Maximum principle preserving high order schemes for convection-dominated diffusion equations

The maximum principle is an important property of solutions to PDE. Correspondingly, it's of great interest for people to design a high order numerical scheme solving PDE with this property maintained. In this thesis, our particular interest is solving convection-dominated diffusion equation. We first review a nonconventional maximum principle preserving(MPP) high order finite volume(FV) WENO scheme, and then propose a new parametrized MPP high order finite difference(FD) WENO framework, which is generalized from the one solving hyperbolic conservation laws. A formal analysis is presented to show that a third order finite difference scheme with this parametrized MPP flux limiters maintains the third order accuracy without extra CFL constraint when the low order monotone flux is chosen appropriately. Numerical tests in both one and two dimensional cases are performed on the simulation of the incompressible Navier-Stokes equations in vorticity stream-function formulation and several other problems to show the effectiveness of the proposed method.

Living with Differences: From Everyday Fundamentalisms to Invitational Communication

This project examines fundamentalism understood as an everyday way of living poorly with difference. It demonstrates that the fundamentalist is not reducible to stereotypes of the terrorist, extremist, irrational madman, or religious zealot. All of these characterizations--common in mainstream media--depict the fundamentalist as them, and rarely, if ever, as us. Rather, this project understands fundamentalism in terms of fundamental interpretive constructs that constrain our ways of being-with others, skew our interpretive and responsive possibilities, distort our perceptions of difference, and affirm our poor treatment of others. Following Martin Heidegger's conception of the hermeneutic structure of existence, this dissertation calls attention to the ways in which such fundamentalisms filter our interpretation. Yet the hermeneutic character of existence also highlights the incompleteness of any particular frame of interpretation and indicates the possibility of alternative interpretive responses. The project turns to a feminist theological hermeneutic in order to indicate more hopeful and liberating ways of living with difference, ways that point beyond everyday fundamentalism toward invitational communication. Through new readings of familiar biblical narratives, this dissertation revisits the fundamentalisms that trigger these narratives in order to draw out an alternative feminist theological hermeneutic, or what is termed here an invitational hermeneutic. Each story offers unique ways of making sense of being-with and sharing the world with others of difference that redress the impoverished and fundamentalist forms of self-preserving care and understanding. By examining the well-loved stories of the Good Samaritan, Ruth and Naomi, Queen Esther, and the Apostle Paul and Lydia, the dissertation identifies interpretive and responsive possibilities that together issue an alternative hermeneutical invitation: to understand difference compassionately, to engage strangers and family members alike with rehabilitative care and concernful reticence, and to extend graceful hospitality to others. In these ways, the dissertation indicates possibilities beyond the horizon of fundamentalism, invitational possibilities of living and communicating with difference.

Preserving and interpreting the mining company office : landscape, space and technological change in the management of the copper industry

The purpose of this research is to examine the role of the mining company office in the management of the copper industry in Michigan’s Keweenaw Peninsula between 1901 and 1946. Two of the largest and most influential companies were examined – the Calumet & Hecla Mining Company and the Quincy Mining Company. Both companies operated for more than forty years under general managers who were arguably the most influential people in the management of each company. James MacNaughton, general manager at Calumet and Hecla, worked from 1901 through 1941; Charles Lawton, general manager at Quincy Mining Company, worked from 1905 through 1946. In this case, both of these managers were college-educated engineers and adopted scientific management techniques to operate their respective companies. This research focused on two main goals. The first goal of this project was to address the managerial changes in Michigan’s copper mining offices of the early twentieth century. This included the work of MacNaughton and Lawton, along with analysis of the office structures themselves and what changes occurred through time. The second goal of the project was to create a prototype virtual exhibit for use at the Quincy Mining Company office. A virtual exhibit will allow visitors the opportunity to visit the office virtually, experiencing the office as an office worker would have in the early twentieth century. To meet both goals, this project used various research materials, including archival sources, oral histories, and material culture to recreate the history of mining company management in the Copper Country.