Open Access. Powered by Scholars. Published by Universities.®
- Discipline
-
- Engineering (76)
- Electrical and Computer Engineering (24)
- Operations Research, Systems Engineering and Industrial Engineering (23)
- Numerical Analysis and Computation (19)
- Aerospace Engineering (18)
-
- Operational Research (17)
- Computer Sciences (16)
- Signal Processing (15)
- Business (8)
- Other Applied Mathematics (8)
- Physics (7)
- Social and Behavioral Sciences (7)
- Environmental Sciences (6)
- Statistics and Probability (6)
- Partial Differential Equations (5)
- Civil and Environmental Engineering (4)
- Electrical and Electronics (4)
- Environmental Engineering (4)
- Mathematics (4)
- Navigation, Guidance, Control and Dynamics (4)
- Business Administration, Management, and Operations (3)
- Education (3)
- Electromagnetics and Photonics (3)
- Life Sciences (3)
- Non-linear Dynamics (3)
- Optics (3)
- Ordinary Differential Equations and Applied Dynamics (3)
- Other Operations Research, Systems Engineering and Industrial Engineering (3)
- Keyword
-
- Algorithms (8)
- Differential equations (6)
- Wavelets (Mathematics) (6)
- Mathematical models (5)
- #antcenter (4)
-
- Image processing (4)
- Machine learning (4)
- Mathematical optimization (4)
- Monte Carlo method (4)
- Numerical analysis (4)
- Programming (Mathematics) (4)
- Signal processing--Digital techniques (4)
- Finite element analysis (3)
- Groundwater--Pollution (3)
- Neural networks (Computer science) (3)
- Optimization (3)
- Target acquisition (3)
- #csra (2)
- Acoustic filters (2)
- Acquisition (2)
- Cost estimation (2)
- Discriminant analysis (2)
- Eigenvalues (2)
- Finite element method (2)
- Goodness of fit tests (2)
- Goodness-of-fit tests (2)
- Groundwater flow--Mathematical models (2)
- Groundwater--Pollution--Mathematical models (2)
- Linear programming (2)
- Mathematical modeling (2)
- Publication Year
- Publication Type
Articles 1 - 30 of 186
Full-Text Articles in Applied Mathematics
Analysis And Machine Learning Adaptation Of A Cognitive Model For Human Memory, Trevor Cross, Aihua W. Wood
Analysis And Machine Learning Adaptation Of A Cognitive Model For Human Memory, Trevor Cross, Aihua W. Wood
Faculty Publications
In this paper, we use the Duolingo SLAM dataset to analyze several cognitive models of second language acquisition and develop new approaches for enhanced performance. In particular, we consider the Predictive Performance Equation and some of its underlying power laws. Leveraging insights from machine learning, we develop simple one-feature models as building blocks for combined models that match or in certain cases outperform the existing models at much reduced computational cost. In addition, a neural network with one fully connected hidden layer is constructed that outperforms all other models on sufficiently large datasets.
Equiangularity From Compatible Orthobiangularity, Tyler J. Myers
Equiangularity From Compatible Orthobiangularity, Tyler J. Myers
Theses and Dissertations
An equiangular tight frame (ETF) is an equal norm sequence of vectors in a Hilbert space whose coherence achieves equality in the Welch bound. Such sequences necessarily have minimal coherence and thus are, in some sense, as "spread out" in space as possible. ETFs have a variety of applications, such as compressed sensing and waveform design. The main problem in the study of ETFs is determining the pairs (D, N) for which an ETF with N vectors in a D-dimensional space exists. Real ETFs are moreover equivalent to a special subset of a well-studied class of graphs known as strongly …
Analyzing And Comparing Refinement Indicators For Rbf-Fd Adaptive Algorithms, Anders R. Johnson
Analyzing And Comparing Refinement Indicators For Rbf-Fd Adaptive Algorithms, Anders R. Johnson
Theses and Dissertations
Recent progress has been made in the development of collocation-based iterative algorithms that approximate solutions to PDEs. These algorithms rely on the ability to identify regions within a domain where a finer discretization is required. Such iterative algorithms are beneficial particularly when solution functions have highly localized behavior. This thesis proposes an indicator for node refinement that is constructed by approximating the forward error. This proposed indicator also helps to establish confidence in the accuracy of a given solution estimate. The proposed error estimator is theoretically examined and compared with contemporary refinement indicators. It is shown that an iterative algorithm, …
Impact Of Stochastic Travel Times On The Military Port Selection Problem: A Stochastic Programming Approach, William M. Titus
Impact Of Stochastic Travel Times On The Military Port Selection Problem: A Stochastic Programming Approach, William M. Titus
Theses and Dissertations
This research models and analyzes the impact of stochastic travel times on port selection during a large-scale mobilization of equipment from continental United States installations to deployment locations using sealift ships. A stochastic mixed-integer programming model is developed to minimize the average arrival time of equipment into theater. The model is solved using Sample Average Approximation. In the first stage, the model selects ports to open and assigns installations, equipment, and ships to open ports. In the second stage, travel times are realized, and equipment is assigned to specific ships that are scheduled to depart. Results show that the marginal …
Grassmannian Codes From Stratified Frames, William J. Brinkley
Grassmannian Codes From Stratified Frames, William J. Brinkley
Theses and Dissertations
An equichordal tight fusion frame (ECTFF) is a finite sequence of equi-dimensional subspaces of a Euclidean space that achieves equality in Conway, Hardin and Sloane's simplex bound. Every ECTFF is an optimal Grassmannian code with respect to the chordal distance. We introduce a method for constructing an ECTFF from any finite sequence of unit norm tight frames that happen to be stratified in a certain sense. We moreover show how to construct stratified unit norm tight frames from a difference family for a finite abelian group, as well as from a suitable combination of a resolvable balanced incomplete block design …
Advancing Defense Software Cost Estimation Through Regression, Probabilistic, And Machine Learning Models, Stephen D. Chatterton
Advancing Defense Software Cost Estimation Through Regression, Probabilistic, And Machine Learning Models, Stephen D. Chatterton
Theses and Dissertations
Accurately estimating software costs is critical for effective project management within the Department of Defense (DoD), where early decisions shape resource allocation and risk management. This work evaluates regression-based Cost Estimating Relationships (CERs), probabilistic models, and machine learning techniques to address limitations of traditional estimation methods. Using records from two DoD repositories, the analysis applied Ordinary Least Squares (OLS) regression, Multinomial Logistic Regression (MLR), Random Forest, and neural networks to model and classify software costs, with key predictors including Source Lines of Code (SLOC), Equivalent Source Lines of Code (ESLOC), and programming hours. The findings highlight strengths and trade-offs of …
Investigation Of Node Refinement Methods In Local Adaptive Kernel Based Approximation, Shelby W. Woodrum
Investigation Of Node Refinement Methods In Local Adaptive Kernel Based Approximation, Shelby W. Woodrum
Theses and Dissertations
This thesis explores computational efficiency and accuracy of six node refinement methods for local adaptive kernel-based approximations of solutions to the two-dimensional Poisson equation. Using an adaptive kernel-based approximation algorithm, this research investigates performance of Delaunay triangulation-based methods (shifted barycenters and edge midpoints), refinement via approximate Fekete and discrete Leja points, and a meshless predefined shift refinement method across two domains with varying complexities. Computational experiments reveal that Delaunay triangulation-based methods achieve a practical balance between accuracy and efficiency, particularly in square domains. Refinement via approximate Fekete and discrete Leja points produce accurate results but incur greater computational costs, making …
Production Box Cost Estimating Relationships For Dod Avionics, Carla J. Cisneros, Edward D. White, Brandon M. Lucas, Jonathan D. Ritschel, Robert D. Fass, Shawn M. Valentine
Production Box Cost Estimating Relationships For Dod Avionics, Carla J. Cisneros, Edward D. White, Brandon M. Lucas, Jonathan D. Ritschel, Robert D. Fass, Shawn M. Valentine
Faculty Publications
The authors use historical information obtained from the Cost Assessment Data Enterprise to estimate recurring production unit cost for DoD avionics via cost estimating relationships (CERs). The specific modeled responses include mean unit cost, median unit cost, and the 100th production unit cost (T100) utilizing learning curve theory. For T100, the authors adopt both a multiplicative and an additive error for CER comparison. Recommended CERs consist of the mean unit cost and the T100 utilizing a multiplicative error. Moreover, results reveal that weight has a significant effect on cost as well as a potential underaccounting of real price change or …
Malware Classification Through Abstract Syntax Trees And L-Moments, Anthony J. Rose, Christine M. Schubert Kabban, Scott R. Graham, Wayne C. Henry, Christopher M. Rondeau
Malware Classification Through Abstract Syntax Trees And L-Moments, Anthony J. Rose, Christine M. Schubert Kabban, Scott R. Graham, Wayne C. Henry, Christopher M. Rondeau
Faculty Publications
The ongoing evolution of malware presents a formidable challenge to cybersecurity: identifying unknown threats. Traditional detection methods, such as signatures and various forms of static analysis, inherently lag behind these evolving threats. This research introduces a novel approach to malware detection by leveraging the robust statistical capabilities of L-moments and the structural insights provided by Abstract Syntax Trees (ASTs) and applying them to PowerShell. L-moments, recognized for their resilience to outliers and adaptability to diverse distributional shapes, are extracted from network analysis measures like degree centrality, betweenness centrality, and closeness centrality of ASTs. These measures provide a detailed structural representation …
Deterministic Global 3d Fractal Cloud Model For Synthetic Scene Generation, Aaron M. Schinder, Shannon R. Young, Bryan J. Steward, Michael L. Dexter, Andrew Kondrath, Stephen Hinton, Ricardo Davila
Deterministic Global 3d Fractal Cloud Model For Synthetic Scene Generation, Aaron M. Schinder, Shannon R. Young, Bryan J. Steward, Michael L. Dexter, Andrew Kondrath, Stephen Hinton, Ricardo Davila
Faculty Publications
This paper describes the creation of a fast, deterministic, 3D fractal cloud renderer for the AFIT Sensor and Scene Emulation Tool (ASSET). The renderer generates 3D clouds by ray marching through a volume and sampling the level-set of a fractal function. The fractal function is distorted by a displacement map, which is generated using horizontal wind data from a Global Forecast System (GFS) weather file. The vertical windspeed and relative humidity are used to mask the creation of clouds to match realistic large-scale weather patterns over the Earth. Small-scale detail is provided by the fractal functions which are tuned to …
Numerical Simulation Of Nonlinear Wave Equations With Machine Learning, Kristina O. F. Williams
Numerical Simulation Of Nonlinear Wave Equations With Machine Learning, Kristina O. F. Williams
Theses and Dissertations
A machine learning procedure is proposed to create numerical schemes for solutions of certain types of nonlinear wave equations on coarse grids. This method trains stencil weights of a discretization of the equation, with the truncation error of the scheme as the objective function for training. A neural network is used as a model for the stencil weights. The method uses centered finite differences to initialize the optimization routine and a second-order implicit-explicit time solver as a framework. Symmetry conditions are enforced on the learned operator to ensure a stable method. The procedure is applied to the Korteweg - de …
Methods Of Evaluating Quantum Phase Estimation Circuit Output, Charles A. Woodrum
Methods Of Evaluating Quantum Phase Estimation Circuit Output, Charles A. Woodrum
Theses and Dissertations
The quantum phase estimation (QPE) algorithm is one of the most important quantum computing algorithms that has been developed. The QPE algorithm estimates the phase or phases of the eigenvalue or eigenvalues of a unitary operator. It is a critical step for applications like Shor’s algorithm for factoring and the HHL algorithm for solving linear systems of equations, but it remains difficult to implement on current quantum computers due to small numbers of logical qubits and high error rates. This investigation derives a more accurate estimation of the phase of a unitary operator than would otherwise be attained with the …
Accurate Covariance Estimation For Pose Data From Iterative Closest Point Algorithm, Rick H. Yuan, Clark N. Taylor, Scott L. Nykl
Accurate Covariance Estimation For Pose Data From Iterative Closest Point Algorithm, Rick H. Yuan, Clark N. Taylor, Scott L. Nykl
Faculty Publications
One of the fundamental problems of robotics and navigation is the estimation of the relative pose of an external object with respect to the observer. A common method for computing the relative pose is the iterative closest point (ICP) algorithm, where a reference point cloud of a known object is registered against a sensed point cloud to determine relative pose. To use this computed pose information in downstream processing algorithms, it is necessary to estimate the uncertainty of the ICP output, typically represented as a covariance matrix. In this paper, a novel method for estimating uncertainty from sensed data is …
Failure Distributions For Parallel Dependent Identical Weibull Components, Gina S. Sigler
Failure Distributions For Parallel Dependent Identical Weibull Components, Gina S. Sigler
Theses and Dissertations
For a parallel system, when one component fails, the failure distribution of the remaining components will have an increased failure rate. This dissertation takes a novel approach to finding the associated failure distribution of the full system using ordinal statistic distributions for correlated Weibull components, allowing for unknown correlations between the dependent components. A Taylor series approximation is presented for the two component; system failure time distributions are also derived for two failures in a two component system, two failures in an n component system, three failures in a three component system, and k failures in an n component system. …
Evolution Of Coronal Magnetic Field Parameters During X5.4 Solar Flare, Seth H. Garland, Benjamin F. Akers, Vasyl B. Yurchyshyn, Robert D. Loper, Daniel J. Emmons
Evolution Of Coronal Magnetic Field Parameters During X5.4 Solar Flare, Seth H. Garland, Benjamin F. Akers, Vasyl B. Yurchyshyn, Robert D. Loper, Daniel J. Emmons
Faculty Publications
The coronal magnetic field over NOAA Active Region 11,429 during a X5.4 solar flare on 7 March 2012 is modeled using optimization based Non-Linear Force-Free Field extrapolation. Specifically, 3D magnetic fields were modeled for 11 timesteps using the 12-min cadence Solar Dynamics Observatory (SDO) Helioseismic and Magnetic Imager photospheric vector magnetic field data, spanning a time period of 1 hour before through 1 hour after the start of the flare. Using the modeled coronal magnetic field data, seven different magnetic field parameters were calculated for 3 separate regions: areas with surface |Bz| ≥ 300 G, areas of flare brightening seen …
Student Performance In Traditional In-Person Vs. Online Sections Of An Introductory Graduate Mathematics Course, Lauran E. Kittle
Student Performance In Traditional In-Person Vs. Online Sections Of An Introductory Graduate Mathematics Course, Lauran E. Kittle
Theses and Dissertations
The growth of technology impacts nearly every aspect of everyday life, to include education and learning. The availability of distance learning (online) classes has increased drastically in the last few decades, expanding access to education for millions of people. However, it is imperative to consider exactly how the growth of technology impacts education – whether it is a positive, negative, or neutral impact. Previous research comparing distance learning and in-residence (traditional) classes have widely mixed, disparate conclusions. This type of research, two-stage analysis, and modeling has yet to be conducted on a graduate school level. For this reason, a detailed …
Leveraging Subject Matter Expertise To Optimize Machine Learning Techniques For Air And Space Applications, Philip Y. Cho
Leveraging Subject Matter Expertise To Optimize Machine Learning Techniques For Air And Space Applications, Philip Y. Cho
Theses and Dissertations
We develop new machine learning and statistical methods that are tailored for Air and Space applications through the incorporation of subject matter expertise. In particular, we focus on three separate research thrusts that each represents a different type of subject matter knowledge, modeling approach, and application. In our first thrust, we incorporate knowledge of natural phenomena to design a neural network algorithm for localizing point defects in transmission electron microscopy (TEM) images of crystalline materials. In our second research thrust, we use Bayesian feature selection and regression to analyze the relationship between fighter pilot attributes and flight mishap rates. We …
Classification And Keyword Identification Of Covid 19 Misinformation On Social Media: A Framework For Semantic Analysis, Grace Y. Smith
Classification And Keyword Identification Of Covid 19 Misinformation On Social Media: A Framework For Semantic Analysis, Grace Y. Smith
Theses and Dissertations
The growing surge of misinformation among COVID-19 communication can pose great hindrance to truth, magnify distrust in policy makers and/or degrade authorities’ credibility, and it can even harm public health. Classification of textual context on social media data relating to COVID-19 is an effective tool to combat misinformation on social media platforms. In this research, Twitter data was leveraged to 1) develop classification methods to detect misinformation and identify Tweet sentiment with respect to COVID-19 and 2) develop a human-in-the-loop interactive framework to enable identification of keywords associated with social context, here, being misinformation regarding COVID-19. 1) Six fusion-based classification …
Robust Error Estimation Based On Factor-Graph Models For Non-Line-Of-Sight Localization, O. Arda Vanli, Clark N. Taylor
Robust Error Estimation Based On Factor-Graph Models For Non-Line-Of-Sight Localization, O. Arda Vanli, Clark N. Taylor
Faculty Publications
This paper presents a method to estimate the covariances of the inputs in a factor-graph formulation for localization under non-line-of-sight conditions. A general solution based on covariance estimation and M-estimators in linear regression problems, is presented that is shown to give unbiased estimators of multiple variances and are robust against outliers. An iteratively re-weighted least squares algorithm is proposed to jointly compute the proposed variance estimators and the state estimates for the nonlinear factor graph optimization. The efficacy of the method is illustrated in a simulation study using a robot localization problem under various process and measurement models and measurement …
Equichordal Tight Fusion Frames And Biangular Orthopartitionable Tight Frames, Benjamin R. Mayo
Equichordal Tight Fusion Frames And Biangular Orthopartitionable Tight Frames, Benjamin R. Mayo
Theses and Dissertations
An equichordal tight fusion frame (ECTFF) is a sequence of equidimensional subspaces of a Euclidean space that achieves equality in Conway, Hardin and Sloane's simplex bound, and so is a type of optimal Grassmannian code. In the special case where its subspaces have dimension one, an ECTFF corresponds to an equiangular tight frame (ETF); such frames have minimal coherence and so are useful for compressed sensing. More generally, an ECTFF will yield a frame with minimal block coherence when its subspaces are pairwise isoclinic, namely when it is an equi-isoclinic tight fusion frame (EITFF). In this dissertation, we generalize the …
Instabilities Of Overturned Traveling Waves, Tyler B. Pierce
Instabilities Of Overturned Traveling Waves, Tyler B. Pierce
Theses and Dissertations
The instabilities of overturned traveling waves are determined by the use of spectral methods. Two separate numerical methods, Spectral Stability Analysis and Dynamic Stability Analysis, are used to assess the instabilities of branches of waves solved from conformally-mapped Euler equations. The branches of waves with Bond number less than two were found to be spectrally stable to super-harmonic perturbations. The branches of waves with Bond number in [2,3) had some waves that were stable and some that were unstable. All overturned waves with Bond number greater than or equal to two were unstable.
Correlated Positron-Electron Orbital (Cpeo): A Novel Method That Models Positron-Electron Correlation In Virtual Ps At The Mean-Field Level, Kevin E. Blaine
Correlated Positron-Electron Orbital (Cpeo): A Novel Method That Models Positron-Electron Correlation In Virtual Ps At The Mean-Field Level, Kevin E. Blaine
Theses and Dissertations
The Correlated Positronic-Electronic Orbital (CPEO) method was developed and implemented to capture correlation effects at between the positron and electron in the modeling of systems that involve a bound positron. Methods that effectively model these systems require many hundred basis functions and use a mean field approach as the beginning step. CPEO builds an orbital for virtual Positronium (Ps) that contains a positron in a bound state along with an accompanying electron to the larger system. Assigning the virtual Ps orbital allows for the two particle variational optimization in conjunction with the other particles that compose the whole system. This …
An Analysis Of The Effects Of Technology Readiness Levels On Cost Growth, Christopher R. Bissing
An Analysis Of The Effects Of Technology Readiness Levels On Cost Growth, Christopher R. Bissing
Theses and Dissertations
This research seeks to evaluate the effects of Technology Readiness Levels (TRL) on Cost Growth. It makes use of data from Technology Readiness Assessments (TRA) and Selected Acquisition Reports (SAR) to explore relationships between TRLs at Milestone B and cost growth in Major Defense Acquisition Programs (MDAP) and Major Automated Information Systems (MAIS). Programs using higher proportions of critical technologies rated below TRL 7 tend to experience greater cost growth than programs that use more mature technologies. Current DoD doctrine requires TRL 6 to enter Milestone B. The results of this research seek to evaluate the merit of this requirement. …
Extending Critical Infrastructure Element Longevity Using Constellation-Based Id Verification, Christopher M. Rondeau, Michael A. Temple, J. Addison Betances, Christine M. Schubert Kabban
Extending Critical Infrastructure Element Longevity Using Constellation-Based Id Verification, Christopher M. Rondeau, Michael A. Temple, J. Addison Betances, Christine M. Schubert Kabban
Faculty Publications
This work supports a technical cradle-to-grave protection strategy aimed at extending the useful lifespan of Critical Infrastructure (CI) elements. This is done by improving mid-life operational protection measures through integration of reliable physical (PHY) layer security mechanisms. The goal is to improve existing protection that is heavily reliant on higher-layer mechanisms that are commonly targeted by cyberattack. Relative to prior device ID discrimination works, results herein reinforce the exploitability of constellation-based PHY layer features and the ability for those features to be practically implemented to enhance CI security. Prior work is extended by formalizing a device ID verification process that …
A Learning Curve Model Accounting For The Flattening Effect In Production Cycles, Evan R. Boone, John J. Elshaw, Clay M. Koschnick, Jonathan D. Ritschel, Adedeji B. Badiru
A Learning Curve Model Accounting For The Flattening Effect In Production Cycles, Evan R. Boone, John J. Elshaw, Clay M. Koschnick, Jonathan D. Ritschel, Adedeji B. Badiru
Faculty Publications
We investigate production cost estimates to identify and model modifications to a prescribed learning curve. Our new model examines the learning rate as a decreasing function over time as opposed to a constant rate that is frequently used. The purpose of this research is to determine whether a new learning curve model could be implemented to reduce the error in cost estimates for production processes. A new model was created that mathematically allows for a “flattening effect,” which typically occurs later in the production process. This model was then compared to Wright’s learning curve, which is a popular method used …
Modeling And Simulation Techniques Used In High Strain Rate Projectile Impact, Derek G. Spear, Anthony N. Palazotto, Ryan A. Kemnitz
Modeling And Simulation Techniques Used In High Strain Rate Projectile Impact, Derek G. Spear, Anthony N. Palazotto, Ryan A. Kemnitz
Faculty Publications
A series of computational models and simulations were conducted for determining the dynamic responses of a solid metal projectile impacting a target under a prescribed high strain rate loading scenario in three-dimensional space. The focus of this study was placed on two different modeling techniques within finite element analysis available in the Abaqus software suite. The first analysis technique relied heavily on more traditional Lagrangian analysis methods utilizing a fixed mesh, while still taking advantage of the finite difference integration present under the explicit analysis approach. A symmetry reduced model using the Lagrangian coordinate system was also developed for comparison …
Residual-Based Multi-Filter Methodology For All-Source Fault Detection, Exclusion, And Performance Monitoring, Juan Jurado, John F. Raquet, Christine M. Schubert Kabban Air Force Institute Of Technology, Jonathon S. Gipson
Residual-Based Multi-Filter Methodology For All-Source Fault Detection, Exclusion, And Performance Monitoring, Juan Jurado, John F. Raquet, Christine M. Schubert Kabban Air Force Institute Of Technology, Jonathon S. Gipson
Faculty Publications
All-source navigation has become increasingly relevant over the past decade with the development of viable alternative sensor technologies. However, as the number and type of sensors informing a system increases, so does the probability of corrupting the system with sensor modeling errors, signal interference, and undetected faults. Though the latter of these has been extensively researched, the majority of existing approaches have constrained faults to biases and designed algorithms centered around the assumption of simultaneously redundant, synchronous sensors with valid measurement models, none of which are guaranteed for all-source systems. As part of an overall all-source assured or resilient navigation …
Through-The-Wall Radar Detection Using Machine Learning, Aihua W. Wood, Ryan Wood, Matthew Charnley
Through-The-Wall Radar Detection Using Machine Learning, Aihua W. Wood, Ryan Wood, Matthew Charnley
Faculty Publications
This paper explores the through-the-wall inverse scattering problem via machine learning. The reconstruction method seeks to discover the shape, location, and type of hidden objects behind walls, as well as identifying certain material properties of the targets. We simulate RF sources and receivers placed outside the room to generate observation data with objects randomly placed inside the room. We experiment with two types of neural networks and use an 80-20 train-test split for reconstruction and classification.
Modeling Nonlinear Heat Transfer For A Pin-On-Disc Sliding System, Brian A. Boardman
Modeling Nonlinear Heat Transfer For A Pin-On-Disc Sliding System, Brian A. Boardman
Theses and Dissertations
The objective of this research is to develop a numerical method to characterize heat transfer and wear rates for samples of Vascomax® 300, or Maraging 300, steel. A pin-on-disc experiment was conducted in which samples were exposed to a high-pressure, high-speed, sliding contact environment. This sliding contact generates frictional heating that influences the temperature distribution and wear characteristics of the test samples. A two-dimensional nonlinear heat transfer equation is discretized and solved via a second-order explicit finite difference scheme to predict the transient temperature distribution of the pin. This schematic is used to predict the removal of material from the …
An Ultra-Sparse Approximation Of Kinetic Solutions To Spatially Homogeneous Flows Of Non-Continuum Gas, Alexander Alekseenko, Amy Grandilli, Aihua W. Wood
An Ultra-Sparse Approximation Of Kinetic Solutions To Spatially Homogeneous Flows Of Non-Continuum Gas, Alexander Alekseenko, Amy Grandilli, Aihua W. Wood
Faculty Publications
We consider a compact approximation of the kinetic velocity distribution function by a sum of isotropic Gaussian densities in the problem of spatially homogeneous relaxation. Derivatives of the macroscopic parameters of the approximating Gaussians are obtained as solutions to a linear least squares problem derived from the Boltzmann equation with full collision integral. Our model performs well for flows obtained by mixing upstream and downstream conditions of normal shock wave with Mach number 3. The model was applied to explore the process of approaching equilibrium in a spatially homogeneous flow of gas. Convergence of solutions with respect to the model …