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abstract: A mathematical approach was developed to evaluate the resilience of coupled power-water networks using a variant of contingency analysis adapted from electric transmission studies. In particular, the “what if” scenarios explored in power systems research were extended and applied for coupled power-water network research by evaluating how stressors and failures in the water network can propagate across system boundaries and into the electric network. Reduction in power system contingency reserves was the metric for determining violation of N-1 contingency reliability. Geospatial considerations were included using high-resolution, publicly available Geographic Information System data on infrastructure in the Phoenix Metropolitan Area that was used to generate a power network with 599 transmission lines and total generation capacity of 18.98 GW and a water network with 2,624 water network lines and capacity to serve up to 1.72M GPM of surface water. The steady-state model incorporated operating requirements for the power network—e.g., contingency reserves—and the water network—e.g., pressure ranges—while seeking to meet electric load and water demand. Interconnections developed between the infrastructures demonstrated how alternations to the system state and/or configuration of one network affect the other network, with results demonstrated through co-simulation of the power network and water network using OpenDSS and EPANET, respectively. Results indicate four key findings that help operators understand the interdependent behavior of the coupled power-water network: (i) two water failure scenarios (water flowing out of Waddell dam and CAP canal flowing west of Waddell dam) are critical to power-water network N-1 contingency reliability above 60% power system loading and at 100% water system demand, (ii) fast-starting natural gas generating units are necessary to maintain N-1 contingency reliability below 60% power system loading, (iii) Coolidge Station was the power plant to most frequently undergo a reduction in reserves amongst the water failure scenarios that cause a violation of N-1 reliability, (iv) power network vulnerability to water network failures was non-linear because it depends on the generating units that are dispatched, which can vary as line thermal limits or unit generation capacities are reached. / Dissertation/Thesis / Doctoral Dissertation Civil, Environmental and Sustainable Engineering 2020

Systems such as the power grid, world wide web (WWW), and internet are categorized as complex systems because of the presence of a large number of interacting elements. For example, the WWW is estimated to have a billion webpages and understanding the dynamics of such a large number of individual agents (whose individual interactions might not be fully known) is a challenging task. Complex network representations of these systems have proved to be of great utility. Statistical physics is the study of emergence of macroscopic properties of systems from the characteristics of the interactions between individual molecules. Hence, statistical physics of complex networks has been an effective approach to study these systems. In this dissertation, I have used statistical physics to study two distinct phenomena in complex systems: i) Cascading failures and ii) Shortest paths in complex networks. Understanding cascading failures is considered to be one of the “holy grails“ in the study of complex systems such as the power grid, transportation networks, and economic systems. Studying failures of these systems as percolation on complex networks has proved to be insightful. Previously, cascading failures have been studied extensively using two different models: k-core percolation and interdependent networks. The first part of this work combines the two models into a general model, solves it analytically, and validates the theoretical predictions through extensive computer simulations. The phase diagram of the percolation transition has been systematically studied as one varies the average local k-core threshold and the coupling between networks. The phase diagram of the combined processes is very rich and includes novel features that do not appear in the models which study each of the processes separately. For example, the phase diagram consists of first- and second-order transition regions separated by two tricritical lines that merge together and enclose a two-stage transition region. In the two-stage transition, the size of the giant component undergoes a first-order jump at a certain occupation probability followed by a continuous second-order transition at a smaller occupation probability. Furthermore, at certain fixed interdependencies, the percolation transition cycles from first-order to second-order to two-stage to first-order as the k-core threshold is increased. We setup the analytical equations describing the phase boundaries of the two-stage transition region and we derive the critical exponents for each type of transition. Understanding the shortest paths between individual elements in systems like communication networks and social media networks is important in the study of information cascades in these systems. Often, large heterogeneity can be present in the connections between nodes in these networks. Certain sets of nodes can be more highly connected among themselves than with the nodes from other sets. These sets of nodes are often referred to as ’communities’. The second part of this work studies the effect of the presence of communities on the distribution of shortest paths in a network using a modular Erdős-Rényi network model. In this model, the number of communities and the degree of modularity of the network can be tuned using the parameters of the model. We find that the model reaches a percolation threshold while tuning the degree of modularity of the network and the distribution of the shortest paths in the network can be used as an indicator of how the communities are connected.

Since the advent of the computer in the late 1950s, scientists and engineers have pushed the limits of the computing power available to them to solve physical problems via computational simulations. Early computer languages evaluated program logic in a sequential manner, thereby forcing the designer to think of the problem solution in terms of a sequential process. Object-oriented analysis and design have introduced new concepts for solving systems of engineering problems. The term object-oriented was first introduced by Alan Kay [1] in the late 1960s; however, mainstream incorporation of object-oriented programming did not occur until the mid- to late 1990s. The principles and methods underlying object-oriented programming center around objects that communicate with one another and work together to model the physical system. Program functions and data are grouped together to represent the objects. This dissertation extends object-oriented modeling concepts to model algorithms in a generic manner for solving interconnected, multi-domain problems. This work is based on an extension of Graph Trace Analysis (GTA) which was originally developed in the 1990's for power distribution system design. Because of GTA's ability to combine and restructure analysis methodologies from a variety of problem domains, it is now being used for integrated power distribution and transmission system design, operations and control. Over the last few years research has begun to formalize GTA into a multidiscipline approach that uses generic algorithms and a common model-based analysis framework. This dissertation provides an overview of the concepts used in GTA, and then discusses the main problems and potential generic algorithm based solutions associated with design and control of interdependent reconfigurable systems. These include: • Decoupling analysis into distinct component and system level equations. • Using iterator based topology management and algorithms instead of matrices. • Using composition to implement polymorphism and simplify data management. • Using dependency components to structure analysis across different systems types. • Defining component level equations for power, gas and fluid systems in terms of across and though variables. This dissertation presents a methodology for solving interdependent, multi-domain networks with generic algorithms. The methodology enables modeling of very large systems and the solution of the systems can be accomplished without the need for matrix solvers. The solution technique incorporates a binary search algorithm for accelerating the solution of looped systems. Introduction of generic algorithms enables the system solver to be written such that it is independent of the system type. Example fluid and electrical systems are solved to illustrate the generic nature of the approach. / Ph. D.

Mining of uranium ore and its extraction using the milling process generates solid and liquid waste, commonly termed uranium mine tailings. Uranium mine tailings is radioactive, as it consists of residual uranium, thorium, and radium, which amounts to 85% of the original ore’s radioactivity. Due to the extensively long half-lives of uranium (4.5x109 years), thorium (75,400 years), and radium (1,620 years) and their harmful radioactive, it is imperative to isolate uranium mine tailings from the environment for a longer period. Containment of uranium mine tailings in dam-like structures, called uranium mine tailings dam (UMTD), is the most followed disposal and storage method. Like a conventional water retention dam, UMTDs are also susceptible to failure, mainly due to adverse weather conditions. Once the UMTD fails, a fraction of the radioactive tailings infiltrates and migrate through the vadose zone contaminating the groundwater sources underlying it. Radionuclide behavior and migration in the subsurface are affected by several environmental factors. To minimize the uncertainty and improve current radionuclide fate and transport models, it is vital to study these factors and any interdependence existing between them. This study aims to understand these environmental factors by i) enlisting the factors affecting subsurface radionuclide migration through scoping review of articles and reports, and ii) analyzing the interdependence existing between the factors using the complex network theory (CNT) approach and identifying the dominant factors among them. Factors such as chemical and biological characteristics of soil stratigraphy, groundwater, and radioactive tailings plume, meteorological, and hydrogeological are found to influence radionuclide behavior and transport mechanisms in the vadose zone. CNT approach described soil microorganisms, fraction of organic carbon, infiltration rate of the soil, transmissivity, clay fraction in the soil, particulates in groundwater, and infiltrating rainwater as dominant factors in the NoF based on their centrality measures and sensitivity analysis of the network of factors (NoF). Any uncertainty associated with these factors will affect and propagate through the model. Hence, sufficient resources should be directed in the future to characterize these factors and minimize their uncertainty, which will lead to developing reliable fate and transport models for radionuclides. / Thesis / Master of Applied Science (MASc) / Waste products from uranium mining and milling operations are called uranium mine tailings, which are radioactive. Generally, uranium mine tailings are disposed of and isolated in dam-like structures referred to as uranium mine tailings dams (UMTD). One of the most common causes of UMTD failure is extreme weather conditions. When a UMTD fails, a part of tailings, consisting of radionuclides uranium, thorium, and radium, infiltrate into the subsurface through the vadose zone. Radionuclide behavior and transport in the subsurface is influenced by several environmental factors. The objective of the present study is to understand the factors affecting radionuclide migration by i) conducting a scoping review on radionuclide migration in the subsurface to describe the factors studied in the literature, and ii) understanding and analyzing any relation among the factors and deriving the most dominant factors based on their relation. This study can be used further to develop accurate and reliable radionuclide fate and transport models with minimal uncertainty.

The purpose of the current study is to examine the effects of the Caught Being Good Game (CBGG) on students’ classroom behaviors. The CBGG is a positive variation of the Good Behavior Game, which has been identified as an evidenced-based intervention designed for managing classroom behavior across students, behaviors, and settings. In the current study, the effectiveness of the CBGG intervention was examined within 2 high school special education classrooms located at two school districts in rural southeastern United States. Using a multiple baseline design, the data were analyzed using visual inspection and calculation of non-overlapping data. Results revealed that the percentage of intervals in which on-task behavior occurred increased during the implementation of the CBGG game, while the students’ level of off-task behavior decreased. Acceptability of the intervention of both teachers was favorable. Given the results, the implications of this classroom management tool are positive. Future directions are discussed and the literature base regarding the CBGG was expanded.

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Recent studies have addressed the importance of identifying determinants of parental emotion socialization (ES) to clarify how and why parents engage in ES practices. Furthermore, emotions occur within cultural contexts. Recent work has drawn attention to the importance of cross-cultural research for developmental science. Consistent with these calls for research, I examined parents' beliefs about emotions and self-construals as two sets of distinct factors guiding parental ES responses in China and the United States (US). Three emotion-related beliefs (manipulation [children can use emotions to manipulate parents]; parental knowledge [parents have to know all about their child's emotions]; autonomy [children can work through emotions on their own]) and two self-construals (independence [view self as unique entity]; interdependence [view self as connected with others]) were highlighted. One hundred seven parents with 7- to 11-year-old children (75 Chinese, 32 US; 90 mothers, 17 fathers) completed online questionnaires in their native language. MANCOVA analyses indicated cultural differences. Compared with Chinese parents, US parents less strongly endorsed beliefs about manipulation, parental knowledge, and autonomy. US parents endorsed more supportive and less nonsupportive responses towards children's emotions than Chinese parents. There was a trend for Chinese parents to endorse more interdependence than independence in self-construals, whereas no within-person difference was found for US parents' endorsement of these two self-construals. For both Chinese and US parents, beliefs about emotions and self-construals were significantly associated with ES responses. Linear regressions showed that parents' stronger manipulation belief was associated with higher nonsupportive responses to positive and negative emotions. Parents with stronger parental knowledge or autonomy beliefs reported more supportive responses to negative emotions and explanations of positive emotions. Stronger belief in parental knowledge was also related to more endorsed encouragement of positive emotions and lower nonsupportive responses to negative emotions. After controlling for the effects of beliefs, parents with higher interdependent self-construal reported more supportive responses to negative emotions and more explanatory responses to positive emotions. Parents who endorsed higher independent self-construal reported more encouraging responses to positive emotions and less nonsupportive responses to negative emotions. Results are discussed in relation to meaning and significance within socio-cultural contexts. / Doctor of Philosophy / Parental emotion socialization (ES) refers to the process through which parents socialize children's social and emotional competence. Parents from different cultures may enact different ES practices. To better clarify the cross-cultural similarities and differences as well as to better understand how and why parents endorse various ES practices, I conducted the current study. I worked with Chinese and US families and examined how parents' beliefs and perceptions of self (self-construal) as guiding factors were associated with parental ES responses to children's emotions. I focused on three beliefs about emotions: manipulation (children can use emotions to manipulate parents); parental knowledge (parents need to know all about their child's emotions); autonomy (children can handle emotions on their own) and two self-construals: independence (view self as unique entity); interdependence (view self as connected with others). One hundred seven parents (75 Chinese, 32 US; 90 mothers, 17 fathers) participated and their children were 7- to 11-year-old. Parents completed online questionnaires in their native language. I found cultural differences in parents' beliefs and ES responses. Compared with Chinese parents, US parents believed less strongly in children using emotions as manipulations, in parents knowing all about their child's emotions, and in children being able to work through emotions on their own. US parents reported more supportive and less nonsupportive responses to children's emotions than Chinese parents. I found no cultural differences in how parents' beliefs and self-construals associated with their ES responses. For both Chinese and US parents, the more strongly they believed children using emotions to manipulate others, the more nonsupportive responses they endorsed towards children's emotions. Parents' stronger beliefs in parents knowing their child's every emotion and in child's own capability of handling emotions were both related to their more supportive and exploratory responses to children's emotions. In terms of the effects of parents' self-construals, the higher parents viewed themselves as connected to others, the more support and explanation they reported in reaction to children's emotions. Meanwhile, the higher parents viewed themselves as unique and independent, the more encouraging and less nonsupportive responses towards children's emotions they reported. Overall, findings contributed to the understanding of parental ES within the cultural context in relation to parents' beliefs about emotions and perceptions of self.