Application of Numerical Methods to Study Arrangement and Fracture of Lithium-Ion Microstructure

The focus of this work is to develop and employ numerical methods that provide characterization of granular microstructures, dynamic fragmentation of brittle materials, and dynamic fracture of three-dimensional bodies.

We first propose the fabric tensor formalism to describe the structure and evolution of lithium-ion electrode microstructure during the calendaring process. Fabric tensors are directional measures of particulate assemblies based on inter-particle connectivity, relating to the structural and transport properties of the electrode. Applying this technique to X-ray computed tomography of cathode microstructure, we show that fabric tensors capture the evolution of the inter-particle contact distribution and are therefore good measures for the internal state of and electronic transport within the electrode.

We then shift focus to the development and analysis of fracture models within finite element simulations. A difficult problem to characterize in the realm of fracture modeling is that of fragmentation, wherein brittle materials subjected to a uniform tensile loading break apart into a large number of smaller pieces. We explore the effect of numerical precision in the results of dynamic fragmentation simulations using the cohesive element approach on a one-dimensional domain. By introducing random and non-random field variations, we discern that round-off error plays a significant role in establishing a mesh-convergent solution for uniform fragmentation problems. Further, by using differing magnitudes of randomized material properties and mesh discretizations, we find that employing randomness can improve convergence behavior and provide a computational savings.

The Thick Level-Set model is implemented to describe brittle media undergoing dynamic fragmentation as an alternative to the cohesive element approach. This non-local damage model features a level-set function that defines the extent and severity of degradation and uses a length scale to limit the damage gradient. In terms of energy dissipated by fracture and mean fragment size, we find that the proposed model reproduces the rate-dependent observations of analytical approaches, cohesive element simulations, and experimental studies.

Lastly, the Thick Level-Set model is implemented in three dimensions to describe the dynamic failure of brittle media, such as the active material particles in the battery cathode during manufacturing. The proposed model matches expected behavior from physical experiments, analytical approaches, and numerical models, and mesh convergence is established. We find that the use of an asymmetrical damage model to represent tensile damage is important to producing the expected results for brittle fracture problems.

The impact of this work is that designers of lithium-ion battery components can employ the numerical methods presented herein to analyze the evolving electrode microstructure during manufacturing, operational, and extraordinary loadings. This allows for enhanced designs and manufacturing methods that advance the state of battery technology. Further, these numerical tools have applicability in a broad range of fields, from geotechnical analysis to ice-sheet modeling to armor design to hydraulic fracturing.

Leading from the Edge: Marginal Leadership at Cultural Crossroads

If a church reflects its larger community, it will have more dynamic interactions among different people. Current U.S. communities consist of very diverse people who have different socioeconomic and cultural backgrounds. Since the mid 20th century, various immigrant communities who have dissimilar cultural, religious, and linguistic traditions have accelerated the need of change in American churches. The drastic cultural change has demanded churches to equip their lay and clergy leaders with multicultural competencies for effective ministries.

My thesis explores imaginative leadership in cultural crossroads. Emphasizing the leadership imagination of cross-cultural ministry, I approach it in biblical, theological, and missional perspectives. In this dynamic cultural milieu, the study topic may help the church renew its ecclesial purpose by seeing cross-cultural ministry as a creative opportunity to reach out to more diverse people of God. I begin with a conceptual framework for cross-cultural ministry and cultural intelligence. Then I explain why cross-cultural ministry is significant and how it enhances the spirit of Christ Jesus. As I develop the thesis, I discuss leadership challenge and development in the cross-cultural ministry context. This thesis may contribute to equipping lay and clergy leaders by overcoming the homogeneous ‘in-group’ mindset in the church.

The primary focus is on developing marginal leadership of church in the post-Christendom era. Church leaders must creatively hold the tension between the current church context and Christian faith resources and seek a hopeful resolution as a third way through integrative thought process. While conventional leadership emphasizes a better choice out of the given options, marginal leadership takes time for integrative thought process to seek a new direction for the future. Conventional leaders take the center with their power, status, and prestige, but marginal leaders position themselves on the edge. Leading from the edge is a distinctive cross-cultural leadership and is based on the servant leadership of Jesus Christ who put himself as a servant for the marginalized. By serving and relating to others on the margin, this imaginative leadership may make appropriate changes desired in today’s American churches.

In addition to academic research, I looked into the realities of cross-cultural leadership in the local churches through congregational studies. I speculated that church leadership involves both laity and clergy and that it can be enhanced. All Christians are called to serve the Lord according to their gifts, and it is crucial for lay and clergy persons to develop their leadership character and skills. In particular, as humans are contextualized with their own cultures, church leaders often confront great challenges in cross-cultural or multicultural situations. Through critical thoughts and imaginative leadership strategies, however, they can overcome intrinsic human prejudice and obstacles.

Through the thesis project, I have reached four significant conclusions. First, cultural intelligence is an essential leadership capacity for all church leaders. As the church consists of more diverse cultural people today, its leaders need to have cultural competencies. In particular, cross-cultural leaders must be equipped with cultural intelligence. Cross-cultural ministry is not a simple byproduct of social change, but a creative strategy to open a door to bring God’s reconciliation among diverse people. Accordingly, church leaders are to be well prepared to effectively cope with the challenges of cultural interactions. Second, both lay and clergy leaders’ imaginative leadership is crucial for leading the congregation. While conventional leadership puts an emphasis on selecting a better choice based on the principle of opportunity cost, imaginative leaders critically consider the present church situations and Christian faith values together in integrative thoughts and pursue a third way as the congregation’s future hope. Third, cross-cultural leadership has a unique characteristic of leading from the edge and promotes God’s justice and peaceable relationships among different people. By leading the congregation from the edge, church leaders may experience the heart of Christ Jesus who became the friend of the marginalized. Fourth, the ‘homogeneous unit principle’ theory has its limit for today’s complex ‘inter-group’ community context. The church must be a welcoming and embracing faith community for all people. Cross-cultural ministry may become an entrance door for a more peaceable and reconciling life among different people. By building solidarity with others, the church may experience a kingdom reality.

This thesis focuses on the mission of the church and marginal leadership of church leaders in ever-changing cultural crossroads. The church becomes a hope in the broken and apathetic world, and Christians are called to build relationships inside and beyond the church. It is significant for church leaders to be faithfully present on the margin and relate to diverse people. By consistently positioning themselves on the margin, they can build relationships with new and diverse people and shape a faithful life pattern for others.

Inter-Species Microbial Sharing in Rural Madagascar: A Study of Environmental Influences on the Skin Microbiome

The skin is home to trillions of microbes, many of which are recently implicated in immune system regulation and various health conditions (33). The skin is continuously exposed to the outside environment, inviting microbial transfer between human skin and the people, animals, and surfaces with which an individual comes into contact. Thus, the aim of this study is to assess how different environmental exposures influence skin microbe communities, as this can strengthen our understanding of how microbial variation relates to health outcomes. This study investigated the skin microbial communities of humans and domesticated cattle living in rural Madagascar. The V3 region of the 16S rRNA gene was sequenced from samples of zebu (the domesticated cattle of Madagascar), zebu owners, and non-zebu owners. Overall, human armpits were the least diverse sample site, while ankles were the most diverse. The diversity of zebu samples was significantly different from armpits, irrespective of zebu ownership (one-way ANOVA and Tukey’s HSD, p<0.05). However, zebu owner samples (from the armpit, ankle forearm, and hand) were more similar to other zebu owner samples than they were to zebu, yet no more similar to other zebu owner samples than they were to non-zebu owner samples (unweighted UniFrac distances, p<0.05). These data suggest a lack of a microbial signature shared by zebu owners and zebu, though further taxonomic analysis is required to explain the role of additional environmental variables in dictating the microbial communities of various samples sites. Understanding the magnitude and directionality of microbial sharing has implications for a breadth of microbe-related health outcomes, with the potential to explain mosquito host preference and mitigate the threats of vector-borne diseases.

Inter-site and inter-scanner diffusion MRI data harmonization.

We propose a novel method to harmonize diffusion MRI data acquired from multiple sites and scanners, which is imperative for joint analysis of the data to significantly increase sample size and statistical power of neuroimaging studies. Our method incorporates the following main novelties: i) we take into account the scanner-dependent spatial variability of the diffusion signal in different parts of the brain; ii) our method is independent of compartmental modeling of diffusion (e.g., tensor, and intra/extra cellular compartments) and the acquired signal itself is corrected for scanner related differences; and iii) inter-subject variability as measured by the coefficient of variation is maintained at each site. We represent the signal in a basis of spherical harmonics and compute several rotation invariant spherical harmonic features to estimate a region and tissue specific linear mapping between the signal from different sites (and scanners). We validate our method on diffusion data acquired from seven different sites (including two GE, three Philips, and two Siemens scanners) on a group of age-matched healthy subjects. Since the extracted rotation invariant spherical harmonic features depend on the accuracy of the brain parcellation provided by Freesurfer, we propose a feature based refinement of the original parcellation such that it better characterizes the anatomy and provides robust linear mappings to harmonize the dMRI data. We demonstrate the efficacy of our method by statistically comparing diffusion measures such as fractional anisotropy, mean diffusivity and generalized fractional anisotropy across multiple sites before and after data harmonization. We also show results using tract-based spatial statistics before and after harmonization for independent validation of the proposed methodology. Our experimental results demonstrate that, for nearly identical acquisition protocol across sites, scanner-specific differences can be accurately removed using the proposed method.