Search results for "fusion"

Generalized Wiener Process and Kolmogorov's Equation for Diffusion induced by Non-Gaussian Noise Source

2005

We show that the increments of generalized Wiener process, useful to describe non-Gaussian white noise sources, have the properties of infinitely divisible random processes. Using functional approach and the new correlation formula for non-Gaussian white noise we derive directly from Langevin equation, with such a random source, the Kolmogorov's equation for Markovian non-Gaussian process. From this equation we obtain the Fokker-Planck equation for nonlinear system driven by white Gaussian noise, the Kolmogorov-Feller equation for discontinuous Markovian processes, and the fractional Fokker-Planck equation for anomalous diffusion. The stationary probability distributions for some simple cas…

On the Reliability of Error Indication Methods for Problems with Uncertain Data

2012

This paper is concerned with studying the effects of uncertain data in the context of error indicators, which are often used in mesh adaptive numerical methods. We consider the diffusion equation and assume that the coefficients of the diffusion matrix are known not exactly, but within some margins (intervals). Our goal is to study the relationship between the magnitude of uncertainty and reliability of different error indication methods. Our results show that even small values of uncertainty may seriously affect the performance of all error indicators.

Editorial of Critical Phenomena and Diffusion in Complex Systems

2008

Diffusion process of molecular oxygen in silica nanoparticles

2012

On the scavenging of SO2 by large and small rain drops: V. A wind tunnel and theoretical study of the desorption of SO2 from water drops containing S…

1993

An experimental and theoretical study has been carried out to investigate the rate of desorption of SO2 from water drops falling at terminal velocity in air. The experiments were carried out in the Mainz vertical wind tunnel in which water drops of various sizes containing S(IV) in various concentrations were freely suspended in the vertical airstream of the tunnel. The results of these experiments were compared with the predictions of three theoretical models, and with the experiments of Walceket al. This comparison shows that the predictions of the diffusion model of Kronig and Brink in the formulation given by Walcek and Pruppacher agree well with the experimental results for all relevan…

Diffusion, thermodiffusion, and thermal diffusion of polystyrene in solution

1962

The role of melt-fracture degassing in defusing explosive rhyolite eruptions at volcán Chaitén

2012

Explosive volcanic eruptions of silicic magma often evolve towards non-explosive emissions of lava. The mechanisms underlying this transition remain unclear, however, a widely cited idea holds that shear-induced magma fragmentation plays a critical role by fostering volatile loss from fragmentary magma and through ash-filled cracks termed tuffisite. We test this hypothesis by measuring H2O concentrations within glassy tuffisite from the 2008–2011 rhyolitic eruption at volcan Chaiten, Chile. We show that while H2O concentrations decrease next to tuffisite veins and at the margins of obsidian fragments, the depletions cannot account for the disparity in H2O between explosively and effusively …

Functional A Posteriori Error Estimate for a Nonsymmetric Stationary Diffusion Problem

2015

In this paper, a posteriori error estimates of functional type for a stationary diffusion problem with nonsymmetric coefficients are derived. The estimate is guaranteed and does not depend on any particular numerical method. An algorithm for the global minimization of the error estimate with respect to an auxiliary function over some finite dimensional subspace is presented. In numerical tests, global minimization is done over the subspace generated by Raviart-Thomas elements. The improvement of the error bound due to the p-refinement of these spaces is investigated.

Stochastic homogenization: Theory and numerics

2015

In this chapter, we pursue two related goals. First, we derive a theoretical stochastic homogenization result for the stochastic forward problem introduced in the first chapter. The key ingredient to obtain this result is the use of the Feynman-Kac formula for the complete electrode model. The proof is constructive in the sense that it yields a strategy to achieve our second goal, the numerical approximation of the effective conductivity. In contrast to periodic homogenization, which is well understood, numerical homogenization of random media still poses major practical challenges. In order to cope with these challenges, we propose a new numerical method inspired by a highly efficient stoc…

Physics, Techniques and Review of Neuroradiological Applications of Diffusion Kurtosis Imaging (DKI)

2016

In recent years many papers about diagnostic applications of diffusion tensor imaging (DTI) have been published. This is because DTI allows to evaluate in vivo and in a non-invasive way the process of diffusion of water molecules in biological tissues. However, the simplified description of the diffusion process assumed in DTI does not permit to completely map the complex underlying cellular components and structures, which hinder and restrict the diffusion of water molecules. These limitations can be partially overcome by means of diffusion kurtosis imaging (DKI). The aim of this paper is the description of the theory of DKI, a new topic of growing interest in radiology. DKI is a higher or…