A perturbation basis for calculating NMR Diffusometry
Abstract
An approximative method for solving the Bloch-Torrey equation in general porous media is presented. The method expand the boundaries defining the porous media using electrostatic charges. As a result the eigenvalue problem of the Laplace operator in a confined geometry can approximately solved. Importantly the approximative solution is orthogonal in the low-frequent region of Fourier space. This gives a natural approach for studying spin magnetization in presence of magnetic fields. The error in the approximation scales with N^{-2} times the magnitude of each eigenvalue, where N is the size of the expansion matrix. From a computational point of view, the calculations scale quadratically with the number of basis functions using fast multipole methods.
Cite
@article{arxiv.1308.5987,
title = {A perturbation basis for calculating NMR Diffusometry},
author = {Matias Nordin},
journal= {arXiv preprint arXiv:1308.5987},
year = {2013}
}