Juncture stress fields in multicellular shell structures. Volume I - Numerical methods of solving large matrices Final report

Numerical techniques for digital computer solution of algebraic simultaneous linear equations from finite difference approximation of partial differential equations of thin elastic shell

Ground Operations of the ISS GNC Babb-Mueller Atmospheric Density Model

The ISS GNC system was updated recently with a new software release that provides onboard state determination capability. Prior to this release, only the Russian segment maintained and propagated the onboard state, which was periodically updated through Russian ground tracking. The new software gives the US segment the capability for maintaining the onboard state, and includes new GPS and state vector propagation capabilities. Part of this software package is an atmospheric density model based on the Babb-Mueller algorithm. Babb-Mueller efficiently mimics a full analytical density model, such as the Jacchia model. While lacchia is very robust and is used in the Mission Control Center, it is too computationally intensive for use onboard. Thus, Babb-Mueller was chosen as an alternative. The onboard model depends on a set of calibration coefficients that produce a curve fit to the lacchia model. The ISS GNC system only maintains one set of coefficients onboard, so a new set must be uplinked by controllers when the atmospheric conditions change. The onboard density model provides a real-time density value, which is used to calculate the drag experienced by the ISS. This drag value is then incorporated into the onboard propagation of the state vector. The propagation of the state vector, and therefore operation of the BabbMueller algorithm, will be most critical when GPS updates and secondary state vector sources fail. When GPS is active, the onboard state vector will be updated every ten seconds, so the propagation error is irrelevant. When GPS is inactive, the state vector must be updated at least every 24 hours, based on current protocol. Therefore, the Babb-Mueller coefficients must be accurate enough to fulfill the state vector accuracy requirements for at least one day. A ground operations concept was needed in order to manage both the on board Babb-Mueller density model and the onboard state quality. The Babb-Mueller coefficients can be determined operationally in two ways. The first method is to calibrate the coefficients in real-time, where a set of custom coefficients is generated for the real-time atmospheric conditions. The second approach is to generate pre-canned sets of coefficients that encompass the expected atmospheric conditions over the lifetime of the vehicle. These predetermined sets are known as occurrences. Even though a particular occurrence will not match the true atmospheric conditions, the error will be constrained by limiting the breadth of each occurrence. Both methods were investigated and the advantages and disadvantages of each were considered. The choice between these implementations was a trade-off between the additional accuracy of the real-time calibration and the simpler development for the approach using occurrences. The operations concept for the frequency of updates was also explored, and depends on the deviation in solar flux that still achieves the necessary accuracy of the coefficients. This was determined based on historical solar flux trends. This analysis resulted in an accurate and reliable implementation of the Babb-Mueller coefficients and how flight controllers use them during realtime operations

Leaders of Change: An Exploration of Relationships Between International School Administrators’ Mindsets and Their Preferred Leadership Styles

At the heart of educational leadership is the ability to manage change. Leaders who can successfully manage change invariably will be more effective. This is especially true in the often-transient world of international schools, where change happens frequently in response to evolving internal and external environments. K-12 international schools that use the English language as the medium of instruction have proliferated since the end of the Cold War. There has been exponential growth, especially in China, India, and other developed and developing nations. The quality of leadership in these schools is extremely important to stakeholders, especially students, and, consequently, it is important that those hiring managers/leaders for such schools hire people who have what Dweck called an incremental/growth mindset which is defined as people who believe that their intelligence and talents are malleable. The purpose of this quantitative research study was to understand the relationship, if any, between international school leadership team members’ preferred leadership styles and their embrace of an incremental/growth mindset. The study surveyed 122 middle- and senior-level international school leaders. The survey instrument included (a) demographic questions; (b) items from the Multifactor Leadership Questionnaire (MLQ) developed by Bass & Avolio which assessed whether a leader embraces what Burns characterized as transformative or transactional leadership styles; and (c) questions adapted from the Implicit Theories of Intelligence scale developed by Dweck to determine whether leaders hold more of an incremental/growth mindset or a fixed mindset. The collected data were analyzed using both independent sample t-tests and multiple regression analysis. The findings from this study indicate those hiring leaders can reasonably infer whether a candidate is likely to have a growth mindset once they determine if the candidate’s leadership style is not laissez-faire. In fact, the findings indicate that a growth mindset is negatively associated with a preference for a laissez-faire leadership style, even though there were no statistically significant findings linking either transformational or transactional leadership with the growth mindset construct. The impact of these findings can lead to selecting leadership candidates committed to making whatever changes are necessary to ensure student success