Open Access. Powered by Scholars. Published by Universities.®
Articles 1 - 4 of 4
Full-Text Articles in Other Mathematics
Smooth Representation Of Functions On Non-Periodic Domains By Means Of The Fourier Continuation Method, Nicholas Rubel, David Bilyeu, Justin Koo
Smooth Representation Of Functions On Non-Periodic Domains By Means Of The Fourier Continuation Method, Nicholas Rubel, David Bilyeu, Justin Koo
STAR Program Research Presentations
This report examines a new methodology in solving Partial Differential Equations (PDEs) numerically. The report also studies the accuracy of this new method as a PDE solver. This new Fourier Continuation (FC) method is one of a few that avoids the well-known Gibbs Phenomenon, which is the overestimation or underestimation of a function. These estimations are oscillations around a “jump” when a non-periodic function is expressed in terms of sines and cosines. Instead, the FC algorithm creates a smooth, periodic extension of a function over a general domain, as demonstrated by the many examples presented here. The FC algorithm was …
Evolution Of Perturbations In Flow Field Mechanics, Samantha R. Bell, David Forliti, Nils Sedano, Kriss Vanderhyde
Evolution Of Perturbations In Flow Field Mechanics, Samantha R. Bell, David Forliti, Nils Sedano, Kriss Vanderhyde
STAR Program Research Presentations
This project explores the stability analysis of a given flow field. Specifically, where the peak disturbance occurs in a flow as this is the disturbance that is most likely to occur. In rocket combustion, it is important to understand where the maximum disturbance occurs so that the mixing of fuel can be stabilized. The instabilities are the results of frequencies in the area surrounding the flow field. The linear stability governing equations are employed to better understand the disturbance. The governing equations for continuity and momentum in the x and y directions are used to form an equation for the …
Using Modeling And Simulation To Analyze Complex Aircraft, Kimberlee Margosian, Jason Lechniak
Using Modeling And Simulation To Analyze Complex Aircraft, Kimberlee Margosian, Jason Lechniak
STAR Program Research Presentations
Modeling and Simulation (M&S) is used at the Air Force Flight Test Center (AFFTC) on Edwards Air Force Base (AFB) to better understand physical phenomena on aircraft. M&S allows for the reduction of cost and risk by providing a better understanding of required flight tests and the interactions between various forces and the aircraft (i.e. wind resistance, pressure change, and temperature change). Without this process, the lives of pilots would be at a much greater risk when testing their aircraft and there would be little to no funds to fly due to the cost to repair or modify the aircraft. …
Automated Theorem Prover Axiom Management, Ashley T. Holeman, Ewen Denney
Automated Theorem Prover Axiom Management, Ashley T. Holeman, Ewen Denney
STAR Program Research Presentations
Automated Theorem Provers (ATPs), are computer programs that use collections of axioms,which are logical statements assumed to be true, in order to prove conjectures. NASA uses these programs to verify safety and functional requirements in domains like Guidance, Navigation, and Control. There are about 30 axioms on each major topic including the theory of coordinate systems, elementary arithmetic and linear algebra. These axioms have been created over the duration of many projects and combined into a single file. One task is to manage the axioms by arranging them into logical sections, deleting unnecessary ones and rewriting some into a more …