随机非线性磁场下自旋相演化的有效相扩散

IF 2.4 3区 物理与天体物理 Q1 Mathematics
Guoxing Lin
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引用次数: 0

摘要

提出了非线性梯度磁场下自旋自扩散的一般理论描述,扩展了线性梯度磁场的有效相扩散方法。基于相扩散,提出的方法揭示了非线性梯度磁场中相演化的一般特征。相位演化有三种类型:相位扩散、浮动相位演化和基于起始位置的位移演化。对于非线性场原点附近的自旋扩散,这三种相位演化会显著影响核磁共振(NMR)信号。传统方法很难处理这些三相演变。值得注意的是,在传统方法中,浮动相演变的相位会被遗漏或错位,从而导致不正确的核磁共振信号衰减或相移。本文的方法表明,扩散和浮动相位演化来自梯度场的一阶和二阶导数。根据这三种相位演化,可以得到相位方差和相应的 NMR 信号衰减,这一点通过计算抛物线场和立方场下的相位扩散得到了证明。结果表明,信号衰减在短时间内遵从高斯衰减,然后随着时间的增加而改变为遵从洛伦兹函数或米塔格-勒弗勒函数衰减,这与高斯衰减有很大不同。对于远离场梯度原点开始扩散的自旋来说,信号衰减是高斯衰减,但浮动相位对偶阶梯度场的总相移仍有重要影响,可用于直接测量扩散系数。我们进行了随机漫步模拟,这支持了所获得的理论结果。得到的一般理论表达式可以处理随机阶非线性梯度场。这些结果有助于在核磁共振和磁共振成像中开发基于非线性梯度场的先进实验技术。
本文章由计算机程序翻译,如有差异,请以英文原文为准。

Effective phase diffusion for spin phase evolution under random nonlinear magnetic field

Effective phase diffusion for spin phase evolution under random nonlinear magnetic field
The general theoretical description of spin self-diffusion under a nonlinear gradient magnetic field is proposed, which extends the effective phase diffusion method for a linear gradient field. Based on the phase diffusion, the proposed method reveals the general features of phase evolutions in nonlinear gradient fields. There are three types of phase evolutions: phase diffusion, float phase evolution, and shift evolution based on the starting position. For spin diffusion near the origin of the nonlinear field, these three phase evolutions significantly affect the nuclear magnetic resonance (NMR) signal. The traditional methods have difficulties in handling these three-phase evolutions. Notably, the phase from float phase evolution is missed or misplaced in traditional methods, which leads to incorrect NMR signal attenuation or phase shift. The method here shows that the diffusing and float phase evolutions come from the first and second derivatives of the gradient field. Based on these three phase evolutions, the phase variance and corresponding NMR signal attenuation are obtained, as demonstrated by calculating the phase diffusions under both parabolic and cubic fields. The results indicate that signal attenuation obeys Gaussian attenuation for a short time, then changes to follow Lorentzian or Mittag-Leffler function attenuations as time increases, significantly different from Gaussian attenuation. For spins starting diffusion far away from the origin of the field gradient, the signal attenuation is Gaussian, but the float phase still has an important effect on the total phase shift of even-order gradient fields, which could be used to measure the diffusion coefficient directly. Random walk simulations were performed, which support the obtained theoretical results. General theoretical expressions are obtained, which can handle random order nonlinear gradient fields. The results could help develop advanced experimental techniques based on a nonlinear gradient field in NMR and magnetic resonance imaging.
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来源期刊
Physical review. E
Physical review. E 物理-物理:流体与等离子体
CiteScore
4.60
自引率
16.70%
发文量
0
审稿时长
3.3 months
期刊介绍: Physical Review E (PRE), broad and interdisciplinary in scope, focuses on collective phenomena of many-body systems, with statistical physics and nonlinear dynamics as the central themes of the journal. Physical Review E publishes recent developments in biological and soft matter physics including granular materials, colloids, complex fluids, liquid crystals, and polymers. The journal covers fluid dynamics and plasma physics and includes sections on computational and interdisciplinary physics, for example, complex networks.
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