A perturbation basis for calculating NMR Diffusometry

Matias Nordin

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arXiv · 1308.5987

A perturbation basis for calculating NMR Diffusometry

Matias Nordin

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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.

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Matias Nordin. 2013-08-27. A perturbation basis for calculating NMR Diffusometry. https://arxiv.org/abs/1308.5987

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