Global (in Time) Solutions to the 3D-Navier-Stokes Equations on R^3

A well-known unsolved problem (in the classical theory of fluid mechanics) is to identify a set of initial velocities, which may depend on the viscosity, the body forces and possibly the boundary of the fluid that will allow global in time solutions to the three-dimensional Navier-Stokes equations. (These equations describe the time evolution of the fluid velocity and pressure of an incompressible viscous homogeneous Newtonian fluid in terms of a given initial velocity and given external body forces.) A related problem is to provide conditions under which we can be assured that the numerical approximation of these equations, used in a variety of fields from weather prediction to submarine design, have only one solution. In earlier papers, we solved this problem for a bounded domain. In this paper, we use an approach based on additional physical insight, that allows us to prove that there exists unique global in time solutions to the Navier-Stokes equations on R^3

Developing computational models for pulsed-inductive plasma formation

Pulsed-inductive discharges are a common method of producing a plasma. They provide a mechanism for quickly and efficiently generating a large volume of plasma for rapid use and are seen in applications including propulsion, fusion power, and high-power lasers. However, some common designs see a delayed response time due to the plasma forming when the magnitude of the magnetic field in the device is at a minimum. New designs are difficult to evaluate due to the amount of time needed to construct a new geometry and the high monetary cost of changing the power generation circuit. To more quickly evaluate new designs and better understand the shortcomings of existing designs, two computational models have been developed for use in Mathematica. The first model uses a modified single-electron model to determine how the energy distribution in a system changes with regards to time and location. The second model uses Townsend breakdown to obtain the time rate of change of electron number density. This rate is then integrated to obtain an electron number density distribution that varies with regards to time and location. By analyzing the energy distribution and the density distribution, the approximate times and locations of initial plasma breakdown and bulk plasma formation can be predicted. The results from these codes are then compared to existing data to show their validity and shortcomings --Abstract, page iii

Code-Switching Practices in the Foreign-Language Classroom: Instructor Nativeness and Students\u27 Perceptions

In this study we investigated code-switching practices in the foreign language classroom among instructors who are native speakers of the target language (Spanish) and instructors who are non-native speakers of the target language, as well as students’ perceptions of L1 use. Participants were three college instructors of Spanish and 38 college students in an intermediate level Spanish course. The participants were observed and recorded during two hour-long classes involving group work. After the observations, the instructors completed an interview, and the students completed an online questionnaire. This study found that native instructors use less English than non-native instructors and the native English-speaking Spanish instructor used the most amount of English. Students’ perceptions of English use in the classroom align with the amount of English used in the classroom. Students with the native instructor found English use less advantageous while students with the non-native instructors found English more advantageous. The findings in this study suggest that students’ perceptions may be influenced by the amount of English to which they are exposed

‘A CATEGORY OF THEIR OWN’: QUANTITATIVE METHODS IN THE USE OF PILE-SORT DATA IN PERCEPTUAL DIALECTOLOGY

The purpose of this study is to investigate how Mississippi Gulf Coast Creoles perceive language differences in their home area. A pile-sort task was carried out in which respondents were given stacks of cards with local communities written on them and instructed to stack together the regions where people “talk the same.” Once the piles were made, the fieldworker discussed their sortings with the respondents. The stacks were analyzed by means of a hierarchal agglomerative cluster analysis and non-parametric multidimensional scaling with k-means cluster analysis overlays to extract the perceived dialect areas. The groupings reveal that respondent strategies are based on geographical concerns (e.g. distance), linguistic facts, and related ethnic identity beliefs. These areas were also analyzed using qualitative data from the post-pile-sort discussion and revealed the respondent’s attitudes, stances, and presupposed and implicated meanings that aided in the interpretation of their perceptions and attitudes with regard to local language ideology in the region. The results show that there are six perceived dialect areas on the Mississippi Gulf Coast. The Principal Component Analysis revealed that urban and rural is the biggest differentiation among dialect groups, followed by Frenchness and Southernness