Related papers: Continuity, the Bloch-Torrey equation, and Diffusi…
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…
Magnetic Resonance Imaging (MRI) is a widely applied non-invasive imaging modality based on non-ionizing radiation which gives excellent images and soft tissue contrast of living tissues. We consider the modified Bloch problem as a model of…
In this paper commutator expansions for solving the Bloch-Torrey's equation are derived. An exact solution for free diffusion in a constant magnetic field gradient is found. Furthermore the moments of the signal in the short gradient pulse…
We study the influence of diffusion on NMR experiments when the molecules undergo random motion under the influence of a force field, and place special emphasis on parabolic (Hookean) potentials. To this end, the problem is studied using…
High diffusion-sensitizing magnetic field gradients have been more and more often applied nowadays to achieve a better characterization of the microstructure. As the resulting spin-echo signal significantly deviates from the conventional…
Recently, there has been an examination of the nonexponential relaxation profiles of the NMR signal. The exponential relaxation from Bloch-Torrey equations with constant diffusion coefficients are known to be an approximation, and research…
We study magnetic fluctuations in a system of interacting spins on a lattice at high temperatures and in the presence of a spatially varying magnetic field. Starting from a microscopic Hamiltonian we derive effective equations of motion for…
An approximative method for solving the Bloch-Torrey equation in general porous media is presented. The method expand the boundaries defining the porous media using electrostatic charges. As a result the eigenvalue problem of the Laplace…
We report an implementation of the lattice Boltzmann method (LBM) to integrate the Bloch-Torrey equation, which describes the evolution of the transverse magnetization vector and the fate of the signal of diffusion magnetic resonance…
Simultaneous diffusive and inertial motion of Brownian particles in laminar Couette flow is investigated via Lagrangian and Eulerian descriptions to determine the effect of particle inertia on diffusive transport in the long-time. The…
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…
The diffusion limit of the linear Boltzmann equation with a strong magnetic field is performed. The giration period of particles around the magnetic field is assumed to be much smaller than the collision relaxation time which is supposed to…
The absorption cross section of M\"{o}ssbauer radiation in magnetic liquids is calculated, taking into consideration both translational and rotational Brownian motion of magnetic nanoparticles. Stochastic reversals of their magnetization…
Aims: We aim to determine the effect of converging flows on the evolution of a bipolar magnetic region (BMR), and to investigate the role of these inflows in the generation of poloidal flux. We also discuss whether the flux dispersal due to…
Aim of this note is to analyse branching Brownian motion within the class of models introduced in the recent paper [4] and called chemical diffusion master equations. These models provide a description for the probabilistic evolution of…
Purpose: The paper introduces a classical model to describe the dynamics of large spin-1/2 ensembles associated with nuclei bound in large molecule structures, commonly referred to as the semi-solid spin pool, and their magnetization…
We are interested in numerically solving a transitional model derived from the Bloch model. The Bloch equation describes the time evolution of the density matrix of a quantum system forced by an electromagnetic wave. In a high frequency and…
In astrophysics, turbulent diffusion is often used in place of microphysical diffusion to avoid resolving the small scales. However, we expect this approach to break down when time and length scales of the turbulence become comparable with…
The paper contains mathematical justification of basic facts concerning the Brownian motor theory. The homogenization theorems are proved for the Brownian motion in periodic tubes with a constant drift. The study is based on an application…
A thorough review of the q-space technique is presented starting from a discussion of Fick's laws. The work presented here is primarily conceptual, theoretical and hopefully pedagogical. We offered the notion of molecular concentration to…