Related papers: Localization regime in diffusion NMR: theory and e…
We report initial NMR studies of i) xenon gas diffusion in model heterogeneous porous media, and ii) continuous flow laser-polarized xenon gas. Both areas utilize the Pulsed Gradient Spin Echo techniques in the gas-phase, with the aim of…
When a beam of light is laterally confined, its field distribution can exhibit points where the local magnetic and electric field vectors spin in a plane containing the propagation direction of the electromagnetic wave. The phenomenon…
We study the magnetic excitation spectrum in three-dimensional diluted ferromagnetic nearest-neighbor systems down to the percolation threshold. The disorder effects resulting from the dilution are handled accurately within self-consistent…
As a follow up of our work on the electromagnetic four-current, we study for the first time the relativistic polarization and magnetization spatial distributions inside a spin-$\frac{1}{2}$ target within the quantum phase-space approach.…
Diffusion models generate high-quality samples but can also memorize training data, raising serious privacy concerns. Understanding the mechanisms governing when memorization versus generalization occurs remains an active area of research.…
The diffusion of hard-core particles subject to a global bias is described by a nonlinear, anisotropic generalization of the diffusion equation with conserved, local noise. Using renormalization group techniques, we analyze the effect of an…
We rigorously calculate the propagation and scattering of electromagnetic waves by rectangular and random arrays of dielectric cylinders in a uniform medium. For regular arrays, the band structures are computed and complete bandgaps are…
A scaling theory is developed for diffusion-limited cluster aggregation in a porous medium, where the primary particles and clusters stick irreversibly to the walls of the pore space as well as to each other. Three scaling regimes are…
Diffusion models are state-of-the-art tools for various generative tasks. Yet training these models involves estimating high-dimensional score functions, which in principle suffers from the curse of dimensionality. It is therefore important…
Diffusive transport is among the most common phenomena in nature [1]. However, as predicted by Anderson [2], diffusion may break down due to interference. This transition from diffusive transport to localization of waves should occur for…
We consider the behaviour of precessional angle (phase) carried by molecules of a diffusing specimen under magnetic fields typical of magnetic resonance experiments. An evolution equation for the ensemble of particles is constructed, which…
We present an extended microcanonical Lanczos method (MCLM) for a direct evaluation of the diffusion constant and its frequency dependence within the disordered Anderson model of noninteracting particles. The method allows to study systems…
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…
Densely packed systems of thermal particles in curved geometries are frequently encountered in biological and microfluidic systems. In 2D systems, at sufficiently high surface coverage, diffusive motion is widely known to be strongly…
Nonlocal neural networks have been proposed and shown to be effective in several computer vision tasks, where the nonlocal operations can directly capture long-range dependencies in the feature space. In this paper, we study the nature of…
Fast radio bursts (FRBs) are observed to be highly polarized. Most have high linear polarization but a small fraction show significant circular polarization. We systematically investigate a variety of polarization mechanisms of FRBs within…
The localization transition and the critical properties of the Lorentz model in three dimensions are investigated by computer simulations. We give a coherent and quantitative explanation of the dynamics in terms of continuum percolation…
Random matrix theory of the transition strengths is applied to transport in the strongly localized regime. The crossover distribution function between the different ensembles is derived and used to predict quantitatively the {\sl universal}…
A mechanism for the localization of spatially periodic, self-organized patterns in anisotropic media which requires systems extended in all three spatial dimensions is presented: When the anisotropy axis is twisted the pattern becomes…
The theory of localized spin-wave excitations in random-anisotropy magnets has been developed. Starting with a pure Heisenberg ferromagnet, we study the evolution of standing spin waves in a finite-size sample towards localized modes on…