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Full-Text Articles in Physical Sciences and Mathematics
Modeling Celiac Disease, Jillian M. Trask
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 …
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.
Mathematical Modeling Of T Cell Clustering Following Malaria Infection In Mice, Reka Katalin Kelemen
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
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 X0.
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 …