Topics in equilibrium and nonequilibrium thermodynamics: computing crystalline free energies and engineering Maxwell’s demon.

This dissertation covers two separate topics in statistical physics. The first part of the dissertation focuses on computational methods of obtaining the free energies (or partition functions) of crystalline solids. We describe a method to compute the Helmholtz free energy of a crystalline solid by direct evaluation of the partition function. In the many-dimensional conformation space of all possible arrangements of N particles inside a periodic box, the energy landscape consists of localized islands corresponding to different solid phases. Calculating the partition function for a specific phase involves integrating over the corresponding island. Introducing a natural order parameter that quantifies the net displacement of particles from lattices sites, we write the partition function in terms of a one-dimensional integral along the order parameter, and evaluate this integral using umbrella sampling. We validate the method by computing free energies of both face-centered cubic (FCC) and hexagonal close-packed (HCP) hard sphere crystals with a precision of $10^{-5}k_BT$ per particle. In developing the numerical method, we find several scaling properties of crystalline solids in the thermodynamic limit. Using these scaling properties, we derive an explicit asymptotic formula for the free energy per particle in the thermodynamic limit. In addition, we describe several changes of coordinates that can be used to separate internal degrees of freedom from external, translational degrees of freedom. The second part of the dissertation focuses on engineering idealized physical devices that work as Maxwell's demon. We describe two autonomous mechanical devices that extract energy from a single heat bath and convert it into work, while writing information onto memory registers. Additionally, both devices can operate as Landauer's eraser, namely they can erase information from a memory register, while energy is dissipated into the heat bath. The phase diagrams and the efficiencies of the two models are solved and analyzed. These two models provide concrete physical illustrations of the thermodynamic consequences of information processing.

Advanced Adhesion Strength Testing Methods of Thin Film Multilayers in Electronic Packaging Systems

With the continued miniaturization and increasing performance of electronic devices, new technical challenges have arisen. One such issue is delamination occurring at critical interfaces inside the device. This major reliability issue can occur during the manufacturing process or during normal use of the device. Proper evaluation of the adhesion strength of critical interfaces early in the product development cycle can help reduce reliability issues and time-to-market of the product. However, conventional adhesion strength testing is inherently limited in the face of package miniaturization, which brings about further technical challenges to quantify design integrity and reliability. Although there are many different interfaces in today's advanced electronic packages, they can be generalized into two main categories: 1) rigid to rigid connections with a thin flexible polymeric layer in between, or 2) a thin film membrane on a rigid structure. Knowing that every technique has its own advantages and disadvantages, multiple testing methods must be enhanced and developed to be able to accommodate all the interfaces encountered for emerging electronic packaging technologies. For evaluating the adhesion strength of high adhesion strength interfaces in thin multilayer structures a novel adhesion test configuration called “single cantilever adhesion test (SCAT)” is proposed and implemented for an epoxy molding compound (EMC) and photo solder resist (PSR) interface. The test method is then shown to be capable of comparing and selecting the stronger of two potential EMC/PSR material sets. Additionally, a theoretical approach for establishing the applicable testing domain for a four-point bending test method was presented. For evaluating polymeric films on rigid substrates, major testing challenges are encountered for reducing testing scatter and for factoring in the potentially degrading effect of environmental conditioning on the material properties of the film. An advanced blister test with predefined area test method was developed that considers an elasto-plastic analytical solution and implemented for a conformal coating used to prevent tin whisker growth. The advanced blister testing with predefined area test method was then extended by employing a numerical method for evaluating the adhesion strength when the polymer’s film properties are unknown.

Ready for Transition: Factors that facilitate transfer to undergraduate engineering programs among Black African and American students

This study examines the factors facilitating the transfer admission of students broadly classified as Black from a single community college into a selective engineering college. The work aims to further research on STEM preparation and performance for students of color, as well as scholarship on increasing access to four-year institutions from two-year schools. Factors illuminating Underrepresented Racial and Ethnic Minority (URM) student pathways through Science, Technology, Engineering, and Mathematics (STEM) degree programs have often been examined through large-scale quantitative studies. However, this qualitative study complements quantitative data through demographic questionnaires, as well as semi-structured individual and group. The backgrounds and voices of diverse Black transfer students in four-year engineering degree programs were captured through these methods. Major findings from this research include evidence that community college faculty, peer networks, and family members facilitated transfer. Other results distinguish Black African from Black American transfers; included in these distinctions are depictions of different K-12 schooling experiences and differences in how participants self-identified. The findings that result from this research build upon the few studies that account for expanded dimensions of student diversity within the Black population. Among other demographic data, participants’ countries of birth and years of migration to the U.S. (if applicable) are included. Interviews reveal participants’ perceptions of factors impacting their educational trajectories in STEM and subsequent ability to transfer into a competitive undergraduate engineering program. This study is inclusive of, and reveals an important shifting demographic within the United States of America, Black Africans, who represent one of the fastest-growing segments of the immigrant population.

STATISTICAL METHODS FOR ADVANCED ECONOMETRIC MODELS WITH APPLICATIONS TO VEHICLE HOLDING AND SPEED QUANTILES DISTRIBUTION

This dissertation proposes statistical methods to formulate, estimate and apply complex transportation models. Two main problems are part of the analyses conducted and presented in this dissertation. The first method solves an econometric problem and is concerned with the joint estimation of models that contain both discrete and continuous decision variables. The use of ordered models along with a regression is proposed and their effectiveness is evaluated with respect to unordered models. Procedure to calculate and optimize the log-likelihood functions of both discrete-continuous approaches are derived, and difficulties associated with the estimation of unordered models explained. Numerical approximation methods based on the Genz algortithm are implemented in order to solve the multidimensional integral associated with the unordered modeling structure. The problems deriving from the lack of smoothness of the probit model around the maximum of the log-likelihood function, which makes the optimization and the calculation of standard deviations very difficult, are carefully analyzed. A methodology to perform out-of-sample validation in the context of a joint model is proposed. Comprehensive numerical experiments have been conducted on both simulated and real data. In particular, the discrete-continuous models are estimated and applied to vehicle ownership and use models on data extracted from the 2009 National Household Travel Survey. The second part of this work offers a comprehensive statistical analysis of free-flow speed distribution; the method is applied to data collected on a sample of roads in Italy. A linear mixed model that includes speed quantiles in its predictors is estimated. Results show that there is no road effect in the analysis of free-flow speeds, which is particularly important for model transferability. A very general framework to predict random effects with few observations and incomplete access to model covariates is formulated and applied to predict the distribution of free-flow speed quantiles. The speed distribution of most road sections is successfully predicted; jack-knife estimates are calculated and used to explain why some sections are poorly predicted. Eventually, this work contributes to the literature in transportation modeling by proposing econometric model formulations for discrete-continuous variables, more efficient methods for the calculation of multivariate normal probabilities, and random effects models for free-flow speed estimation that takes into account the survey design. All methods are rigorously validated on both real and simulated data.

ENGINEERING HIERARCHICAL MESO-/MICROPOROUS LAMELLAR ZEOLITES WITH VARIABLE TEXTURAL AND CATALYTIC PROPERTIES

Meso-/microporous zeolites combine the charactersitics of well-defined micropores of zeolite with efficient mass transfer consequences of mesopores to increase the efficiency of the catalysts in reactions involving bulky molecules. Different methods such as demetallation and templating have been explored for the synthesis of meso-/microporous zeolites. However, they all have limitations in production of meso-/microporous zeolites with tunable textural and catalytic properties using few synthesis steps. To address this challenge, a simple one-step dual template synthesis approach has been developed in this work to engineer lamellar meso-/microporous zeolites structures with tunable textural and catalytic properties. First, one-step dual template synthesis of meso-/microporous mordenite framework inverted (MFI) zeolite structures was investigated. Tetrapropyl ammonium hydroxide (TPAOH) and diquaternary ammonium surfactant ([C22H45-N+(CH3)2-C6H12-N+(CH3)2-C6H13]Br2, C22-6-6) were used as templates to produce micropores and mesopores, respectively. The variation in concentration ratios of dual templates and hydrothermal synthesis conditions resulted in production of multi-lamellar MFI and the hybrid lamellar-bulk MFI (HLBM) zeolite structures. The relationship between the morphology, porosity, acidity, and catalytic properties of these catalysts was systematically studied. Then, the validity of the proposed synthesis approach for production of other types of zeolites composites was examined by creating a meso-/microporous bulk polymorph A (BEA)-lamellar MFI (BBLM) composite. The resulted composite samples showed higher catalytic stability compared to their single component zeolites. The studies demonstrated the high potential of the one-step dual template synthesis procedure for engineering the textural and catalytic properties of the synthesized zeolites.