Related papers: Conceptual Foundations of Diffusion in Magnetic Re…
Quantifying the myelin sheath radius of myelinated axons in vivo is important for understanding, diagnosing, and monitoring various neurological disorders. Despite advancements in diffusion MRI (dMRI) microstructure techniques, there are…
Magnetic fields and magnetic materials have promising microfluidic applications. For example, magnetic micro-convection can enhance mixing considerably. However, previous studies have not explained increased effective diffusion during this…
We study the mechanisms responsible for quantum diffusion in the quasiperiodic kicked rotor. We report experimental measurements of the diffusion constant on the atomic version of the system and develop a theoretical approach (based on the…
Diffusion in inhomogeneous materials can be described by both the Fick and Fokker--Planck diffusion equations. Here, we study a mixed Fick and Fokker-Planck diffusion problem with coefficients rapidly oscillating both in space and time. We…
We analyse diffusion at low temperature by bringing the fluctuation-dissipation theorem (FDT) to bear on a physically natural, viscous response-function R(t). The resulting diffusion-law exhibits several distinct regimes of time and…
Diffusion MRI affords valuable insights into white matter microstructures, but suffers from low signal-to-noise ratio (SNR), especially at high diffusion weighting (i.e., b-value). To avoid time-intensive repeated acquisition,…
The Markovian diffusion theory in the phase space is generalized within the framework of the general theory of relativity. The introduction of moving orthonormal frame vectors both for the position as well the velocity space enables to…
Nuclear magnetic resonance (NMR) and magnetic resonance imaging (MRI) are versatile tools with broad applications from physics and chemistry to geology and medical studies. In this mini-review, we consider the concepts of NMR and MRI…
A detailed distribution of the force of electromagnetic radiation in and around dielectric media can be obtained by a direct application of the Lorentz law of force in conjunction with Maxwell's equations. We develop a theory of the force…
Generative diffusion models showed high success in many fields with a powerful theoretical background. They convert the data distribution to noise and remove the noise back to obtain a similar distribution. Many existing reviews focused on…
To offer a view into the rapidly developing theory of fractional diffusion processes we describe in some detail three topics of present interest: (i) the well-scaled passage to the limit from continuous time random walk under power law…
This paper introduces the historical development of the symmetries for describing magnetic structures culminating in the derivation of the black and white and colored space groups. Beginning from the Langevin model of the Curie law, it aims…
Statistical properties of coherent radiation propagating in a quasi - 1D random media is studied in the framework of random matrix theory. Distribution functions for the total transmission coefficient and the angular transmission…
For the last decade, there has been a push to use multi-dimensional (latent) spaces to represent concepts; and yet how to manipulate these concepts or reason with them remains largely unclear. Some recent methods exploit multiple latent…
A nonlinear Lorentz invariant kinetic diffusion equation is introduced, which is consistent with the conservation laws of particles number, energy and momentum. The equilibrium solution converges to the Maxwellian density in the Newtonian…
On the basis of the relativistic symmetry of Minkowski space, we derive a Lorentz invariant equation for a spread electron. This equation slightly differs from the Dirac equation and includes additional terms originating from the spread of…
We study diffusion in systems of classical particles whose dynamics conserves the total center of mass. This conservation law leads to several interesting consequences. In finite systems, it allows for equilibrium distributions that are…
Magnetic Resonance Imaging (MRI), including diffusion MRI (dMRI), serves as a ``microscope'' for anatomical structures and routinely mitigates the influence of low signal-to-noise ratio scans by compromising temporal or spatial resolution.…
The Markovian diffusion theory is generalized within the framework of the special theory of relativity using a modification of the mathematical calculus of diffusion on Riemannian manifolds (with definite metric) to describe diffusion on…
We discuss some aspects of the propagation of high-energy cosmic rays (CRs) in turbulent magnetic fields, and propose a formula for the diffusion coefficient based on accurate simulations in a wide energy range. We discuss the transition…