The truncated Levy-flight process: Application to the random spin phase change in non-linear magnetic fields
In NMR experiments, self-diffusion of water molecules leads to a random spin phase distribution which is Gaussian in linear magnetic fields. The rate of convergence of the random phase distribution to the Gaussian distribution is very slow. Moreover, a small departure from linear magnetic fields results in significant changes in the spin phase distribution, especially in the central part, and the distribution can be described by Levy-flight process. However, the far-tails of the Levy-like distribution conserve information about the Gaussian prehistory and can validate the degree of non-linearity of the magnetic field. In this paper, the rate, α, of convergence to the Gaussian distribution is calculated for the case of the variation of the power of non-linearity of the magnetic field p and it is shown that α(p)∈(0,0.66] when p∈[1,∞).
Year of publication: |
2006
|
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Authors: | Posnansky, Oleg ; Huang, Ruiwang ; Jon Shah, N. |
Published in: |
Physica A: Statistical Mechanics and its Applications. - Elsevier, ISSN 0378-4371. - Vol. 370.2006, 2, p. 553-564
|
Publisher: |
Elsevier |
Subject: | Levy-flight process | Random walk | NMR | Non-linear field | Crossover | Convergence rate | Monte-Carlo simulations |
Saved in:
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