English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Zendy Plus

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Zendy Tools

Zendy Open

Pulsed field gradient (PFG) has been increasingly employed to study anomalousdiffusions in Nuclear Magnetic Resonance (NMR) and Magnetic Resonance Imaging(MRI). However, the analysis of PFG anomalous diffusion is complicated. In thispaper, a fractal derivative model based modified Gaussian phase distributionmethod is proposed to describe PFG anomalous diffusion. By using the phasedistribution obtained from the effective phase shift diffusion method based onfractal derivatives, and employing some of the traditional Gaussian phasedistribution approximation techniques, a general signal attenuation expressionfor free fractional diffusion is derived. This expression describes a stretchedexponential function based attenuation, which is distinct from both theexponential attenuation for normal diffusion obtained from conventionalGaussian phase distribution approximation, and the Mittag-Leffler functionbased attenuation for anomalous diffusion obtained from fractional derivative.The obtained signal attenuation expression can analyze the finite gradientpulse width (FGPW) effect. Additionally, it can generally be applied to allthree types of PFG fractional diffusions classified based on time derivativeorder alpha and space derivative order beta. These three types of fractionaldiffusions include time-fractional diffusion, space-fractional diffusion, andgeneral fractional diffusion. The results in this paper are consistent withreported results based on effective phase shift diffusion equation method andinstantaneous signal attenuation method. This method provides a new, convenientapproximation formalism for analyzing PFG anomalous diffusion experiments.

Analyzing Signal Attenuation in PFG Anomalous Diffusion via a Modified Gaussian Phase Distribution Approximation Based on Fractal Derivative Model