Monte Carlo Random Walk Algorithm Research Articles

Na+ and solute diffusion in aqueous channels of Myverol bicontinuous cubic phase: PGSE NMR and computer modelling.

The apparent diffusion coefficients of 23 Na+ ions and the solute 2-fluoroethylamine present in the aqueous domain of a Myverol/water bulk bicontinuous cubic phase (BCP) were measured using pulsed field-gradient spin echo (PGSE) NMR spectroscopy. The measured values were dependent on the diffusion time interval, which is a characteristic of restricted diffusion. The translational motion of 23 Na+ and water in the aqueous channels of a cubic phase were simulated using a Monte-Carlo random walk algorithm, and the simulation results were compared with those from real PGSE NMR experiments. The simulations indicated that diffusion of 23 Na+ ions and water would appear to be restricted even on the shortest timescales available to PGSE NMR experiments. The micro-viscosity of the aqueous domain of the BCPs was estimated from the longitudinal relaxation times of 23 Na+ and 2-fluoroethylamine; this was three times higher than in free solution and suggests one of (but not the only) likely impediments to the release of hydrophilic drugs from stabilised aqueous dispersions of BCPs (cubosomes) when they are used therapeutically in vivo. Monte Carlo simulations of diffusive efflux from cubosomes suggest that the principal impediment to drug release is presented by a surfactant or lipid barrier at the cubosome surface, which separates the BCP aqueous channels from the bulk solution. The dynamics inferred from these studies informs quantitative predictions of drug delivery from cubosomes. Copyright © 2016 John Wiley & Sons, Ltd.

Numerical Calculation of NMR Response for the 3D Digital Core Constructed with CT Images of the Tight Rock

The tight rock often has low porosity, low permeability and poor pore connectivity, which it is difficult for formation evaluation. Nuclear Magnetic Resonance (NMR) logging is widely used in fluid typing and reservoir parameters determination to provide the information of porosity, permeability and pore size distribution. NMR relaxation mechanisms are characterized by the pore-scale petrophysical models. Monte Carlo algorithm describes the Brownian motion of fluid molecules in pore space. In the paper we setup a 3D digital core of the tight sandstone with X-ray computer tomography (CT) images to model NMR response with Monte Carlo random walk algorithm. We compared T2 distributions from the numerical calculated pulse echo trains from the measurements. The results show that the simulated NMR response is consisted with the experiment.

Diffusion tensor tractography of the arcuate fasciculus in patients with brain tumors: Comparison between deterministic and probabilistic models.

The purpose of this study was to compare the deterministic and probabilistic tracking methods of diffusion tensor white matter fiber tractography in patients with brain tumors. We identified 29 patients with left brain tumors <2 cm from the arcuate fasciculus who underwent pre-operative language fMRI and DTI. The arcuate fasciculus was reconstructed using a deterministic Fiber Assignment by Continuous Tracking (FACT) algorithm and a probabilistic method based on an extended Monte Carlo Random Walk algorithm. Tracking was controlled using two ROIs corresponding to Broca's and Wernicke's areas. Tracts in tumoraffected hemispheres were examined for extension between Broca's and Wernicke's areas, anterior-posterior length and volume, and compared with the normal contralateral tracts. Probabilistic tracts displayed more complete anterior extension to Broca's area than did FACT tracts on the tumor-affected and normal sides (p < 0.0001). The median length ratio for tumor: normal sides was greater for probabilistic tracts than FACT tracts (p < 0.0001). The median tract volume ratio for tumor: normal sides was also greater for probabilistic tracts than FACT tracts (p = 0.01). Probabilistic tractography reconstructs the arcuate fasciculus more completely and performs better through areas of tumor and/or edema. The FACT algorithm tends to underestimate the anterior-most fibers of the arcuate fasciculus, which are crossed by primary motor fibers.

Multifractal scaling analysis of reactions over fractal surfaces

Simulations of the Eley-Rideal diffusion-limited reaction mechanism and its modified versions over surfaces of different fractal objects having different fractal dimensions were performed using the Monte Carlo random walk algorithm. Effects on the reaction probability distribution (RPD) were examined by employing various sticking probability functions. Other effects also studied included cluster size effects and noise reduction. Multifractal analyses were then carried out on the reaction probability distribution to study the effects of those factors on model chemical reactions.

Multifractal analysis of diffusion-limited reactions over surfaces of diffusion-limited aggregates

Simulations of diffusion-limited reactions over surfaces of Witten—Sander diffusion-limited aggregates (DLA) were performed using a Monte Carlo random walk algorithm. Multifractal analyses were then carried out on the reaction probability distribution to investigate the effect of fractal environment of DLA surfaces on model chemical reactions. Multifractality of the reaction probability distribution in DLA was revealed from analysis of size effects. Comparisons were made to diffusion-limited reactions over Cantor set and devil's staircase reported by Avnir et al.

Evaluation of the Boltzmann Density Matrix with Coupling Term by Monte Carlo Random Walk Method11The project supported by National Natural Science Foundation of China.

A Monte Carlo random walk algorithm for evaluating the path integral expression for coordinate matrix elements of the Boltzmann operator with the coupling term is suggested and discussed.