Symmetry solutions for variations of the Torrey-Bloch equation

Abstract

A nuclear magnetic resonance signal is generated when a net magnetic moment precesses in the presence of a detector coil. The Torrey-Bloch equation models the change in net magnetic moment over time, while accounting for self-diffusion of nuclear spins. However, more general forms make the Torrey-Bloch equation difficult to solve analytically. Symmetry methods provide a unified approach to solving differential equations, which can remove some of the guesswork, and sometimes yield new analytical solutions. In this thesis, classical symmetry solutions are investigated for variations of the Torrey-Bloch equation involving relaxation, linear gradient, and Fokker-Planck terms.

Date of Award	2018
Original language	English