EPJ Web Conf.
Volume 173, 2018Mathematical Modeling and Computational Physics 2017 (MMCP 2017)
|Number of page(s)||4|
|Section||Mathematical Modeling and Methods|
|Published online||14 February 2018|
Fractional Langevin Equation Model for Characterization of Anomalous Brownian Motion from NMR Signals
1 Laboratory of Radiation Biology, Joint Institute for Nuclear Research, 141980 Dubna, Moscow Region, Russia
2 Department of Physics, Faculty of Electrical Engineering and Informatics, Technical University of Košice, Park Komenského 2, 042 00 Košice, Slovakia
Published online: 14 February 2018
Nuclear magnetic resonance is often used to study random motion of spins in different systems. In the long-time limit the current mathematical description of the experiments allows proper interpretation of measurements of normal and anomalous diffusion. The shorter-time dynamics is however correctly considered only in a few works that do not go beyond the standard Langevin theory of the Brownian motion (BM). In the present work, the attenuation function S (t) for an ensemble of spins in a magnetic-field gradient, expressed in a form applicable for any kind of stationary stochastic dynamics of spins with or without a memory, is calculated in the frame of the model of fractional BM. The solution of the model for particles trapped in a harmonic potential is obtained in a simple way and used for the calculation of S (t). In the limit of free particles coupled to a fractal heat bath, the results compare favorably with experiments acquired in human neuronal tissues.
© The Authors, published by EDP Sciences, 2018
This is an Open Access article distributed under the terms of the Creative Commons Attribution License 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (http://creativecommons.org/licenses/by/4.0/).
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