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Articles 1 - 11 of 11
Full-Text Articles in Mathematics
Complete Solution Of The Lady In The Lake Scenario, Alexander Von Moll, Meir Pachter
Complete Solution Of The Lady In The Lake Scenario, Alexander Von Moll, Meir Pachter
Faculty Publications
In the Lady in the Lake scenario, a mobile agent, L, is pitted against an agent, M, who is constrained to move along the perimeter of a circle. L is assumed to begin inside the circle and wishes to escape to the perimeter with some finite angular separation from M at the perimeter. This scenario has, in the past, been formulated as a zero-sum differential game wherein L seeks to maximize terminal separation and M seeks to minimize it. Its solution is well-known. However, there is a large portion of the state space for which the canonical solution does not …
Piezoelectric Sensor Crack Detection On Airframe Systems, Kevin J. Lin
Piezoelectric Sensor Crack Detection On Airframe Systems, Kevin J. Lin
Theses and Dissertations
In 2008, the Department of Defense published a guidebook for a methodology named Condition-Based Maintenance Plus (CBM+) which capabilities include improving productivity, shortening maintenance cycles, lowering costs, and increasing availability and reliability. This push replaces existing inspection criteria, often conducted as non-destructive testing (NDT), with structural health monitoring (SHM) systems. The SHM system addressed utilizes guided Lamb waves generated by piezoelectric wafer active sensors (PWAS) to detect the existence, size, and location of damage from through-thickness cracks around a rivet hole. The SHM field lacks an experiment testing how small changes in receiver sensor distances affect damage detection. In addition, …
Wall Model Large Eddy Simulation Of A Diffusing Serpentine Inlet Duct, Ryan J. Thompson
Wall Model Large Eddy Simulation Of A Diffusing Serpentine Inlet Duct, Ryan J. Thompson
Theses and Dissertations
The modeling focus on serpentine inlet ducts (S-duct), as with any inlet, is to quantify the total pressure recovery and ow distortion after the inlet, which directly impacts the performance of a turbine engine fed by the inlet. Accurate prediction of S-duct ow has yet to be achieved amongst the computational fluid dynamics (CFD) community to improve the reliance on modeling reducing costly testing. While direct numerical simulation of the turbulent ow in an S-duct is too cost prohibitive due to grid scaling with Reynolds number, wall-modeled large eddy simulation (WM-LES) serves as a tractable alternative. US3D, a hypersonic research …
Schlieren Imaging And Flow Analysis On A Cone/Flare Model In The Afrl Mach 6 Ludwieg Tube Facility, David A. Labuda
Schlieren Imaging And Flow Analysis On A Cone/Flare Model In The Afrl Mach 6 Ludwieg Tube Facility, David A. Labuda
Theses and Dissertations
High-speed Schlieren photography was utilized to visualize flow in the Air Force Research Laboratory Mach 6 Ludwieg tube facility. A 7° half-angle cone/flare model with variable nosetip radius and flare angle options was used in the study. Testing was performed at two driver tube pressures, generating freestream Reynolds numbers of 10.0x106 and 19.8x106 per meter. The variable-angle flare portion of the model provided a method for adjusting the intensity of the adverse pressure gradient at the cone/flare junction. As expected from existing literature, boundary layer separation along the cone frustum occurred further upstream as the magnitude of the …
Relocatable Field Programmable Gate Array Bitstreams For Fault Tolerance, David P. Montminy, Rusty O. Baldwin, Paul D. Williams
Relocatable Field Programmable Gate Array Bitstreams For Fault Tolerance, David P. Montminy, Rusty O. Baldwin, Paul D. Williams
AFIT Patents
A Field Programmable Gate Array (FPGA) circuit capable of operating through at least one fault. The FPGA circuit includes a configuration memory and an embedded microprocessor. The embedded microprocessor having access to the configuration memory, static modules, at least one relocatable module, and at least one spare module. The relocatable module being relocatable from a first target area to a second target area. The relocatable module being relocatable by manipulating a partial bitstream with the embedded microprocessor. The microprocessor calculating a plurality of bitstream changes, to relocate the at least one relocatable module using at least triple modular redundancy (TMR).
Numerical Investigation Of Pre-Detonator Geometries For Pde Applications, Robert T. Fievisohn
Numerical Investigation Of Pre-Detonator Geometries For Pde Applications, Robert T. Fievisohn
Theses and Dissertations
A parametric study was performed to determine optimal geometries to allow the successful transition of a detonation from a pre-detonator into the thrust tube of a pulse detonation engine. The study was performed using a two-dimensional Euler solver with progress variables to model the chemistry. The geometrical configurations for the simulations look at the effect of shock reflections, flow obstructions, and detonation diffraction to determine successful geometries. It was observed that there are success and failure rates associated with pre-detonators. These success rates appear to be determined by the transverse wave structure of a stably propagating detonation wave and must …
Verification Of Kam Theory On Earth Orbiting Satellites, Christian L. Bisher
Verification Of Kam Theory On Earth Orbiting Satellites, Christian L. Bisher
Theses and Dissertations
This paper uses KAM torus theory and Simplified General Perturbations 4 (SGP4) orbit prediction techniques compiled by Dr. William Wiesel and compares it to Analytical Graphics ® Incorporated (AGI) Satellite Toolkit ® (STK) orbit data. The goal of this paper is to verify KAM torus theory can be used to describe and propagate an Earth satellite orbit with similar accuracy to existing general perturbation techniques. Using SGP4 code including only truncated geopotential effects, KAM torus generating code, and other utilities were used to describe a particular satellite orbit as a torus and then propagate the satellite using traditional and KAM …
Validation Of A Novel Approach To Solving Multibody Systems Using Hamilton's Weak Principle, Ashton D. Hainge
Validation Of A Novel Approach To Solving Multibody Systems Using Hamilton's Weak Principle, Ashton D. Hainge
Theses and Dissertations
A novel approach for formulating and solving for the dynamic response of multibody systems has been developed using Hamilton’s Law of Varying Action as its unifying principle. In order to assure that the associated computer program is sufficiently robust when applied across a wide range of dynamic systems, the program must be verified and validated. The purpose of the research was to perform the verification and validation of the program. Results from the program were compared with closed-form and numerical solutions of simple systems, such as a simple pendulum and a rotating pendulum. The accuracy of the program for complex …
Evaluating The Performance Of Multiple Classifier Systems: A Matrix Algebra Representation Of Boolean Fusion Rules, Justin M. Hill
Evaluating The Performance Of Multiple Classifier Systems: A Matrix Algebra Representation Of Boolean Fusion Rules, Justin M. Hill
Theses and Dissertations
Given a finite collection of classifiers one might wish to combine, or fuse, the classifiers in hopes that the multiple classifier system (MCS) will perform better than the individuals. One method of fusing classifiers is to combine their final decision using Boolean rules (e.g., a logical OR, AND, or a majority vote of the classifiers in the system). An established method for evaluating a classifier is measuring some aspect of its Receiver Operating Characteristic (ROC) curve, which graphs the trade-off between the conditional probabilities of detection and false alarm. This work presents a unique method of estimating the performance of …
A Group Theoretic Tabu Search Approach To The Traveling Salesman Problem, Shane N. Hall
A Group Theoretic Tabu Search Approach To The Traveling Salesman Problem, Shane N. Hall
Theses and Dissertations
The traveling salesman problem (TSP) is a combinatorial optimization problem that is mathematically modeled as a binary integer program. The TSP is a very important problem for the operations research academician and practitioner. This research demonstrates a Group Theoretic Tabu Search (GTTS) Java algorithm for the TSP. The tabu search metaheuristic continuously finds near-optimal solutions to the TSP under various different implementations. Algebraic group theory offers a more formal mathematical setting to study the TSP providing a theoretical foundation for describing tabu search. Specifically, this thesis uses the Symmetric Group on n letters, S(n), which is the set of all …
Representations, Approximations, And Algorithms For Mathematical Speech Processing, Laura R. Suzuki
Representations, Approximations, And Algorithms For Mathematical Speech Processing, Laura R. Suzuki
Theses and Dissertations
Representing speech signals such that specific characteristics of speech are included is essential in many Air Force and DoD signal processing applications. A mathematical construct called a frame is presented which captures the important time-varying characteristic of speech. Roughly speaking, frames generalize the idea of an orthogonal basis in a Hilbert space, Specific spaces applicable to speech are L2(R) and the Hardy spaces Hp(D) for p> 1 where D is the unit disk in the complex plane. Results are given for representations in the Hardy spaces involving Carleson's inequalities (and its extensions), …