-augmented level set method (GALSM) for incompressible multiphase Navier-Stokes flow. This is the first use of the high-order GALSM for a fluid flow application, and its reliability and accuracy in modeling ocean environments is tested extensively. The method demonstrates numerous advantages over the traditional level set method, among these a heightened conservation of fluid volume and the representation of subgrid structures.

Next, we present a finite-volume algorithm for solving the incompressible Euler equations in two and three dimensions in the presence of a flow-driven free surface and a dynamic rigid body. In this development, the chief concerns are efficiency, scalability, and extensibility (to higher-order and truly conservative methods). These priorities informed a number of important choices: The air phase is substituted by a pressure boundary condition in order to greatly reduce the size of the computational domain, a cut-cell finite-volume approach is chosen in order to minimize fluid volume loss and open the door to higher-order methods, and adaptive mesh refinement (AMR) is employed to focus computational effort and make large-scale 3D simulations possible. This algorithm is shown to produce robust and accurate results that are well-suited for the study of ocean waves and the development of wave energy conversion (WEC) devices.

Mathematical Modeling of Perifusion Cell Culture Experiments

In perifusion cell cultures, the culture medium flows continuously through a chamber containing immobilized cells and the effluent is collected at the end. In our main applications, gonadotropin releasing hormone (GnRH) or oxytocin is introduced into the chamber as the input. They stimulate the cells to secrete luteinizing hormone (LH), which is collected in the effluent. To relate the effluent LH concentration to the cellular processes producing it, we develop and analyze a mathematical model consisting of coupled partial differential equations describing the intracellular signaling and the movement of substances in the cell chamber. We analyze three different data sets and give cellular mechanisms that explain the data. Our model indicates that two negative feedback loops, one fast and one slow, are needed to explain the data and we give their biological bases. We demonstrate that different LH outcomes in oxytocin and GnRH stimulations might originate from different receptor dynamics. We analyze the model to understand the influence of parameters, like the rate of the medium flow or the fraction collection time, on the experimental outcomes. We investigate how the rate of binding and dissociation of the input hormone to and from its receptor influence its movement down the chamber. Finally, we formulate and analyze simpler models that allow us to predict the distortion of a square pulse due to hormone-receptor interactions and to estimate parameters using perifusion data. We show that in the limit of high binding and dissociation the square pulse moves as a diffusing Gaussian and in this limit the biological parameters can be estimated.

Sequence and Structural Determinants of Specificity Differences between Paralogous Transcription Factors

Transcription factors (TFs) control the temporal and spatial expression of target genes by interacting with DNA in a sequence-specific manner. Recent advances in high throughput experiments that measure TF-DNA interactions in vitro and in vivo have facilitated the identification of DNA binding sites for thousands of TFs. However, it remains unclear how each individual TF achieves its specificity, especially in the case of paralogous TFs that recognize distinct target genomic sites despite sharing very similar DNA binding motifs. In my work, I used a combination of high throughput in vitro protein-DNA binding assays and machine-learning algorithms to characterize and model the binding specificity of 11 paralogous TFs from 4 distinct structural families. My work proves that even very closely related paralogous TFs, with indistinguishable DNA binding motifs, oftentimes exhibit differential binding specificity for their genomic target sites, especially for sites with moderate binding affinity. Importantly, the differences I identify in vitro and through computational modeling help explain, at least in part, the differential in vivo genomic targeting by paralogous TFs. Future work will focus on in vivo factors that might also be important for specificity differences between paralogous TFs, such as DNA methylation, interactions with protein cofactors, or the chromatin environment. In this larger context, my work emphasizes the importance of intrinsic DNA binding specificity in targeting of paralogous TFs to the genome.

Essays in Empirical Operations Management: Bayesian Learning of Service Quality and Structural Estimation of Complementary Product Pricing and Inventory Management

This dissertation contributes to the rapidly growing empirical research area in the field of operations management. It contains two essays, tackling two different sets of operations management questions which are motivated by and built on field data sets from two very different industries --- air cargo logistics and retailing.

The first essay, based on the data set obtained from a world leading third-party logistics company, develops a novel and general Bayesian hierarchical learning framework for estimating customers' spillover learning, that is, customers' learning about the quality of a service (or product) from their previous experiences with similar yet not identical services. We then apply our model to the data set to study how customers' experiences from shipping on a particular route affect their future decisions about shipping not only on that route, but also on other routes serviced by the same logistics company. We find that customers indeed borrow experiences from similar but different services to update their quality beliefs that determine future purchase decisions. Also, service quality beliefs have a significant impact on their future purchasing decisions. Moreover, customers are risk averse; they are averse to not only experience variability but also belief uncertainty (i.e., customer's uncertainty about their beliefs). Finally, belief uncertainty affects customers' utilities more compared to experience variability.

The second essay is based on a data set obtained from a large Chinese supermarket chain, which contains sales as well as both wholesale and retail prices of un-packaged perishable vegetables. Recognizing the special characteristics of this particularly product category, we develop a structural estimation model in a discrete-continuous choice model framework. Building on this framework, we then study an optimization model for joint pricing and inventory management strategies of multiple products, which aims at improving the company's profit from direct sales and at the same time reducing food waste and thus improving social welfare.

Collectively, the studies in this dissertation provide useful modeling ideas, decision tools, insights, and guidance for firms to utilize vast sales and operations data to devise more effective business strategies.

Essays on Energy Economics and Industrial Organization

The dissertation consists of three chapters related to the low-price guarantee marketing strategy and energy efficiency analysis. The low-price guarantee is a marketing strategy in which firms promise to charge consumers the lowest price among their competitors. Chapter 1 addresses the research question "Does a Low-Price Guarantee Induce Lower Prices'' by looking into the retail gasoline industry in Quebec where there was a major branded firm which started a low-price guarantee back in 1996. Chapter 2 does a consumer welfare analysis of low-price guarantees to drive police indications and offers a new explanation of the firms' incentives to adopt a low-price guarantee. Chapter 3 develops the energy performance indicators (EPIs) to measure energy efficiency of the manufacturing plants in pulp, paper and paperboard industry.

Chapter 1 revisits the traditional view that a low-price guarantee results in higher prices by facilitating collusion. Using accurate market definitions and station-level data from the retail gasoline industry in Quebec, I conducted a descriptive analysis based on stations and price zones to compare the price and sales movement before and after the guarantee was adopted. I find that, contrary to the traditional view, the stores that offered the guarantee significantly decreased their prices and increased their sales. I also build a difference-in-difference model to quantify the decrease in posted price of the stores that offered the guarantee to be 0.7 cents per liter. While this change is significant, I do not find the response in comeptitors' prices to be significant. The sales of the stores that offered the guarantee increased significantly while the competitors' sales decreased significantly. However, the significance vanishes if I use the station clustered standard errors. Comparing my observations and the predictions of different theories of modeling low-price guarantees, I conclude the empirical evidence here supports that the low-price guarantee is a simple commitment device and induces lower prices.

Chapter 2 conducts a consumer welfare analysis of low-price guarantees to address the antitrust concerns and potential regulations from the government; explains the firms' potential incentives to adopt a low-price guarantee. Using station-level data from the retail gasoline industry in Quebec, I estimated consumers' demand of gasoline by a structural model with spatial competition incorporating the low-price guarantee as a commitment device, which allows firms to pre-commit to charge the lowest price among their competitors. The counterfactual analysis under the Bertrand competition setting shows that the stores that offered the guarantee attracted a lot more consumers and decreased their posted price by 0.6 cents per liter. Although the matching stores suffered a decrease in profits from gasoline sales, they are incentivized to adopt the low-price guarantee to attract more consumers to visit the store likely increasing profits at attached convenience stores. Firms have strong incentives to adopt a low-price guarantee on the product that their consumers are most price-sensitive about, while earning a profit from the products that are not covered in the guarantee. I estimate that consumers earn about 0.3% more surplus when the low-price guarantee is in place, which suggests that the authorities should not be concerned and regulate low-price guarantees. In Appendix B, I also propose an empirical model to look into how low-price guarantees would change consumer search behavior and whether consumer search plays an important role in estimating consumer surplus accurately.

Chapter 3, joint with Gale Boyd, describes work with the pulp, paper, and paperboard (PP&PB) industry to provide a plant-level indicator of energy efficiency for facilities that produce various types of paper products in the United States. Organizations that implement strategic energy management programs undertake a set of activities that, if carried out properly, have the potential to deliver sustained energy savings. Energy performance benchmarking is a key activity of strategic energy management and one way to enable companies to set energy efficiency targets for manufacturing facilities. The opportunity to assess plant energy performance through a comparison with similar plants in its industry is a highly desirable and strategic method of benchmarking for industrial energy managers. However, access to energy performance data for conducting industry benchmarking is usually unavailable to most industrial energy managers. The U.S. Environmental Protection Agency (EPA), through its ENERGY STAR program, seeks to overcome this barrier through the development of manufacturing sector-based plant energy performance indicators (EPIs) that encourage U.S. industries to use energy more efficiently. In the development of the energy performance indicator tools, consideration is given to the role that performance-based indicators play in motivating change; the steps necessary for indicator development, from interacting with an industry in securing adequate data for the indicator; and actual application and use of an indicator when complete. How indicators are employed in EPA’s efforts to encourage industries to voluntarily improve their use of energy is discussed as well. The chapter describes the data and statistical methods used to construct the EPI for plants within selected segments of the pulp, paper, and paperboard industry: specifically pulp mills and integrated paper & paperboard mills. The individual equations are presented, as are the instructions for using those equations as implemented in an associated Microsoft Excel-based spreadsheet tool.