Time correlation during anomalous diffusion in fractal systems and signal attenuation in NMR field-gradient spectroscopy

Kärger, Jörg; Pfeifer, H.; Vojta, G.

doi:10.1103/physreva.37.4514

Cited by 79 publications

(79 citation statements)

References 18 publications

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“…Previous attempts (Banavar et al 1985;Jug 1986;Kärger & Vojta 1987;Kärger et al 1988;Widom & Chen 1995) to address the issue of the form of the NMR signal decay, S(q, ∆), due to fractional Brownian motion, as measured in a PFG experiment, have all concluded similarly that…”

Section: Q-space Behaviourmentioning

confidence: 99%

Predictions for pulsed-field–gradient NMR experiments of diffusion in fractal spaces

Damion

Packer

1997

Proc. R. Soc. Lond. A

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Section: Q-space Behaviourmentioning

confidence: 99%

Predictions for pulsed-field–gradient NMR experiments of diffusion in fractal spaces

Damion

Packer

1997

Proc. R. Soc. Lond. A

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“…The torque changes the spin angular momentum direction, which leads the spin to precess about the magnetic field with Larmor frequency ω(z, t) = −γB(z, t). In a rotating frame with angular frequency ω 0 = −γB 0 , a diffusing spin at position z(t ) has a time-dependent angular frequency γg(t ) · z(t ), and its phase accumulated along the diffusion path is [13][14][15]19] …”

Section: The Phase-space Method: the Effective Phase-shift Diffusion mentioning

confidence: 99%

“…PFG anomalous diffusion [17][18][19][20][21][22][23] is different from PFG normal diffusion. Unlike normal diffusion, anomalous diffusion has a non-Gaussian probability distribution [2,24], and its mean square …”

Section: Introductionmentioning

confidence: 99%

Analysis of PFG Anomalous Diffusion via Real-Space and Phase-Space Approaches

Lin

2018

Mathematics

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Pulsed-field gradient (PFG) diffusion experiments can be used to measure anomalous diffusion in many polymer or biological systems. However, it is still complicated to analyze PFG anomalous diffusion, particularly the finite gradient pulse width (FGPW) effect. In practical applications, the FGPW effect may not be neglected, such as in clinical diffusion magnetic resonance imaging (MRI). Here, two significantly different methods are proposed to analyze PFG anomalous diffusion: the effective phase-shift diffusion equation (EPSDE) method and a method based on observing the signal intensity at the origin. The EPSDE method describes the phase evolution in virtual phase space, while the method to observe the signal intensity at the origin describes the magnetization evolution in real space. However, these two approaches give the same general PFG signal attenuation including the FGPW effect, which can be numerically evaluated by a direct integration method. The direct integration method is fast and without overflow. It is a convenient numerical evaluation method for Mittag-Leffler function-type PFG signal attenuation. The methods here provide a clear view of spin evolution under a field gradient, and their results will help the analysis of PFG anomalous diffusion.

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“…Here, without this assumption, it is easy from (10) to find φ 2 (t) that determines the damping of the spin echo signal and generalizes (12). At the echo time it reduces to a simple formula obtained in [16] in a much more tedious way…”

Section: Anomalous Diffusion Of Spinsmentioning

confidence: 99%

“…In Ref. [16], the expressions for the attenuation of the NMR signal due to anomalous diffusion were obtained assuming that X(t) is equal to the mean square distance x 2 (t) . Here, without this assumption, it is easy from (10) to find φ 2 (t) that determines the damping of the spin echo signal and generalizes (12).…”

Section: Anomalous Diffusion Of Spinsmentioning

confidence: 99%

Effect of Stochastic Dynamics on the Nuclear Magnetic Resonance in a Field Gradient

Tóthová

Lisý

2017

Acta Phys. Pol. A

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In the present contribution, the attenuation function S(t) for an ensemble of spins in a magnetic-field gradient is calculated through an accumulation of the phase shifts in the rotating frame resulting from the changes of the particle displacements. The found S(t) is applicable for any kind of the stochastic motion of spins, including their non-Markovian dynamics with memory. Depending on the considered system, both the classical expressions valid for normal diffusion at long times and new formulae for the short-time Brownian motion can be obtained. Our method is also applicable to the NMR pulse sequences based on the refocusing principle. This is demonstrated by describing the spin echo experiment developed by Hahn.

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Time correlation during anomalous diffusion in fractal systems and signal attenuation in NMR field-gradient spectroscopy

Cited by 79 publications

References 18 publications

Predictions for pulsed-field–gradient NMR experiments of diffusion in fractal spaces

Predictions for pulsed-field–gradient NMR experiments of diffusion in fractal spaces

Analysis of PFG Anomalous Diffusion via Real-Space and Phase-Space Approaches

Effect of Stochastic Dynamics on the Nuclear Magnetic Resonance in a Field Gradient

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