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Full-Text Articles in Physics
Modeling And Numerical Analysis Of The Cholesteric Landau-De Gennes Model, Andrew L. Hicks
Modeling And Numerical Analysis Of The Cholesteric Landau-De Gennes Model, Andrew L. Hicks
LSU Doctoral Dissertations
This thesis gives an analysis of modeling and numerical issues in the Landau-de Gennes (LdG) model of nematic liquid crystals (LCs) with cholesteric effects. We derive various time-step restrictions for a (weighted) $L^2$ gradient flow scheme to be energy decreasing. Furthermore, we prove a mesh size restriction, for finite element discretizations, that is critical to avoid spurious numerical artifacts in discrete minimizers that is not well-known in the LC literature, particularly when simulating cholesteric LCs that exhibit ``twist''. Furthermore, we perform a computational exploration of the model and present several numerical simulations in 3-D, on both slab geometries and spherical …
Framework For Algorithmically Optimizing Longitudinal Health Outcomes: Examples In Cancer Radiotherapy And Occupational Radiation Protection, Lydia Joyce Wilson
Framework For Algorithmically Optimizing Longitudinal Health Outcomes: Examples In Cancer Radiotherapy And Occupational Radiation Protection, Lydia Joyce Wilson
LSU Doctoral Dissertations
Background: Advancements in the treatment of non-infectious disease have enabled survival rates to steadily increase in recent decades (e.g., diabetes, heart disease, and cancer). Epidemiological studies have revealed that the treatments for these diseases can have life-threatening and/or life–altering effects. Thus, realizing the full beneficial potential of advanced treatments necessitates new tools to algorithmically consider all major components of the health outcome, including benefit and detriment. The goal of this dissertation was to develop a framework for improving projected health outcomes following planned radiation exposures in consideration of all beneficial and detrimental, early and late, and fatal and non-fatal …