THE HEALTH OF YOUNG ADULTS WITH DISABILITIES IN THE UNITED STATES: THE COLLECTIVE ROLES OF RISK FACTORS IN SOCIAL ECOLOGIC FRAMEWORK

Background: Over the last few decades, the prevalence of young adults with disabilities (YAD) has steadily risen as a result of advances in medicine, clinical treatment, and biomedical technologythat enhanced their survival into adulthood. Despite investments in services, family supports, and insurance, they experience poor health status and barriers to successful transition into adulthood. Objectives: We investigated the collective roles of multi-faceted factors at intrapersonal, interpersonal and community levels within the social ecological framework on health related outcome including self-rated health (SRH) of YAD. The three specific aims are: 1) to examine sociodemographic differences and health insurance coverage in adolescence; 2) to investigate the role of social skills in relationships with family and peers developed in adolescence; and 3) to collectively explore the association of sociodemographic characteristics, social skills, and community participation in adolescence on SRH. Methods: Using longitudinal data (N=5,020) from the National Longitudinal Transition Study (NLTS2), we conducted multivariate logistic regression analyses to understand the association between insurance status as well as social skills in adolescence and YAD’s health related outcomes. Structural equation modeling (SEM) assessed the confluence of multi-faceted factors from the social ecological model that link to health in early adulthood. Results: Compared with YAD who had private insurance, YAD who had public health insurance in adolescence are at higher odds of experiencing poorer health related outcomes in self-rated health [adjusted odds ratio (aOR=2.89, 95% confidence interval (CI): 1.16, 7.23), problems with health (aOR=2.60, 95%CI: 1.26, 5.35), and missing social activities due to health problems (aOR=2.86, 95%CI: 1.39, 5.85). At the interpersonal level, overall social skills developed through relationship with family and peers in adolescence do not appear to have association with health related outcomes in early adulthood. Finally, at the community level, community participation in adolescence does not have an association with SRH in early adulthood. Conclusions: Having public health insurance coverage does not equate to good health. YAD need additional supports to achieve positive health outcomes. The findings in social skills and community participation suggest other potential factors may be at play for health related outcomes for YAD and the need for further investigation.

Security through Obscurity: Layout Obfuscation of Digital Integrated Circuits using Don't Care Conditions

Contemporary integrated circuits are designed and manufactured in a globalized environment leading to concerns of piracy, overproduction and counterfeiting. One class of techniques to combat these threats is circuit obfuscation which seeks to modify the gate-level (or structural) description of a circuit without affecting its functionality in order to increase the complexity and cost of reverse engineering. Most of the existing circuit obfuscation methods are based on the insertion of additional logic (called “key gates”) or camouflaging existing gates in order to make it difficult for a malicious user to get the complete layout information without extensive computations to determine key-gate values. However, when the netlist or the circuit layout, although camouflaged, is available to the attacker, he/she can use advanced logic analysis and circuit simulation tools and Boolean SAT solvers to reveal the unknown gate-level information without exhaustively trying all the input vectors, thus bringing down the complexity of reverse engineering. To counter this problem, some ‘provably secure’ logic encryption algorithms that emphasize methodical selection of camouflaged gates have been proposed previously in literature [1,2,3]. The contribution of this paper is the creation and simulation of a new layout obfuscation method that uses don't care conditions. We also present proof-of-concept of a new functional or logic obfuscation technique that not only conceals, but modifies the circuit functionality in addition to the gate-level description, and can be implemented automatically during the design process. Our layout obfuscation technique utilizes don’t care conditions (namely, Observability and Satisfiability Don’t Cares) inherent in the circuit to camouflage selected gates and modify sub-circuit functionality while meeting the overall circuit specification. Here, camouflaging or obfuscating a gate means replacing the candidate gate by a 4X1 Multiplexer which can be configured to perform all possible 2-input/ 1-output functions as proposed by Bao et al. [4]. It is important to emphasize that our approach not only obfuscates but alters sub-circuit level functionality in an attempt to make IP piracy difficult. The choice of gates to obfuscate determines the effort required to reverse engineer or brute force the design. As such, we propose a method of camouflaged gate selection based on the intersection of output logic cones. By choosing these candidate gates methodically, the complexity of reverse engineering can be made exponential, thus making it computationally very expensive to determine the true circuit functionality. We propose several heuristic algorithms to maximize the RE complexity based on don’t care based obfuscation and methodical gate selection. Thus, the goal of protecting the design IP from malicious end-users is achieved. It also makes it significantly harder for rogue elements in the supply chain to use, copy or replicate the same design with a different logic. We analyze the reverse engineering complexity by applying our obfuscation algorithm on ISCAS-85 benchmarks. Our experimental results indicate that significant reverse engineering complexity can be achieved at minimal design overhead (average area overhead for the proposed layout obfuscation methods is 5.51% and average delay overhead is about 7.732%). We discuss the strengths and limitations of our approach and suggest directions that may lead to improved logic encryption algorithms in the future. References: [1] R. Chakraborty and S. Bhunia, “HARPOON: An Obfuscation-Based SoC Design Methodology for Hardware Protection,” IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems, vol. 28, no. 10, pp. 1493–1502, 2009. [2] J. A. Roy, F. Koushanfar, and I. L. Markov, “EPIC: Ending Piracy of Integrated Circuits,” in 2008 Design, Automation and Test in Europe, 2008, pp. 1069–1074. [3] J. Rajendran, M. Sam, O. Sinanoglu, and R. Karri, “Security Analysis of Integrated Circuit Camouflaging,” ACM Conference on Computer Communications and Security, 2013. [4] Bao Liu, Wang, B., "Embedded reconfigurable logic for ASIC design obfuscation against supply chain attacks,"Design, Automation and Test in Europe Conference and Exhibition (DATE), 2014 , vol., no., pp.1,6, 24-28 March 2014.

PERCEPTIONS OF THE PREPARATION OF EFFECTIVE MIDDLE SCHOOL PRINCIPALS

The primary purpose of this quantitative study was to examine middle school administrators’ perceptions of their preparation programs. The following research questions were addressed as a part of the study: 1. What skills, behaviors, and attitudes do middle school principals perceive to be important to be an effective middle school principal? 2. How do middle school principals perceive their level of preparedness in relation to the specific skills, behaviors, and attitudes? 3. To what degree do middle school principals believe that their level of preparation has influenced them to stay in their current role? 4. Which components of their preparation program do middle principals perceive to be the most valuable? 5. To what extent do middle school principals believe that the school district should design a program specifically to develop middle school principals? Middle school principals were selected to participate in this study. Quantitative data were gathered via online questionnaires. The research questions were addressed through analysis of the questionnaire data, using descriptive and inferential statistics. This study resulted in recommendations to provide a framework for the development of a principal preparation program designed to train effective middle school principals.

DYNAMICS OF THE SHORT TERM AND LONG TERM AVIAN DISTRIBUTIONS IN NORTH AMERICA - THE ROLES OF VEGETATION HEIGHT HETEROGENEITY AND CLIMATIC FACTORS

Understanding how biodiversity spatially distribute over both the short term and long term, and what factors are affecting the distribution, are critical for modeling the spatial pattern of biodiversity as well as for promoting effective conservation planning and practices. This dissertation aims to examine factors that influence short-term and long-term avian distribution from the geographical sciences perspective. The research develops landscape level habitat metrics to characterize forest height heterogeneity and examines their efficacies in modelling avian richness at the continental scale. Two types of novel vegetation-height-structured habitat metrics are created based on second order texture algorithms and the concepts of patch-based habitat metrics. I correlate the height-structured metrics with the richness of different forest guilds, and also examine their efficacies in multivariate richness models. The results suggest that height heterogeneity, beyond canopy height alone, supplements habitat characterization and richness models of two forest bird guilds. The metrics and models derived in this study demonstrate practical examples of utilizing three-dimensional vegetation data for improved characterization of spatial patterns in species richness. The second and the third projects focus on analyzing centroids of avian distributions, and testing hypotheses regarding the direction and speed of these shifts. I first showcase the usefulness of centroids analysis for characterizing the distribution changes of a few case study species. Applying the centroid method on 57 permanent resident bird species, I show that multi-directional distribution shifts occurred in large number of studied species. I also demonstrate, plain birds are not shifting their distribution faster than mountain birds, contrary to the prediction based on climate change velocity hypothesis. By modelling the abundance change rate at regional level, I show that extreme climate events and precipitation measures associate closely with some of the long-term distribution shifts. This dissertation improves our understanding on bird habitat characterization for species richness modelling, and expands our knowledge on how avian populations shifted their ranges in North America responding to changing environments in the past four decades. The results provide an important scientific foundation for more accurate predictive species distribution modeling in future.

THE USE OF THE EARLY WARNING INDICATOR REPORT TO IMPACT NINTH GRADE PROMOTION RATES IN A LARGE URBAN SCHOOL DISTRICT

Abstract The purpose of this study was to examine how four high schools used an Early Warning Indicator Report (EWIR) to improve ninth grade promotion rates. Ninth grade on-time promotion is an early predictor of a student’s likelihood to graduate (Bornsheuer, Polonyi, Andrews, Fore, & Onwuegbuzie, 2011; Leckrone & Griffith, 2006; Roderick, Kelley-Kemple, Johnson, & Beechum, 2014; Zvoch, 2006). The analysis revealed both similarities and differences in the ways that the four schools used the EWIR. The research took place in a large urban school district in the Mid-Atlantic. Sixteen participants from four high schools and the district’s central office voluntarily participated in face-to-face interviews. The researcher utilized a qualitative case study method to examine the implementation of the EWIR system in Wyatt School District. The interview data was transcribed and analyzed, along with district documents, to identify categories in this cross case analysis. Three primary themes emerged from the data: (1) targeted school structures for EWIR implementation, (2) the EWIR identified necessary supports for students, and (3) the central office support for school staff. The findings revealed the various ways that the target schools implemented the EWIR in their buildings and the level of support that they received from the central office that aided them in using the EWIR to improve ninth grade promotion rates. Based on the findings of this study, the researcher provided a number of key recommendations: (1) Districts should provide professional development to schools to ensure that schools have the support they need to implement the EWIR successfully; (2) There should be increased accountability from the central office for schools using the EWIR to identify impactful interventions for ninth graders; and (3) The district needs to assign dedicated central office staff to support the implementation of the EWIR in high schools across the district. As schools continue to face the challenge of improving ninth grade promotion rates, effective use of an Early Warning Indicator Report is recommended to provide school and district staff with data needed to impact overall student performance.

Identifying the Supports and Challenges of High School Latino English Language Learners

Two out of three English Language Learners (ELLs) graduate from secondary schools nationwide. Of the nearly five million ELLs in public schools, more than 70% of these students’ first language is Spanish. In order to understand and resolve this phenomena and in an effort to increase the number of graduates, this research examined what high school Latino ELLs identified as the major external and internal factors that support or challenge them on the graduation pathway. The study utilized a 32 quantitative and qualitative question student survey, as well as student focus groups. Both the survey and the focus groups were conducted in English and Spanish. The questions considered the following factors: 1) value of education; 2) expectations in achieving their long-term goals; 3) current education levels; 4) expectations before coming to the United States; 5) family obligations; and 6) future aspirations. The survey was administered to 159 Latino ELLs enrolled in grades 9-12. Research took place at three high schools that provide English for Speakers of Other Languages (ESOL) classes in a large school system in the Mid-Atlantic region. The three schools involved in the study have more than 1,500 ELLs. Two of the schools had large ESOL instructional programs, and one school had a comparatively smaller ESOL program. The majority of students surveyed were from El Salvador (72%) and Guatemala (12.6%). Using Qualtrics, an independent facilitator and a bilingual translator administered the online survey tool to the students during their ESOL classes. Two weeks later, the researcher hosted three follow-up focus groups, totaling 37 students from those students who took the survey. Each focus group was conducted at the three schools by the lead researcher and the translator. The purpose of the focus group was to obtain deeper insight on how secondary age Latino ELLs defined success in school, what they identified to be their support factors, and how previous and present experiences helped or hindered their goals. From the research findings, ten recommendations range from suggested policy updates to cross-cultural/equity training for students and staff; they were developed, stemming from the findings and what the students identified.

“PROSPERING BECAUSE THAT’S ITS HISTORY”: BLACK RESILIENCE AND HONORS DEVELOPMENT IN HIGHER EDUCATION: MORGAN STATE UNIVERSITY AND THE STATE OF MARYLAND, 1867-1988

This study explores the origins and development of honors education at a Historically Black College and University (HBCU), Morgan State University, within the context of the Maryland higher education system. During the last decades, public and private institutions have invested in honors experiences for their high-ability students. These programs have become recruitment magnets while also raising institutional academic profiles, justifying additional campus resources. The history of higher education reveals simultaneous narratives such as the tension of post-desegregated Black colleges facing uncertain futures; and the progress of the rise and popularity of collegiate honors programs. Both accounts contribute to tracing seemingly parallel histories in higher education that speaks to the development of honors education at HBCUs. While the extant literature on honors development at Historically White Institutions (HWIs) of higher education has gradually emerged, our understanding of activity at HBCUs is spotty at best. One connection of these two phenomena is the development of honors programs at HBCUs. Using Morgan State University, I examine the role and purpose of honors education at a public HBCU through archival materials and oral histories. Major unexpected findings that constructed this historical narrative beyond its original scope were the impact of the 1935/6 Murray v Pearson, the first higher education desegregation case. Other emerging themes were Morgan’s decades-long efforts to resist state control of its governance, Maryland’s misuse of Morrill Act funds, and the border state’s resistance to desegregation. Also, the broader histories of Black education, racism, and Black citizenship from Dred Scott and Plessy, the 1863 Emancipation Proclamation to Brown, inform this study. As themes are threaded together, Critical Race Theory provides the framework for understanding the emerging themes. In the immediate wake of the post-desegregation era, HBCUs had to address future challenges such as purpose and mission. Competing with HWIs for high-achieving Black students was one of the unanticipated consequences of the Brown decision. Often marginalized from higher education research literature, this study will broaden the research repository of honors education by documenting HBCU contributions despite a challenging landscape.

A case study of a district's intended and unintended results connected to the implementation of a required ninth-grade algebra 1 strategic initiative

There is a long history of debate around mathematics standards, reform efforts, and accountability. This research identified ways that national expectations and context drive local implementation of mathematics reform efforts and identified the external and internal factors that impact teachers’ acceptance or resistance to policy implementation at the local level. This research also adds to the body of knowledge about acceptance and resistance to policy implementation efforts. This case study involved the analysis of documents to provide a chronological perspective, assess the current state of the District’s mathematics reform, and determine the District’s readiness to implement the Common Core Curriculum. The school system in question has continued to struggle with meeting the needs of all students in Algebra 1. Therefore, the results of this case study will be useful to the District’s leaders as they include the compilation and analysis of a decade’s worth of data specific to Algebra 1.

An Investigation of the Impact of an Aspiring Principals Preparation Program on Principal Leadership Effectiveness

School districts need to “build the bench” to ensure that their schools will have effective principals when vacancies arise (Johnson-Taylor & Martin, 2007). Assistant principals represent a potential pool of new school leaders who are prepared to move confidently into the principalship (Oliver, 2005). Although a critical leader in schools, the assistant principal position is underutilized and under-researched (Oleszewski, Shoho, & Barnett, 2012). This lack of focus on assistant principals is concerning because they are part of the school leadership team and often advance to the position of school principal. The purpose of this study was to examine the impact of Bay City Public Schools’ (a pseudonym) Aspiring Principals Preparation Program (AP3; also a pseudonym) on assistant principals’ learning-centered leadership behaviors, as assessed by the Vanderbilt Assessment of Leadership in Education (Val-Ed) survey. The study compared the Val-Ed scores of assistant principals who had participated in one of three cohorts of AP3 training to the scores of assistant principals who did not participate. The results indicated that participation in the AP3 had no significant impact on respondents’ learning-centered leadership behaviors, as assessed on the VAL-ED instrument. This study may be useful as the district seeks to validate the effectiveness of AP3 and identify potential refinements and program modifications.

Defining the Resolution of a Network for Transportation Analyses: a New Method to Improve Transportation Planning Decisions

Travel demand models are important tools used in the analysis of transportation plans, projects, and policies. The modeling results are useful for transportation planners making transportation decisions and for policy makers developing transportation policies. Defining the level of detail (i.e., the number of roads) of the transport network in consistency with the travel demand model’s zone system is crucial to the accuracy of modeling results. However, travel demand modelers have not had tools to determine how much detail is needed in a transport network for a travel demand model. This dissertation seeks to fill this knowledge gap by (1) providing methodology to define an appropriate level of detail for a transport network in a given travel demand model; (2) implementing this methodology in a travel demand model in the Baltimore area; and (3) identifying how this methodology improves the modeling accuracy. All analyses identify the spatial resolution of the transport network has great impacts on the modeling results. For example, when compared to the observed traffic data, a very detailed network underestimates traffic congestion in the Baltimore area, while a network developed by this dissertation provides a more accurate modeling result of the traffic conditions. Through the evaluation of the impacts a new transportation project has on both networks, the differences in their analysis results point out the importance of having an appropriate level of network detail for making improved planning decisions. The results corroborate a suggested guideline concerning the development of a transport network in consistency with the travel demand model’s zone system. To conclude this dissertation, limitations are identified in data sources and methodology, based on which a plan of future studies is laid out.

Teaching Sight-Reading to Undergraduate Choral Ensemble Singers: Lessons from Successful Learners

This study was designed to investigate professional choral singers’ training, perceptions on the importance of sight-reading skill in their work, and thoughts on effective pedagogy for teaching sight-reading to undergraduate choral ensemble singers. Participants in this study (N=48) included self-selected professional singers and choral conductors from the Summer 2015 Oregon Bach Festival’s Berwick Chorus and conducting Master Class. Data were gathered from questionnaire responses and audio recorded focus group sessions. Focus group data showed that the majority of participants developed proficiency in their sight-reading skills from instrumental study, aural skills classes, and through on-the-job training at a church job or other professional choral singing employment. While participants brought up a number of important job skills, sightreading was listed as perhaps the single most important skill that a professional choral singer could develop. When reading music during the rehearsal process, the data revealed two main strategies that professional singers used to interpret the pitches in their musical line: an intervallic approach and a harmonic approach. Participants marked their scores systematically to identify problem spots and leave reminders to aid with future readings, such as marking intervals, solfege syllables, or rhythmic counts. Participants reported using a variety of skills other than score marking to try to accurately find their pitches, such as looking at other vocal or instrumental lines, looking ahead, and using knowledge about a musical style or time period to make more intuitive “guesses” when sight-reading. Participants described using additional approaches when sight-reading in an audition situation, including scanning for anchors or anomalies and positive self-talk. Singers learned these sight-reading techniques from a variety of sources. Participants had many different ideas about how best to teach sight-reading in the undergraduate choral ensemble rehearsal. The top response was that sight-reading needed to be practiced consistently in order for students to improve. Other responses included developing personal accountability, empowering students, combining different teaching methods, and discussing real-life applications of becoming strong sight-readers. There was discussion about the ultimate purpose of choir at the university level and whether it is to teach musicianship skills or produce excellent performances.

Development of gene expression-based biomarkers of exposure to metals and pesticides in the freshwater amphipod Hyalella azteca

Ecological risk assessment (ERA) is a framework for monitoring risks of exposure and adverse effects of environmental stressors to populations or communities of interest. One tool of ERA is the biomarker, which is a characteristic of an organism that reliably indicates exposure to or effects of a stressor like chemical pollution. Traditional biomarkers which rely on characteristics at the tissue level and higher often detect only acute exposures to stressors. Sensitive molecular biomarkers may detect lower stressor levels than traditional biomarkers, which helps inform risk mitigation and restoration efforts before populations and communities are irreversibly affected. In this study I developed gene expression-based molecular biomarkers of exposure to metals and insecticides in the model toxicological freshwater amphipod Hyalella azteca. My goals were to not only create sensitive molecular biomarkers for these chemicals, but also to show the utility and versatility of H. azteca in molecular studies for toxicology and risk assessment. I sequenced and assembled the H. azteca transcriptome to identify reference and stress-response gene transcripts suitable for expression monitoring. I exposed H. azteca to sub-lethal concentrations of metals (cadmium and copper) and insecticides (DDT, permethrin, and imidacloprid). Reference genes used to create normalization factors were determined for each exposure using the programs BestKeeper, GeNorm, and NormFinder. Both metals increased expression of a nuclear transcription factor (Cnc), an ABC transporter (Mrp4), and a heat shock protein (Hsp90), giving evidence of general metal exposure signature. Cadmium uniquely increased expression of a DNA repair protein (Rad51) and increased Mrp4 expression more than copper (7-fold increase compared to 2-fold increase). Together these may be unique biomarkers distinguishing cadmium and copper exposures. DDT increased expression of Hsp90, Mrp4, and the immune response gene Lgbp. Permethrin increased expression of a cytochrome P450 (Cyp2j2) and decreased expression of the immune response gene Lectin-1. Imidacloprid did not affect gene expression. Unique biomarkers were seen for DDT and permethrin, but the genes studied were not sensitive enough to detect imidacloprid at the levels used here. I demonstrated that gene expression in H. azteca detects specific chemical exposures at sub-lethal concentrations, making expression monitoring using this amphipod a useful and sensitive biomarker for risk assessment of chemical exposure.

THE PHYSICS OF IDEAS: INFERRING THE MECHANICS OF OPINION FORMATION FROM MACROSCOPIC STATISTICAL PATTERNS

In a microscopic setting, humans behave in rich and unexpected ways. In a macroscopic setting, however, distinctive patterns of group behavior emerge, leading statistical physicists to search for an underlying mechanism. The aim of this dissertation is to analyze the macroscopic patterns of competing ideas in order to discern the mechanics of how group opinions form at the microscopic level. First, we explore the competition of answers in online Q&A (question and answer) boards. We find that a simple individual-level model can capture important features of user behavior, especially as the number of answers to a question grows. Our model further suggests that the wisdom of crowds may be constrained by information overload, in which users are unable to thoroughly evaluate each answer and therefore tend to use heuristics to pick what they believe is the best answer. Next, we explore models of opinion spread among voters to explain observed universal statistical patterns such as rescaled vote distributions and logarithmic vote correlations. We introduce a simple model that can explain both properties, as well as why it takes so long for large groups to reach consensus. An important feature of the model that facilitates agreement with data is that individuals become more stubborn (unwilling to change their opinion) over time. Finally, we explore potential underlying mechanisms for opinion formation in juries, by comparing data to various types of models. We find that different null hypotheses in which jurors do not interact when reaching a decision are in strong disagreement with data compared to a simple interaction model. These findings provide conceptual and mechanistic support for previous work that has found mutual influence can play a large role in group decisions. In addition, by matching our models to data, we are able to infer the time scales over which individuals change their opinions for different jury contexts. We find that these values increase as a function of the trial time, suggesting that jurors and judicial panels exhibit a kind of stubbornness similar to what we include in our model of voting behavior.

Balancing Belligerents or Feeding the Beast: Transforming Conflict Traps

Since the end of the Cold War, recurring civil conflicts have been the dominant form of violent armed conflict in the world, accounting for 70% of conflicts active between 2000-2013. Duration and intensity of episodes within recurring conflicts in Africa exhibit four behaviors characteristic of archetypal dynamic system structures. The overarching questions asked in this study are whether these patterns are robustly correlated with fundamental concepts of resiliency in dynamic systems that scale from micro-to macro levels; are they consistent with theoretical risk factors and causal mechanisms; and what are the policy implications. Econometric analysis and dynamic systems modeling of 36 conflicts in Africa between 1989 -2014 are combined with process tracing in a case study of Somalia to evaluate correlations between state characteristics, peace operations and foreign aid on the likelihood of observed conflict patterns, test hypothesized causal mechanisms across scales, and develop policy recommendations for increasing human security while decreasing resiliency of belligerents. Findings are that observed conflict patterns scale from micro to macro levels; are strongly correlated with state characteristics that proxy a mix of cooperative (e.g., gender equality) and coercive (e.g., security forces) conflict-balancing mechanisms; and are weakly correlated with UN and regional peace operations and humanitarian aid. Interactions between peace operations and aid interventions that effect conflict persistence at micro levels are not seen in macro level analysis, due to interdependent, micro-level feedback mechanisms, sequencing, and lagged effects. This study finds that the dynamic system structures associated with observed conflict patterns contain tipping points between balancing mechanisms at the interface of micro-macro level interactions that are determined as much by factors related to how intervention policies are designed and implemented, as what they are. Policy implications are that reducing risk of conflict persistence requires that peace operations and aid interventions (1) simultaneously increase transparency, promote inclusivity (with emphasis on gender equality), and empower local civilian involvement in accountability measures at the local levels; (2) build bridges to horizontally and vertically integrate across levels; and (3) pave pathways towards conflict transformation mechanisms and justice that scale from the individual, to community, regional, and national levels.

Existence and weak-strong uniqueness for the Navier-Stokes-Smoluchowski system over moving domains

This dissertation concerns the well-posedness of the Navier-Stokes-Smoluchowski system. The system models a mixture of fluid and particles in the so-called bubbling regime. The compressible Navier-Stokes equations governing the evolution of the fluid are coupled to the Smoluchowski equation for the particle density at a continuum level. First, working on fixed domains, the existence of weak solutions is established using a three-level approximation scheme and based largely on the Lions-Feireisl theory of compressible fluids. The system is then posed over a moving domain. By utilizing a Brinkman-type penalization as well as penalization of the viscosity, the existence of weak solutions of the Navier-Stokes-Smoluchowski system is proved over moving domains. As a corollary the convergence of the Brinkman penalization is proved. Finally, a suitable relative entropy is defined. This relative entropy is used to establish a weak-strong uniqueness result for the Navier-Stokes-Smoluchowski system over moving domains, ensuring that strong solutions are unique in the class of weak solutions.