Related papers: NMR signal for particles diffusing under potential…
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…
The Bloch equation describes the evolution of classical particles tagged with a magnetisation vector in a strong magnetic field and is fundamental to many NMR and MRI contrast methods. The equation can be generalised to include the effects…
The Bloch-Torrey equation governs the evolution of the transverse magnetization in diffusion magnetic resonance imaging, where two mechanisms are at play: diffusion of spins (Laplacian term) and their precession in a magnetic field gradient…
Porous or biological materials comprise a multitude of micro-domains containing water. Diffusion-weighted magnetic resonance measurements are sensitive to the anisotropy of the thermal motion of such water. This anisotropy can be due to the…
In this work we investigate the emergence of the localization regime for diffusion in various geometries: inside slabs, inside cylinders and around rods arranged on a square array. At high gradients, the transverse magnetization is strongly…
The dynamics of viscoelastic fluids are governed by a memory function, essential yet challenging to compute, especially when diffusion faces boundary restrictions. We propose a computational method that captures memory effects by analyzing…
Magnetic resonance imaging (MRI) is the method of choice for noninvasive studies of micrometer-scale structures in biological tissues via their effects on the time/frequency-dependent ("restricted") and anisotropic self-diffusion of water.…
This paper derives the Fokker-Planck (FP) equation for a particle moving in potential by a randomly modulated dipole. The FP equation describes the anomalous diffusion observed in the companion paper [1] and breaks the conservation of the…
We study the problem of homogenization for inertial particles moving in a time dependent random velocity field and subject to molecular diffusion. We show that, under appropriate assumptions on the velocity field, the large--scale,…
The acceleration of energetic particle transport in high amplitude magnetosonic and Alfvenic turbulence is considered using the method of Monte Carlo particle simulations, involving integration of particle equations of motion. We derive the…
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…
We study the diffusive dynamics of a Brownian particle in proximity of a flat surface under non-equilibrium conditions, which are created by an anisotropic thermal environment with different temperatures being active along distinct spatial…
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…
Confinement can substantially alter the physicochemical properties of materials by breaking translational isotropy and rendering all physical properties position-dependent. Molecular dynamics (MD) simulations have proven instrumental in…
Traditional theories of the NMR autocorrelation function for intramolecular dipole pairs assume single-exponential decay, yet the calculated autocorrelation of realistic systems display a rich, multi-exponential behavior resulting in…
This paper employs the general time-space fractional diffusion equation to derive correlation time function for analyzing nuclear magnetic resonance (NMR) relaxation. Both the anomalous rotational and translational diffusion are treated.…
Application of fractional calculus to the description of anomalous diffusion and relaxation processes in complex media provided one of the most impressive impulses to the development of statistical physics during the last decade. In…
Nonlinear diffusion equations of spectral transfer are systematically derived for anisotropic magnetohydrodynamics in the regime of wave turbulence. The background of the analysis is the asymptotic Alfv\'en wave turbulence equations from…
We consider systems of particles hopping stochastically on $d$-dimensional lattices with space-dependent probabilities. We map the master equation onto an evolution equation in a Fock space where the dynamics are given by a quantum…
The Fokker-Planck equation provides complete statistical description of a particle undergoing random motion in a solvent. In the presence of Lorentz force due to an external magnetic field, the Fokker-Planck equation picks up a tensorial…