AN ENTROPIC THEORY OF DAMAGE WITH APPLICATIONS TO CORROSION-FATIGUE STRUCTURAL INTEGRITY ASSESSMENT

This dissertation demonstrates an explanation of damage and reliability of critical components and structures within the second law of thermodynamics. The approach relies on the fundamentals of irreversible thermodynamics, specifically the concept of entropy generation due to materials degradation as an index of damage. All failure mechanisms that cause degradation, damage accumulation and ultimate failure share a common feature, namely energy dissipation. Energy dissipation, as a fundamental measure for irreversibility in a thermodynamic treatment of non-equilibrium processes, leads to and can be expressed in terms of entropy generation. The dissertation proposes a theory of damage by relating entropy generation to energy dissipation via generalized thermodynamic forces and thermodynamic fluxes that formally describes the resulting damage. Following the proposed theory of entropic damage, an approach to reliability and integrity characterization based on thermodynamic entropy is discussed. It is shown that the variability in the amount of the thermodynamic-based damage and uncertainties about the parameters of a distribution model describing the variability, leads to a more consistent and broader definition of the well know time-to-failure distribution in reliability engineering. As such it has been shown that the reliability function can be derived from the thermodynamic laws rather than estimated from the observed failure histories. Furthermore, using the superior advantages of the use of entropy generation and accumulation as a damage index in comparison to common observable markers of damage such as crack size, a method is proposed to explain the prognostics and health management (PHM) in terms of the entropic damage. The proposed entropic-based damage theory to reliability and integrity is then demonstrated through experimental validation. Using this theorem, the corrosion-fatigue entropy generation function is derived, evaluated and employed for structural integrity, reliability assessment and remaining useful life (RUL) prediction of Aluminum 7075-T651 specimens tested.

Spectral graph theory with applications to quantum adiabatic optimization

In this dissertation I draw a connection between quantum adiabatic optimization, spectral graph theory, heat-diffusion, and sub-stochastic processes through the operators that govern these processes and their associated spectra. In particular, we study Hamiltonians which have recently become known as ``stoquastic'' or, equivalently, the generators of sub-stochastic processes. The operators corresponding to these Hamiltonians are of interest in all of the settings mentioned above. I predominantly explore the connection between the spectral gap of an operator, or the difference between the two lowest energies of that operator, and certain equilibrium behavior. In the context of adiabatic optimization, this corresponds to the likelihood of solving the optimization problem of interest. I will provide an instance of an optimization problem that is easy to solve classically, but leaves open the possibility to being difficult adiabatically. Aside from this concrete example, the work in this dissertation is predominantly mathematical and we focus on bounding the spectral gap. Our primary tool for doing this is spectral graph theory, which provides the most natural approach to this task by simply considering Dirichlet eigenvalues of subgraphs of host graphs. I will derive tight bounds for the gap of one-dimensional, hypercube, and general convex subgraphs. The techniques used will also adapt methods recently used by Andrews and Clutterbuck to prove the long-standing ``Fundamental Gap Conjecture''.

Jiao Tong: A Grounded Theory of Chinese International Students' Transition to American Tertiary Education

University students are more globally mobile than ever before, increasingly receiving education outside of their home countries. One significant student exchange pattern is between China and the United States; Chinese students are the largest population of international students in the U.S. (Institute of International Education, 2014). Differences between Chinese and American culture in turn influence higher education praxis in both countries, and students are enculturated into the expectations and practices of their home countries. This implies significant changes for students who must navigate cultural differences, academic expectations, and social norms during the process of transition to a system of higher education outside their home country. Despite the trends in students’ global mobility and implications for international students’ transitions, scholarship about international students does not examine students’ experiences with the transition process to a new country and system of higher education. Related models were developed with American organizations and individuals, making it unlikely that they would be culturally transferable to Chinese international students’ transitions. This study used qualitative methods to deepen the understanding of Chinese international students’ transition processes. Grounded theory methods were used to invite the narratives of 18 Chinese international students at a large public American university, analyze the data, and build a theory that reflects Chinese international students’ experiences transitioning to American university life. Findings of the study show that Chinese international students experience a complex process of transition to study in the United States. Students’ pre-departure experiences, including previous exposure to American culture, family expectations, and language preparation, informed their transition. Upon arrival, students navigate resource seeking to fulfill their practical, emotional, social, intellectual, and ideological needs. As students experienced various positive and discouraging events, they developed responses to the pivotal moments. These behaviors formed patterns in which students sought familiarity or challenge subsequent to certain events. The findings and resulting theory provide a framework through which to better understand the experiences of Chinese international students in the context of American higher education.