Physical Sciences and Mathematics Commons^™

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 …

Decay Estimates For Nonlinear Wave Equations With Variable Coefficients, Michael Jacob Roberts

Masters Theses

We studied the long time behavior of solutions of nonlinear wave equations with variable coefficients and an absorption nonlinearity. Such an equation appears in models for traveling waves in a non-homogeneous gas with damping that changes with position. We established decay estimates of the energy of solutions. We found three different regimes of decay of solutions depending on the exponent of the absorption term. We show the existence of two critical exponents. For the exponents above the larger critical exponent, the decay of solutions of the nonlinear equation coincides with that of the corresponding linear problem. For exponents below the …

Latin Hypercube Sampling And Partial Rank Correlation Coefficient Analysis Applied To An Optimal Control Problem, Boloye Gomero

Masters Theses

Latin Hypercube Sampling/Partial Rank Correlation Coefficient (LHS/PRCC) sensitivity analysis is an efficient tool often employed in uncertainty analysis to explore the entire parameter space of a model. Despite the usefulness of LHS/PRCC sensitivity analysis in studying the sensitivity of a model to the parameter values used in the model, no study has been done that fully integrates Latin Hypercube sampling with optimal control analysis.

In this thesis, we couple the optimal control numerical procedure to the LHS/PRCC procedure and perform a simultaneous examination of the effects of all the LHS parameter on the objective functional value. To test the effectiveness …