165 citations · 276 across the 9 of their papers we have counts for
9 papers
Spectral branch points of the Bloch-Torrey operator
Nicolas Moutal, Denis S. Grebenkov
We investigate the peculiar feature of non-Hermitian operators, namely, the existence of spectral branch points (also known as exceptional or level crossing points), at which two (…
On the spectral properties of the Bloch-Torrey equation in infinite periodically perforated domains
Denis S. Grebenkov, Nicolas Moutal, Bernard Helffer
We investigate spectral and asymptotic properties of the particular Schrödinger operator (also known as the Bloch-Torrey operator), , in infinite periodically perforated…
The localization regime in a nutshell
N. Moutal, D. S. Grebenkov
High diffusion-sensitizing magnetic field gradients have been more and more often applied nowadays to achieve a better characterization of the microstructure. As the resulting spin…
Diffusion NMR in periodic media: efficient computation and spectral properties
Nicolas Moutal, Antoine Moutal, Denis S. Grebenkov
The Bloch-Torrey equation governs the evolution of the transverse magnetization in diffusion magnetic resonance imaging, where two mechanisms are at play: diffusion of spins (Lapla…
The Kärger vs bi-exponential model: theoretical insights and experimental validations
Nicolas Moutal, Markus Nilsson, Daniel Topgaard +1
We revise three common models accounting for water exchange in pulsed-gradient spin-echo measurements: a bi-exponential model with time-dependent water fractions, the Kärger model,…
Diffusion-limited reactions in dynamic heterogeneous media
Yann Lanoiselée, Nicolas Moutal, Denis S. Grebenkov
Most biochemical reactions in living cells rely on diffusive search for target molecules or regions in a heterogeneous overcrowded cytoplasmic medium. Rapid re-arrangements of the…
Localization regime in diffusion NMR: theory and experiments
Nicolas Moutal, Kerstin Demberg, Denis Grebenkov +1
In this work we investigate the emergence of the localization regime for diffusion in various geometries: inside slabs, inside cylinders and around rods arranged on a square array.…
Probing surface-to-volume ratio of an anisotropic medium by diffusion {NMR} with general gradient encoding
Nicolas Moutal, Ivan I. Maximov, Denis S. Grebenkov
Since the seminal paper by Mitra et al., diffusion MR has been widely used in order to estimate surface-to-volume ratios. In the present work we generalize Mitra's formula for arbi…
Diffusion across semi-permeable barriers: spectral properties, efficient computation, and applications
Nicolas Moutal, Denis Grebenkov
We present an efficient method to compute the eigenvalues and eigenmodes of the diffusion operator on one-dimensional heterogeneous structures with multiple semi-…