Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2023
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2312.04200 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866915386911358976 |
|---|---|
| author | Grebenkov, Denis S. |
| author_facet | Grebenkov, Denis S. |
| contents | We consider the Bloch-Torrey operator, $-Δ+ igx$, that governs the time evolution of the transverse magnetization in diffusion magnetic resonance imaging (dMRI). Using the matrix formalism, we compute numerically the eigenvalues and eigenfunctions of this non-Hermitian operator for two bounded three-dimensional domains: a sphere and a capped cylinder. We study the dependence of its eigenvalues and eigenfunctions on the parameter $g$ and on the shape of the domain (its eventual symmetries and anisotropy). In particular, we show how an eigenfunction drastically changes its shape when the associated eigenvalue crosses a branch (or exceptional) point in the spectrum. Potential implications of this behavior for dMRI are discussed. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2312_04200 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Spectral properties of the Bloch-Torrey operator in three dimensions Grebenkov, Denis S. Mathematical Physics Spectral Theory Chemical Physics We consider the Bloch-Torrey operator, $-Δ+ igx$, that governs the time evolution of the transverse magnetization in diffusion magnetic resonance imaging (dMRI). Using the matrix formalism, we compute numerically the eigenvalues and eigenfunctions of this non-Hermitian operator for two bounded three-dimensional domains: a sphere and a capped cylinder. We study the dependence of its eigenvalues and eigenfunctions on the parameter $g$ and on the shape of the domain (its eventual symmetries and anisotropy). In particular, we show how an eigenfunction drastically changes its shape when the associated eigenvalue crosses a branch (or exceptional) point in the spectrum. Potential implications of this behavior for dMRI are discussed. |
| title | Spectral properties of the Bloch-Torrey operator in three dimensions |
| topic | Mathematical Physics Spectral Theory Chemical Physics |
| url | https://arxiv.org/abs/2312.04200 |