Physical Sciences and Mathematics Commons^™

Continuum Modeling Of Active Nematics Via Data-Driven Equation Discovery, Connor Robertson

Dissertations

Data-driven modeling seeks to extract a parsimonious model for a physical system directly from measurement data. One of the most interpretable of these methods is Sparse Identification of Nonlinear Dynamics (SINDy), which selects a relatively sparse linear combination of model terms from a large set of (possibly nonlinear) candidates via optimization. This technique has shown promise for synthetic data generated by numerical simulations but the application of the techniques to real data is less developed. This dissertation applies SINDy to video data from a bio-inspired system of mictrotubule-motor protein assemblies, an example of nonequilibrium dynamics that has posed a significant …

Modeling Dewetting, Demixing, And Thermal Effects In Nanoscale Metal Films, Ryan Howard Allaire

Dissertations

Thin film dynamics, particularly on the nanoscale, is a topic of extensive interest. The process by which thin liquids evolve is far from trivial and can lead to dewetting and drop formation. Understanding this process involves not only resolving the fluid mechanical aspects of the problem, but also requires the coupling of other physical processes, including liquid-solid interactions, thermal transport, and dependence of material parameters on temperature and material composition. The focus of this dissertation is on the mathematical modeling and simulation of nanoscale liquid metal films, which are deposited on thermally conductive substrates, liquefied by laser heating, and subsequently …

Studies Of Two-Phase Flow With Soluble Surfactant, Ryan Peter Atwater

Dissertations

Numerical methods are developed for accurate solution of two-phase flow in the zero Reynolds number limit of Stokes flow, when surfactant is present on a drop interface and in its bulk phase interior. The methods are designed to achieve high accuracy when the bulk Péclet number is large, or equivalently when the bulk phase surfactant has small diffusivity

In the limit of infinite bulk Péclet number the advection-diffusion equation that governs evolution of surfactant concentration in the bulk is singularly perturbed, indicating a separation of spatial scales. A hybrid numerical method based on a leading order asymptotic reduction in this …

Qualitative Modeling Of Chaotic Logical Circuits And Walking Droplets: A Dynamical Systems Approach, Aminur Rahman

Dissertations

Logical circuits and wave-particle duality have been studied for most of the 20th century. During the current century scientists have been thinking differently about these well-studied systems. Specifically, there has been great interest in chaotic logical circuits and hydrodynamic quantum analogs.

Traditional logical circuits are designed with minimal uncertainty. While this is straightforward to achieve with electronic logic, other logic families such as fluidic, chemical, and biological, naturally exhibit uncertainties due to their inherent nonlinearity. In recent years, engineers have been designing electronic logical systems via chaotic circuits. While traditional boolean circuits have easily determined outputs, which renders dynamical models …

Self Similar Flows In Finite Or Infinite Two Dimensional Geometries, Leonardo Xavier Espin Estevez

Dissertations

This study is concerned with several problems related to self-similar flows in pulsating channels. Exact or similarity solutions of the Navier-Stokes equations are of practical and theoretical importance in fluid mechanics. The assumption of self-similarity of the solutions is a very attractive one from both a theoretical and a practical point of view. It allows us to greatly simplify the Navier-Stokes equations into a single nonlinear one-dimensional partial differential equation (or ordinary differential equation in the case of steady flow) whose solutions are also exact solutions of the Navier-Stokes equations in the sense that no approximations are required in order …

Mathematical Problems Arising In Interfacial Electrohydrodynamics, Dmitri Tseluiko

Dissertations

In this work we consider the nonlinear stability of thin films in the presence of electric fields. We study a perfectly conducting thin film flow down an inclined plane in the presence of an electric field which is uniform in its undisturbed state, and normal to the plate at infinity. In addition, the effect of normal electric fields on films lying above, or hanging from, horizontal substrates is considered. Systematic asymptotic expansions are used to derive fully nonlinear long wave model equations for the scaled interface motion and corresponding flow fields. For the case of an inclined plane, higher order …