Search results for "Diffusion process"
showing 10 items of 44 documents
From Feynman–Kac formulae to numerical stochastic homogenization in electrical impedance tomography
2016
In this paper, we use the theory of symmetric Dirichlet forms to derive Feynman–Kac formulae for the forward problem of electrical impedance tomography with possibly anisotropic, merely measurable conductivities corresponding to different electrode models on bounded Lipschitz domains. Subsequently, we employ these Feynman–Kac formulae to rigorously justify stochastic homogenization in the case of a stochastic boundary value problem arising from an inverse anomaly detection problem. Motivated by this theoretical result, we prove an estimate for the speed of convergence of the projected mean-square displacement of the underlying process which may serve as the theoretical foundation for the de…
Dependence of O2 diffusion dynamics on pressure and temperature in silica nanoparticles
2013
An experimental study of the molecular O2 diffusion process in high purity non-porous silica nanoparticles having 50 m2/g BET specific surface and 20 nm average radius was carried out in the temperature range from 127 to 177 °C at O2 pressure in the range from 0.2 to 66 bar. The study was performed by measuring the volume average interstitial O2 concentration by a Raman and photoluminescence technique using a 1,064 nm excitation laser to detect the singlet to triplet emission at 1,272 nm of the molecular oxygen in silica. A dependence of the diffusion kinetics on the O2 absolute pressure, in addition to temperature dependence, was found. The kinetics can be fit by the solution of Fick’s dif…
O2 Diffusion in Amorphous SiO2 Nanoparticles Probed by Outgassing
2012
An experimental study of the O2 diffusion process in nanoparticles of amorphous SiO2 in the temperature range from 98 to 157 °C was carried out by Raman and photoluminescence techniques. We studied O2 diffusion in high purity silica nanoparticles with a mean diameter of 14, 20, and 40 nm detecting the outgassing of molecules trapped during the manufacturing. The kinetics of diffusion is well described for all the investigated nanoparticles by the Fick’s equation proving its applicability to nanoscale systems. The diffusion coefficient features an Arrhenius law temperature dependence in the explored temperature range, and the diffusion coefficient values are in good agreement with extrapolat…
Spatially limited diffusion coupled with ohmic potential drop and/or slow interfacial exchange: a new method to determine the diffusion time constant…
2004
Abstract We have analyzed chronoamperometric curves, I ( t ), after small-amplitude potential steps Δ E (PITT technique) for the model of linear diffusion of a species inside an electroactive film, taking into account ohmic effects in the external media (solution and electrode) as well as a finite rate of the interfacial exchange. For its short-time interval, t ≪ τ d ( τ d is the diffusion time constant, corresponding to unlimited diffusion from the interface), three approximate analytical expressions have been proposed. One of these represents an interpolation formula between the value of the current at the start of the diffusion process, I (0)=Δ E / R ext (after the end of the EDL chargin…
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…
On the property of diffusion in the spatial error model.
2005
International audience; The aim of this paper is to illustrate the property of global spillover effects in the first-order spatial autoregressive error model and the associated diffusion process of spatial shocks. An application is provided on a sample of 145 regions over 1989–1999 and highlights the most influential regions.
Approximation of Pore Space with Ellipsoids: A Comparison of a Geometrical Method with a Statistical one
2018
We work with tomographic images of pore space in soil. The images have large dimensions and so in order to speed-up biological simulations (as drainage or diffusion process in soil), we want to describe the pore space with a number of geometrical primitives significantly smaller than the number of voxels in pore space. In this paper, we use the curve skeleton of a volume to segment it into some regions. We describe the method to compute the curve skeleton and to segment it with a simple segment approximation. We approximate each obtained region with an ellipsoid. The set of final ellipsoids represents the geometry of pore space and will be used in future simulations. We compare this method …
Forward and backward diffusion approximations for haploid exchangeable population models
2001
Abstract The class of haploid population models with non-overlapping generations and fixed population size N is considered such that the family sizes ν1,…,νN within a generation are exchangeable random variables. A criterion for weak convergence in the Skorohod sense is established for a properly time- and space-scaled process counting the number of descendants forward in time. The generator A of the limit process X is constructed using the joint moments of the offspring variables ν1,…,νN. In particular, the Wright–Fisher diffusion with generator Af(x)= 1 2 x(1−x)f″(x) appears in the limit as the population size N tends to infinity if and only if the condition lim N→∞ E((ν 1 −1) 3 )/(N Var …
Logistic Growth Described by Birth-Death and Diffusion Processes
2019
We consider the logistic growth model and analyze its relevant properties, such as the limits, the monotony, the concavity, the inflection point, the maximum specific growth rate, the lag time, and the threshold crossing time problem. We also perform a comparison with other growth models, such as the Gompertz, Korf, and modified Korf models. Moreover, we focus on some stochastic counterparts of the logistic model. First, we study a time-inhomogeneous linear birth-death process whose conditional mean satisfies an equation of the same form of the logistic one. We also find a sufficient and necessary condition in order to have a logistic mean even in the presence of an absorbing endpoint. Then…