Commutator expansions in NMR diffusometry
Matias Nordin
TL;DR
This paper derives commutator expansions to solve the Bloch-Torrey equation, providing exact solutions for free diffusion and moments for restricted geometries, with numerical validation against known solutions.
Contribution
It introduces a novel approach using commutator expansions for solving the Bloch-Torrey equation in NMR diffusometry, including exact solutions and moment calculations.
Findings
Exact solution for free diffusion in constant magnetic field gradient.
Derived moments for spins in restricted geometries.
Numerical validation against known solutions.
Abstract
In this paper commutator expansions for solving the Bloch-Torrey's equation are derived. An exact solution for free diffusion in a constant magnetic field gradient is found. Furthermore the moments of the signal in the short gradient pulse limit for spins confined to a restricted geometry are derived. The moments are tested numerically against the known solution of diffusing spins between two perpendicular plates in the short gradient pulse limit.
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