相关论文: Using NMR to Measure Fractal Dimensions
Small volume nuclear magnetic resonance spectroscopy (NMR) has recently made considerable progress due to rapid developments in the field of quantum sensing using nitrogen vacancy (NV) centers. These optically active defects in the diamond…
The fractal properties of models of randomly placed $n$-dimensional spheres ($n$=1,2,3) are studied using standard techniques for calculating fractal dimensions in empirical data (the box counting and Minkowski-sausage techniques). Using…
We present a general framework for the rigorous numerical analysis of time-fractional nonlinear parabolic partial differential equations, with a fractional derivative of order $\alpha\in(0,1)$ in time. The framework relies on three…
We calculate analytically the fluctuation-dissipation ratio (FDR) for Ising ferromagnets quenched to criticality, both for the long-range model and its short-range analogue in the limit of large dimension. Our exact solution shows that, for…
This article deals with the estimation of fractal dimension of spatio-temporal patterns that are generated by numerically solving the Swift Hohenberg (SH) equation. The patterns were converted into a spatial series (analogous to time…
We have developed x-ray diffraction measurements with high energy-resolution and accuracy to study water structure at three different temperatures (7, 25 and 66 C) under normal pressure. Using a spherically curved Ge crystal an energy…
A physical magnetic field has a divergence of zero. Numerical error in constructing a model field and computing the divergence, however, introduces a finite divergence into these calculations. A popular metric for measuring divergence is…
In this work, we present a numerical method that provides accurate real-time detection for the widths of the fractures in a fractured porous medium based on observational data on porous medium fluid mass and velocity. To achieve this task,…
The diffusion/relaxation behavior of polarized spins of pore filling fluid, as often probed by NMR relaxometry, is widely used to extract information on the pore-geometry. Such information is further interpreted as an indicator of the key…
The diffusion of particles trapped in long narrow channels occurs predominantly in one dimension. Here, molecular dynamics simulation is used to study the inertial dynamics of two-dimensional hard disks, confined to long, narrow,…
The geometry of fracture patterns in a dilute elastic network is explored using molecular dynamics simulation. The network in two dimensions is subjected to a uniform strain which drives the fracture to develop by the growth and coalescence…
X-ray diffractometers primarily designed for surface x-ray diffraction are often used to measure the diffraction from powders, textured materials, and fiber-texture samples in so-called $2\theta$ scans. Unlike high-energy powder diffraction…
Magnetic permeabilities derived for infinite, periodic media are used in the Fresnel equation to calculate the reflection from corresponding semi-infinite media. By comparison to finite-difference-time-domain (FDTD) simulations, we find…
We study the time evolution of wavepackets of non-interacting electrons in a two-dimensional disordered system in strong magnetic field. For wavepackets built from states near the metal-insulator transition in the center of the lowest…
We measure the turbulent diffusion coefficient of dust grains embedded in magnetorotational turbulence in a protoplanetary disc directly from numerical simulations and compare it to the turbulent viscosity of the flow. The simulations are…
Nuclear magnetic resonance (NMR) spectroscopy provides unparalleled access to molecular structure and dynamics but is traditionally limited by weak signal strength, requiring large sample volumes and high magnetic fields. Here, we…
During recent years, dynamical decoupling (DD) has gained relevance as a tool for manipulating quantum systems and extracting information from them. This is particularly relevant for spins involved in nuclear magnetic resonance (NMR), where…
Based on the non-Markov diffusion equation taking into account the spatial fractality and modeling for the generalized coefficient of particle diffusion…
{\bf Purpose}: To develop a geometry-governed diffusion framework that explains differential tissue response under FLASH ultra-high dose rate (UHDR) irradiation by explicitly accounting for structural heterogeneity and anomalous transport…
Static structure factors are computed for large-scale, mechanically stable, jammed packings of frictionless spheres (three dimensions) and disks (two dimensions) with broad, power-law size dispersity characterized by the exponent $-\beta$.…