Abstract

This dissertation examines the power series solutions---and their analytic continuation via gauge transformations---of three classical nonlinear ordinary differential equations arising in fluid mechanics that are mathematically related by their large-distance asymptotic behaviors in semi-infinite domains. The first problem examines the influence of surface tension and gravitational forces to form a static air--liquid interface that intersects a flat wall at a given contact angle and limits to a flat pool away from the wall. The second problem considers the related configuration of an axisymmetric air--liquid interface formed when the flat wall is replaced with a right circular cylinder. In both problems, we show that although power series solutions for the interface shapes are readily obtainable, the series diverge due to the influence of convergence-limiting singularities. In both cases, these singularities are mapped to new locations through transformations that are motivated by long-distance asymptotic behaviors of the solution. Convergent power series solutions to both problems are thus obtained. The third problem considers the Sakiadis boundary layer induced by a rapidly moving wall in a semi-infinite fluid domain, for which no exact analytic solution has been put forward in prior literature. For this problem, we follow the approach of the previous problems, and derive a convergent power series solution for both Newtonian and Ostwald-de Waele power law non-Newtonian fluids. Overall, this dissertation demonstrates that asymptotic behaviors, in conjunction with gauge function choices, can lead to exact convergent power series solutions to problems in mathematical physics.

Library of Congress Subject Headings

Gauge invariance; Power series; Differential equations, Nonlinear--Asymptotic theory

Publication Date

2-27-2024

Document Type

Dissertation

Student Type

Graduate

Degree Name

Mathematical Modeling (Ph.D)

Department, Program, or Center

Mathematics and Statistics, School of

College

College of Science

Advisor

Steven J. Weinstein

Advisor/Committee Member

Mohamed A. Samaha

Advisor/Committee Member

Nathaniel Barlow

Campus

RIT – Main Campus

Plan Codes

MATHML-PHD

Download

Share

COinS