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Articles 1 - 6 of 6
Full-Text Articles in Applied Mathematics
Numerical Methods For Solving Optimal Control Problems, Garrett Robert Rose
Numerical Methods For Solving Optimal Control Problems, Garrett Robert Rose
Masters Theses
There are many different numerical processes for approximating an optimal control problem. Three of those are explained here: The Forward Backward Sweep, the Shooter Method, and an Optimization Method using the MATLAB Optimization Tool Box. The methods will be explained, and then applied to three different test problems to see how they perform. The results show that the Forward Backward Sweep is the best of the three methods with the Shooter Method being a competitor.
Flexible Memory Allocation In Kinetic Monte Carlo Simulations, Aaron David Craig
Flexible Memory Allocation In Kinetic Monte Carlo Simulations, Aaron David Craig
Masters Theses
We introduce two new algorithms for Kinetic Monte Carlo simulations: the minimal and flexible allocation algorithms. The theory and computational challenges associated with K.M.C. simulations are briefly discussed. We outline the simple cubic, solid-on-solid model of epitaxial growth and analyze four methods for its simulation: the linear search, standard inverted list, minimal allocation, and flexible allocation algorithms. We then implement these algorithms, analyze their performances, and discuss implications of the results.
Statistical Mechanics And Schramm-Loewner Evolution With Applications To Crack Propagation Processes, Christopher Borut Mesic
Statistical Mechanics And Schramm-Loewner Evolution With Applications To Crack Propagation Processes, Christopher Borut Mesic
Masters Theses
Schramm-Loewner Evolution (SLE) has both mathematical and physical roots that extend as far back as the early 20th century. We present the progression of these humble roots from the Ideal Gas Law, all the way to the renormalization group and conformal field theory, to better understand the impact SLE has had on modern statistical mechanics. We then explore the potential application of the percolation exploration process to crack propagation processes, illustrating the interplay between mathematics and physics.
Validation Of Weak Form Thermal Analysis Algorithms Supporting Thermal Signature Generation, Elton Lewis Freeman
Validation Of Weak Form Thermal Analysis Algorithms Supporting Thermal Signature Generation, Elton Lewis Freeman
Masters Theses
Extremization of a weak form for the continuum energy conservation principle differential equation naturally implements fluid convection and radiation as flux Robin boundary conditions associated with unsteady heat transfer. Combining a spatial semi-discretization via finite element trial space basis functions with time-accurate integration generates a totally node-based algebraic statement for computing. Closure for gray body radiation is a newly derived node-based radiosity formulation generating piecewise discontinuous solutions, while that for natural-forced-mixed convection heat transfer is extracted from the literature. Algorithm performance, mathematically predicted by asymptotic convergence theory, is subsequently validated with data obtained in 24 hour diurnal field experiments for …
Development And Analysis Of Onboard Translunar Injection Targeting Algorithms, Phillippe Lyles Winters Reed
Development And Analysis Of Onboard Translunar Injection Targeting Algorithms, Phillippe Lyles Winters Reed
Masters Theses
Several targeting algorithms are developed and analyzed for possible future use onboard a spacecraft. Each targeter is designed to determine the appropriate propulsive burn for translunar injection to obtain desired orbital parameters upon arrival at the moon. Primary design objectives are to minimize the computational requirements for each algorithm but also to ensure reasonable accuracy, so that the algorithm’s errors do not force the craft to conduct large mid-course corrections. Several levels of accuracy for dynamical models are explored, the convergence range and speed of each algorithm are compared, and the possible benefits of the Broyden and trust-region targeters are …
Analytical Computation Of Proper Orthogonal Decomposition Modes And N-Width Approximations For The Heat Equation With Boundary Control, Tasha N. Fernandez
Analytical Computation Of Proper Orthogonal Decomposition Modes And N-Width Approximations For The Heat Equation With Boundary Control, Tasha N. Fernandez
Masters Theses
Model reduction is a powerful and ubiquitous tool used to reduce the complexity of a dynamical system while preserving the input-output behavior. It has been applied throughout many different disciplines, including controls, fluid and structural dynamics. Model reduction via proper orthogonal decomposition (POD) is utilized for of control of partial differential equations. In this thesis, the analytical expressions of POD modes are derived for the heat equation. The autocorrelation function of the latter is viewed as the kernel of a self adjoint compact operator, and the POD modes and corresponding eigenvalues are computed by solving homogeneous integral equations of the …