Pulsed field gradient signal attenuation of restricted anomalous diffusions in plate, sphere, and cylinder with wall relaxation.,Physical Review E

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Pulsed field gradient signal attenuation of restricted anomalous diffusions in plate, sphere, and cylinder with wall relaxation.
Physical Review E ( IF 2.2 ) Pub Date : 2020-01-01 , DOI: 10.1103/physreve.101.012128
Xinli Liao ₁ , Shaokuan Zheng ₂ , Guoxing Lin ₃

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The effect of boundary relaxation on pulsed field gradient (PFG) anomalous restricted diffusion is investigated in this paper. The PFG signal attenuation expressions of anomalous diffusion in plate, sphere, and cylinder are derived based on fractional calculus. In addition, approximate expressions for boundary relaxation induced short time signal attenuation under zero gradient field and boundary relaxation affected short time apparent diffusion coefficients are given in this paper. Unlike the exponential signal attenuation in normal diffusion, the PFG signal attenuation in anomalous diffusion with boundary relaxation is either a Mittag-Leffler-function-based attenuation or a stretched-exponential-function-based attenuation. The stretched exponential attenuations of all three structures clearly show the diffractive pattern. In contrast, only in the plate structure does the Mittag-Leffler-function-based attenuation display an obvious diffractive pattern. Additionally, anomalous diffusion with smaller time derivative order α has a weaker diffractive pattern and less signal attenuation. Moreover, the results demonstrate that boundary relaxation induced signal attenuation is significantly affected by the anomalous diffusion when no gradient field is applied. Meanwhile, the boundary relaxation significantly affects PFG signal attenuation of anomalous diffusion in the following ways: The boundary relaxation results in reduced radius from the minimum of the diffractive patterns, and it results in an increased apparent diffusion coefficient and decreased surfaces to volume ratio in varying the diffusion time experiment; the boundary relaxation also substantially affects the apparent diffusion coefficient of sphere structure in the variation of gradient experiment.

中文翻译：

带有壁弛豫的板，球和圆柱体中有限的异常扩散的脉冲场梯度信号衰减。

研究了边界弛豫对脉冲场梯度（PFG）反常限制扩散的影响。基于分数演算，推导了板，球和圆柱体中异常扩散的PFG信号衰减表达式。另外，给出了零梯度场下边界弛豫引起的短时信号衰减的近似表达式，以及边界弛豫影响的短时视在扩散系数。与正常扩散中的指数信号衰减不同，异常扩散中具有边界松弛的PFG信号衰减是基于Mittag-Leffler函数的衰减或基于拉伸指数函数的衰减。所有三个结构的拉伸指数衰减都清楚地显示出衍射图样。相反，仅在板结构中，基于Mittag-Leffler函数的衰减才会显示出明显的衍射图样。另外，具有较小的时间导数阶数α的异常扩散具有较弱的衍射图案和较小的信号衰减。此外，结果表明，当不施加梯度场时，边界弛豫引起的信号衰减会受到异常扩散的显着影响。同时，边界弛豫在以下方面显着影响异常扩散的PFG信号衰减：边界弛豫导致最小衍射图案的半径减小，并且导致表观扩散系数增大，并且在变化的情况下表面积与体积比减小扩散时间实验；

更新日期：2020-01-24

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