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Physical Sciences and Mathematics Commons™

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Mathematics

Air Force Institute of Technology

2019

Articles 1 - 13 of 13

Full-Text Articles in Physical Sciences and Mathematics

Polyphase Equiangular Tight Frames And Abelian Generalized Quadrangles, Matthew C. Fickus, John Jasper, Dustin G. Mixon, Jesse D. Peterson, Cody E. Watson Nov 2019

Polyphase Equiangular Tight Frames And Abelian Generalized Quadrangles, Matthew C. Fickus, John Jasper, Dustin G. Mixon, Jesse D. Peterson, Cody E. Watson

Faculty Publications

An equiangular tight frame (ETF) is a type of optimal packing of lines in a finite-dimensional Hilbert space. ETFs arise in various applications, such as waveform design for wireless communication, compressed sensing, quantum information theory and algebraic coding theory. In a recent paper, signature matrices of ETFs were constructed from abelian distance regular covers of complete graphs. We extend this work, constructing ETF synthesis operators from abelian generalized quadrangles, and vice versa. This produces a new infinite family of complex ETFs as well as a new proof of the existence of certain generalized quadrangles. This work involves designing matrices whose …

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Hadamard Equiangular Tight Frames, Matthew C. Fickus, John Jasper, Dustin G. Mixon, Jesse D. Peterson Aug 2019

Hadamard Equiangular Tight Frames, Matthew C. Fickus, John Jasper, Dustin G. Mixon, Jesse D. Peterson

Faculty Publications

An equiangular tight frame (ETF) is a type of optimal packing of lines in Euclidean space. They are often represented as the columns of a short, fat matrix. In certain applications we want this matrix to be flat, that is, have the property that all of its entries have modulus one. In particular, real flat ETFs are equivalent to self-complementary binary codes that achieve the Grey-Rankin bound. Some flat ETFs are (complex) Hadamard ETFs, meaning they arise by extracting rows from a (complex) Hadamard matrix. These include harmonic ETFs, which are obtained by extracting the rows of a character table …

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Periodic Traveling Interfacial Hydroelastic Waves With Or Without Mass Ii: Multiple Bifurcations And Ripples, Benjamin F. Akers, David M. Ambrose, David W. Sulon Aug 2019

Periodic Traveling Interfacial Hydroelastic Waves With Or Without Mass Ii: Multiple Bifurcations And Ripples, Benjamin F. Akers, David M. Ambrose, David W. Sulon

Faculty Publications

In a prior work, the authors proved a global bifurcation theorem for spatially periodic interfacial hydroelastic traveling waves on infinite depth, and computed such traveling waves. The formulation of the traveling wave problem used both analytically and numerically allows for waves with multi-valued height. The global bifurcation theorem required a one-dimensional kernel in the linearization of the relevant mapping, but for some parameter values, the kernel is instead two-dimensional. In the present work, we study these cases with two-dimensional kernels, which occur in resonant and non-resonant variants. We apply an implicit function theorem argument to prove existence of traveling waves …

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Cocyclic Hadamard Matrices: An Efficient Search Based Algorithm, Jonathan S. Turner Jun 2019

Cocyclic Hadamard Matrices: An Efficient Search Based Algorithm, Jonathan S. Turner

Theses and Dissertations

This dissertation serves as the culmination of three papers. “Counting the decimation classes of binary vectors with relatively prime fixed-density" presents the first non-exhaustive decimation class counting algorithm. “A Novel Approach to Relatively Prime Fixed Density Bracelet Generation in Constant Amortized Time" presents a novel lexicon for binary vectors based upon the Discrete Fourier Transform, and develops a bracelet generation method based upon the same. “A Novel Legendre Pair Generation Algorithm" expands upon the bracelet generation algorithm and includes additional constraints imposed by Legendre Pairs. It further presents an efficient sorting and comparison algorithm based upon symmetric functions, as well …

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Finding The Symmetry Group Of An Lp With Equality Constraints And Its Application To Classifying Orthogonal Arrays, Andrew J. Geyer, Dursun A. Bulutoglu, Kenneth J. Ryan May 2019

Finding The Symmetry Group Of An Lp With Equality Constraints And Its Application To Classifying Orthogonal Arrays, Andrew J. Geyer, Dursun A. Bulutoglu, Kenneth J. Ryan

Faculty Publications

Excerpt: For a given linear program (LP) a permutation of its variables that sends feasible points to feasible points and preserves the objective function value of each of its feasible points is a symmetry of the LP. The set of all symmetries of an LP, denoted by GLP, is the symmetry group of the LP. Margot (2010) described a method for computing a subgroup of the symmetry group GLP of an LP. This method computes GLP when the LP has only non-redundant inequalities and its feasible set satisfies no equality constraints.

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Atmospheric Propagation Of High Energy Lasers: Thermal Blooming Simulation, Jonathan Gustafsson, Benjamin F. Akers, Jonah A. Reeger, Sivaguru S. Sritharan Apr 2019

Atmospheric Propagation Of High Energy Lasers: Thermal Blooming Simulation, Jonathan Gustafsson, Benjamin F. Akers, Jonah A. Reeger, Sivaguru S. Sritharan

Faculty Publications

High Energy Laser (HEL) propagation through turbulent atmosphere is examined via numerical simulation. The beam propagation is modeled with the paraxial equation, which in turn is written as a system of equations for a quantum fluid, via the Madelung transform. A finite volume solver is applied to the quantum fluid equations, which supports sharp gradients in beam intensity. The atmosphere is modeled via a coupled advection-diffusion equation whose initial data have Kolmogorov spectrum. In this model the combined effects of thermal blooming, beam slewing, and deep turbulence are simulated.

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Piezoelectric Sensor Crack Detection On Airframe Systems, Kevin J. Lin Mar 2019

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, …

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Harmonic Equiangular Tight Frames Comprised Of Regular Simplices, Courtney A. Schmitt Mar 2019

Harmonic Equiangular Tight Frames Comprised Of Regular Simplices, Courtney A. Schmitt

Theses and Dissertations

An equiangular tight frame (ETF) is a sequence of equal-norm vectors in a Euclidean space whose coherence achieves equality in the Welch bound, and thus yields an optimal packing in a projective space. A regular simplex is a simple type of ETF in which the number of vectors is one more than the dimension of the underlying space. More sophisticated examples include harmonic ETFs, which are formed by restricting the characters of a finite abelian group to a difference set. Recently, it was shown that some harmonic ETFs are themselves comprised of regular simplices. In this thesis, we continue the …

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Analyzing A Method To Determine The Utility Of Adding A Classification System To A Sequence For Improved Accuracy, Kevin S. Pamilagas Mar 2019

Analyzing A Method To Determine The Utility Of Adding A Classification System To A Sequence For Improved Accuracy, Kevin S. Pamilagas

Theses and Dissertations

Frequently, ensembles of classification systems are combined into a sequence in order to better enhance the accuracy in classifying objects of interest. However, there is a point in which adding an additional system to a sequence no longer enhances the system as either the increase in operational costs exceeds the benefit of improvements in classification or the addition of the system does not increase accuracy at all. This research will examine a utility measure to determine the valid or invalid nature of adding a classification system to a sequence of such systems based on the ratio of the change in …

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Schlieren Imaging And Flow Analysis On A Cone/Flare Model In The Afrl Mach 6 Ludwieg Tube Facility, David A. Labuda Mar 2019

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 …

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Wall Model Large Eddy Simulation Of A Diffusing Serpentine Inlet Duct, Ryan J. Thompson Mar 2019

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 …

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Solving The Traveling Salesman Problem Using Ordered-Lists, Petar D. Jackovich Mar 2019

Solving The Traveling Salesman Problem Using Ordered-Lists, Petar D. Jackovich

Theses and Dissertations

The arc-greedy heuristic is a constructive heuristic utilized to build an initial, quality tour for the Traveling Salesman Problem (TSP). There are two known sub-tour elimination methodologies utilized to ensure the resulting tours are viable. This thesis introduces a third novel methodology, the Greedy Tracker (GT), and compares it to both known methodologies. Computational results are generated across multiple TSP instances. The results demonstrate the GT is the fastest method for instances below 400 nodes while Bentley's Multi-Fragment maintains a computational advantage for larger instances. A novel concept called Ordered-Lists is also introduced which enables TSP instances to be explored …

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Time Series Analysis Of Stochastic Networks With Correlated Random Arcs, Brendon T. Sands Mar 2019

Time Series Analysis Of Stochastic Networks With Correlated Random Arcs, Brendon T. Sands

Theses and Dissertations

While modern day weather forecasting is not perfect, there are many benefits given by the multitude and variety of predictive models. In the interest of routing airplanes, this paper uses time series analysis on successive weather forecasts to predict the optimal path and fuel burn of wind-based, fuel-burn networks with stochastic correlated arcs. Networks are populated with either deterministic or ensemble-based weather data, and the two data sources with and without time series analysis are compared. Methods were compared by fuel burn prediction accuracy and ability to predict a future optimal path. Of the four options, the ensemble-based methods were …

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