Nonlinear Bloch-Torrey Equation
Fredrick Michael

TL;DR
This paper introduces a nonlinear Bloch-Torrey equation incorporating non-constant diffusion, leading to solutions characterized by q-parametrized power-law distributions from Tsallis statistics, advancing the modeling of nonexponential NMR relaxation.
Contribution
It derives a novel nonlinear Bloch-Torrey PDE that models nonexponential relaxation using non-constant diffusion and Tsallis statistics, expanding beyond traditional exponential models.
Findings
Derivation of a nonlinear PDE for NMR relaxation.
Solution exhibits q-parametrized power-law distribution.
Connects nonextensive statistics with magnetic resonance modeling.
Abstract
Recently, there has been an examination of the nonexponential relaxation profiles of the NMR signal. The exponential relaxation from Bloch-Torrey equations with constant diffusion coefficients are known to be an approximation, and research has been in areas that would reproduce non-exponential relaxation. These would be from statistical models, phenomenological models, and microscopic models including a recent fractional derivative approach. In this letter we derive a nonlinear Bloch-Torrey partial differential equation that has equivalently a non-constant diffusion coefficient and a linear probability and for which the solution is of a q-parametrized power-law distribution of the nonextensive Tsallis statistics.
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Taxonomy
TopicsAdvanced Thermodynamics and Statistical Mechanics · Quantum Mechanics and Applications
