Ordinary Differential Equations and Applied Dynamics Commons^™

Modeling Celiac Disease, Jillian M. Trask

Masters Theses

Those who suffer from Celiac Disease have an autoimmune response to the protein complex gluten. The goal of this work is to better understand the biological mechanisms in Celiac Disease through modeling with a system of ordinary differential equations. We first develop a model for the way in which gluten induces a response in zonulin in those with Celiac Disease and estimate parameters for such a model using limited data. We then extend this model to include the interactions between zonulin and the permeability of the intestine, and the effect of this interaction on the immune response. Finally, we perform …

Mathematical Modeling Of T Cell Clustering Following Malaria Infection In Mice, Reka Katalin Kelemen

Masters Theses

Malaria is the result of the immune system's unsuccessful clearance of hepatocytes (liver cells) infected by the eukaryotic pathogen of the Plasmodium genus. It has been shown that CD8 T cells are required and sufficient for protective immunity against malaria in mice [29, 36], but the mechanisms by which they find and eliminate infected hepatocytes are not known yet. Recently we reported the formation of CD8 T cell clusters consisting of up to 25 cells around infected cells [8]. Our mathematical modeling and data analysis revealed that malaria-specific T cells likely recruit each other and also non-malaria-specific T cells to …

The Complementing Condition In Elasticity, Lavanya Ramanan

Masters Theses

We consider a boundary value problem of nonlinear elasticity on a domain [omega] in R³ [3-dimensional space] and compute the Complementing Condition for the linearized equations at a point X₀ [x zero] on boundary of omega. We assume a stored energy function depending on the first and third invariants of the deformation F and that the strong-ellipticity condition holds in [omega] . A surface traction boundary condition is imposed at X_0.
The Complementing Condition is calculated from a system of 3 second-order ordinary differential equations (0 less than and equal to t less than infinity) with boundary …

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 …

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 …

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

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 …