Efficient numerical stability analysis of detonation waves in ZND

As described in the classic works of Lee--Stewart and Short--Stewart, the numerical evaluation of linear stability of planar detonation waves is a computationally intensive problem of considerable interest in applications. Reexamining this problem from a modern numerical Evans function point of view, we derive a new algorithm for their stability analysis, related to a much older method of Erpenbeck, that, while equally simple and easy to implement as the standard method introduced by Lee--Stewart, appears to be potentially faster and more stable

Balanced flux formulations for multidimensional Evans function computations for viscous shocks

The Evans function is a powerful tool for the stability analysis of viscous shock profiles; zeros of this function carry stability information. In the one-dimensional case, it is typical to compute the Evans function using Goodman's integrated coordinates [G1]; this device facilitates the search for zeros of the Evans function by winding number arguments. Although integrated coordinates are not available in the multidimensional case, we show here that there is a choice of coordinates which gives similar advantages

On the shock wave spectrum for isentropic gas dynamics with capillarity

AbstractWe consider the stability problem for shock layers in Slemrod's model of an isentropic gas with capillarity. We show that these traveling waves are monotone in the weak capillarity case, and become highly oscillatory as the capillarity strength increases. Using a spectral energy estimate we prove that small-amplitude monotone shocks are spectrally stable. We also show that monotone shocks have no unstable real spectrum regardless of amplitude; this implies that any instabilities of these monotone traveling waves, if they exist, must occur through a Hopf-like bifurcation, where one or more conjugate pairs of eigenvalues cross the imaginary axis. We then conduct a systematic numerical Evans function study, which shows that monotone and mildly oscillatory profiles in an adiabatic gas are spectrally stable for moderate values of shock and capillarity strengths. In particular, we show that the transition from monotone to nonmonotone profiles does not appear to trigger any instabilities

MS

thesisThe problem of this study was to determine the need for an Occupational Therapy school in Utah. Statistical and historical data were gathered for the first accurately compiled and recorded history of the growth and development of Occupation Therapy in Utah. The method use was historical and survey. The background of Occupation Therapy was necessary to understand and clarify the problem. The data for the survey were collected through interviews and questionnaires. The procedure was as follows: 1. A history was compiled of the Occupation Therapy departments in Utah to show growth and development of Occupation Therapy in the State. 2. A search was made to ascertain if a previous study concerning this subject had been undertaken. 3. Statistical data, secured through questionnaire responses and replies to correspondence, were compiled into charts, graphs, and tables. 4. Personal interviews indicated trends in development and the extent to which Occupation Therapy was understood and utilized. 5. Controversies in the historical development of Occupation Therapy in the State were carefully checked and corrections were made. 6. Approvals for acceptance and printing of data and materials for the study were secured, when necessary, form profession personnel, government officials, hospital directors and administrators. 7. The Occupation Therapy State Organization and Constitution were included in the study. Sources of data were obtained from: 1. Newspapers. The Herald (now obsolete), the Deseret News, the Deseret News Library, and the Salt Lake Tribune. 2. Personal data. Correspondence with therapists, diaries, early brochures, historical reports and scrapbook. 3. Books and other literature. The American Journal of Occupation Therapy, American Medical Journal and Hospital Report, Occupation Therapy Register Yearbook, Pioneer histories, and thesis. 4. Questionnaires and their return responses from: Active and non-active therapists, State Health Departments of the surrounding states, also the surrounding states Rehabilitation departments, hospital in the majors cities of this study, Utah's district nurses, and random sampling of nurses form seven Utah hospitals. 5. Personal interviews with: Educators, State officials, professional and medical directors, supervisors, administrators, and therapists. The findings to substantiate the needs for an Occupation Therapy school in Utah