High-Performance Scientific Computing of Fluid--Structure Interaction, Interbacterial Competition, and Diffusion-Limited Dissolution

Abstract

In this thesis, I present applications of mathematical modeling and high performance computing to three distinct problems in physical and biological sciences.

The first application, presented in chapter 2, simulates three-dimensional fluid--structure interaction (FSI) problems using a numerical method based on the reference map technique (RMT). The RMT is a fully Eulerian method that allows fluids and large-deforming elastic solids to be represented on a single fixed computational grid. This eliminates the need for meshing complex geometries and greatly simplifies the coupling between fluid and solid. We develop the first three-dimensional implementation of the RMT, and demonstrate its accuracy and capabilities by simulating incompressible FSI with neo-Hookean solids and comparing against benchmark results and experiments. A number of examples are discussed: settling of a mixture of heavy and buoyant soft ellipsoids, lid-driven cavity flow containing a soft sphere, and swimmers actuated via active stress.

Chapter 3 discusses modeling and investigations of interbacterial competition mediated by the type VI secretion system (T6SS). The T6SS is a broadly distributed interbacterial weapon. Conserved in 25% of Gram-negative bacteria, it can be used to eliminate competing bacterial populations. The outcome of such competitions is not well understood, neither is the connection between the outcomes and the subcellular details of T6SS. New biological data derived from natural competitors of Vibrio fischeri, light organ symbionts in Euprymna scolopes, is incorporated with mathematical modeling to develop a biochemical model for T6SS function at the single cell level. The model accounts for activation of structure formation, structure assembly, and deployment, and is integrated into a custom agent-based model (ABM) with experimentally matched T6SS parameters. The ABM simulations are used to replicate outcomes of biological competitions, identify winning strategies for T6SS-armed populations, and explore the trade-off between cost of building more T6SS weapon and their competitive benefits.

Chapter 4 discusses scaling behavior and statistical characteristics in the diffusion-limited dissolution (DLD) of two-dimensional finite solids. A discrete model for DLD is presented, where a corrosive Brownian particle diffuses around and annihilates a particle on a solid cluster upon contact. Novel techniques to execute random walk steps that combine conformal mapping and first passage problems are developed to compute exact contact probability between the random walker and the solid cluster, as well as to improve computational efficiency. Monte Carlo simulations reveal the scaling of the roughness of a dissolving circular interface, as well as the effect of lattice orientation on the asymptotic roughness of a flat interface. Simulations also show that spatial distribution of the collapse point is largely independent of initial cluster size, but it is affected by anisotropy in the solid geometry.