The numerical techniques and methodologies are first demonstrated on a homogeneous fluid contained within a three-dimensional lid-driven cavity. The edge state technique and linear stability analysis through Arnoldi iteration are used to resolve the complex dynamics of the canonical shear-driven benchmark problem. The techniques here lead to a dynamical description of an instability mechanism, and the work serves as a basis for the remainder of the dissertation.
This project is a synthesis of the author's learning over the semesters in working with the CFD Group at Arizona State University. The incompressible Navier-Stokes equations are overviewed, starting with the derivation from the continuity equation, then non-dimensionalization, methods of solving and computing quantities of interest. The rest of this document is expository analysis of solutions in a confined fluid flow, building toward a parametrically forced regime that generates complex flow patterns including Faraday waves. The solutions come from recently published studies Dynamics in a stably stratified tilted square cavity (Grayer et al.) and Parametric instabilities of a stratified shear layer (Buchta et al).
Molecular pathology makes use of estimates of tumor content (tumor percentage) for pre-analytic and analytic purposes, such as molecular oncology testing, massive parallel sequencing, or next-generation sequencing (NGS), assessment of sample acceptability, accurate quantitation of variants, assessment of copy number changes (among other applications), determination of specimen viability for testing (since many assays require a minimum tumor content to report variants at the limit of detection) may all be improved with more accurate and reproducible estimates of tumor content. Currently, tumor percentages of samples submitted for molecular testing are estimated by visual examination of Hematoxylin and Eosin (H&E) stained tissue slides under the microscope by pathologists. These estimations can be automated, expedited, and rendered more accurate by applying machine learning methods on digital whole slide images (WSI).