Attenuation of the NMR signal in a field gradient due to stochastic dynamics with memory

Attenuation of the NMR signal due to hydrodynamic Brownian motion

Nuclear magnetic resonance (NMR) is a widely used nondestructive method to study random motion of spin-bearing particles in different systems. In the long-time limit the theoretical description of the NMR experiments is well developed and allows proper interpretation of measurements of normal and anomalous diffusion. The traditional description becomes, however, insufficient for the shorter-time dynamics of the particles. In the present paper, the all-time attenuation function of the NMR signal in a magnetic-field gradient due to the Brownian motion (BM) of particles in incompressible liquids …

NMR diffusion in restricted environment approached by a fractional Langevin model

The diffusion motion of spin-bearing molecules is considerably affected in confined environments. In Nuclear Magnetic Resonance (NMR) experiments, under the presence of magnetic field gradients, this movement can be encoded in spin phase and the NMR signal attenuation due to diffusion can be evaluated. This paper considered this effect in both normal and anomalous diffusion by means of the Langevin stochastic model within the Gaussian phase approximation (GPA) for a constant gradient temporal profile. The phenomenological approach illustrates the emergence of fractional order exponential decay…

NMR measurements and all-time Brownian movement with memory

In the present work, by using the method of accumulation of phase shifts in the rotating frame, the attenuation function S(t) of the NMR signal from an ensemble of spin-bearing particles in a magnetic-field gradient is expressed through the particle mean square displacement in a form applicable for any kind of stationary stochastic dynamics of spins and for any times. S(t) is evaluated providing that the random motion of particles can be modeled by the generalized Langevin equation (GLE) with a colored random force driving the particles. The memory integral in this equation is the convolution …

NMR signals within the generalized Langevin model for fractional Brownian motion

The methods of Nuclear Magnetic Resonance belong to the best developed and often used tools for studying random motion of particles in different systems, including soft biological tissues. In the long-time limit the current mathematical description of the experiments allows proper interpretation of measurements of normal and anomalous diffusion. The shorter-time dynamics is however correctly considered only in a few works that do not go beyond the standard memoryless Langevin description of the Brownian motion (BM). In the present work, the attenuation function S(t) for an ensemble of spin-bea…

How to compare diffusion processes assessed by single-particle tracking and pulsed field gradient nuclear magnetic resonance

Heterogeneous diffusion processes occur in many different fields such as transport in living cells or diffusion in porous media. A characterization of the transport parameters of such processes can be achieved by ensemble-based methods, such as pulsed field gradient nuclear magnetic resonance (PFG NMR), or by trajectory-based methods obtained from single-particle tracking (SPT) experiments. In this paper, we study the general relationship between both methods and its application to heterogeneous systems. We derive analytical expressions for the distribution of diffusivities from SPT and furthe…

异常扩散作为结构记忆：一种扩展的结构动力学方法

Anomalous Diffusion as Structural Memory: An Extended Structural Dynamics Approach

本文提出扩展结构动力学方法，揭示生物系统中亚扩散现象源于不完整相空间的投影，通过结构实体的完整自由度分析，推导出亚扩散指数与分子灵活性的关系，并验证了结构动力学在复杂介质中的实验一致性。