Search results for "Diffusion"
showing 10 items of 1615 documents
Préparation et spéciation d’oxo-clusters de métaux du bloc p
2022
The main subject of this thesis is the use of Pair Distribution Function (PDF) analysis for solution phase speciation during metal-cluster growth. The PDF method allows the extraction of structural information from a sample in the form of an atom-atom distance distribution via Fourier transform of synchrotron X-ray scattering data. The growth mechanisms of two solution-based systems are analysed in this thesis. Precursor materials are synthesized through a mechanochemical method that was developed and shown to be able to access a wide range of related systems.Mechanochemical routes of synthesizing bismuth Active Pharmaceutical Ingredients (APIs) were investigated and optimised. Samples were…
Parallel Schwarz methods for convection-dominated semilinear diffusion problems
2002
AbstractParallel two-level Schwarz methods are proposed for the numerical solution of convection-diffusion problems, with the emphasis on convection-dominated problems. Two variants of the methodology are investigated. They differ from each other by the type of boundary conditions (Dirichlet- or Neumann-type) posed on a part of the second-level subdomain interfaces. Convergence properties of the two-level Schwarz methods are experimentally compared with those of a variant of the standard multi-domain Schwarz alternating method. Numerical experiments performed on a distributed memory multiprocessor computer illustrate parallel efficiency of the methods.
Imaging of Substantia Nigra in Parkinson's Disease: A Narrative Review.
2021
Parkinson’s disease (PD) is a progressive neurodegenerative disorder, characterized by motor and non-motor symptoms due to the degeneration of the pars compacta of the substantia nigra (SNc) with dopaminergic denervation of the striatum. Although the diagnosis of PD is principally based on a clinical assessment, great efforts have been expended over the past two decades to evaluate reliable biomarkers for PD. Among these biomarkers, magnetic resonance imaging (MRI)-based biomarkers may play a key role. Conventional MRI sequences are considered by many in the field to have low sensitivity, while advanced pulse sequences and ultra-high-field MRI techniques have brought many advantages, partic…
Existence and uniqueness for the Prandtl equations
2001
International audience; Under the hypothesis of analyticity of the data with respect to the tangential variable we prove the existence and uniqueness of the mild solution of Prandtl boundary layer equation. This can be considered an improvement of the results of [8] as we do not require analyticity with respect to the normal variable. (C) 2001 Academie des sciences/Editions scientifiques et medicales Elsevier SAS.
Quasi-linear diffusion equations with gradient terms and L1 data
2004
Abstract In this article we study the following quasi-linear parabolic problem: u t − Δ u+|u| β−2 u| ∇ u| q =|u| α−2 u| ∇ u| p in Ω×]0,T[, u(x,t)=0 on ∂Ω×]0,T[, u(x,0)=u 0 (x) in Ω, where Ω is a bounded open set of R N and T>0. We prove that if α,β>1, 0⩽p u 0 ∈L 1 (Ω) .
An algorithmic construction of entropies in higher-order nonlinear PDEs
2006
A new approach to the construction of entropies and entropy productions for a large class of nonlinear evolutionary PDEs of even order in one space dimension is presented. The task of proving entropy dissipation is reformulated as a decision problem for polynomial systems. The method is successfully applied to the porous medium equation, the thin film equation and the quantum drift–diffusion model. In all cases, an infinite number of entropy functionals together with the associated entropy productions is derived. Our technique can be extended to higher-order entropies, containing derivatives of the solution, and to several space dimensions. Furthermore, logarithmic Sobolev inequalities can …
Calculation of heat and moisture distribution in the porous media layer
2007
In this paper we study the problem of the diffusion of one substance through the pores of a porous material which may absorb and immobilize some of the diffusing substances with the evolution or absorption of heat. The transfer of moisture and the heat are described by the model. The system of two partial differential equations (PDEs) is derived, one equation expresses the rate of change of concentration of water vapour in the air spaces and the other the rate of change of temperature. The obtained initial‐boundary value problem is approximated by using the finite volume method. This procedure allows us to reduce the 2D transfer problem described by a system of PDEs to initial value problem…
M/M/1 queue in two alternating environments and its heavy traffic approximation
2018
We investigate an M/M/1 queue operating in two switching environments, where the switch is governed by a two-state time-homogeneous Markov chain. This model allows to describe a system that is subject to regular operating phases alternating with anomalous working phases or random repairing periods. We first obtain the steady-state distribution of the process in terms of a generalized mixture of two geometric distributions. In the special case when only one kind of switch is allowed, we analyze the transient distribution, and investigate the busy period problem. The analysis is also performed by means of a suitable heavy-traffic approximation which leads to a continuous random process. Its d…
A mathematical approach to predict the solids concentration in anaerobic membrane bioreactos (AnMBR): Evaluation of the volatile solids solubilization
2020
[EN] Anaerobic Membrane Bioreactors (AnMBR) are gaining attention as a suitable approach for sustainable low-strength wastewater treatment, as they bring together the advantages of both anaerobic treatments and membrane bioreactors. However, increasing the sludge retention time (SRT) necessary to favor hydrolysis increases the suspended solids concentration potentially leading to decreased permeate flux. Therefore, the availability of a mathematical approach to predict the solids concentration within an AnMBR can be very useful. In this work, a mathematical model describing the volatile solids concentration within the reactor as a function of the operating parameters and the influent charac…
Determination of Diffusion Parameters by a Computer Code (FDP) Based on Mathematica 6.0
2010
A computer code named Fitting for Diffusion Parameters (FDP) based on Mathematica 6.0 has been developed for modeling through- and out-diffusion experiments. FDP was used to determine the diffusion coefficients (De ) and the rock capacity factors (α) for tritiated water (HTO) and 22 Na+ and the distribution coefficient (Kd ) of 22 Na+ in Opalinus Clay (OPA). The values for De and α were obtained by fitting the results of experimental data of both transient and steady-state phases to the analytical solution of accumulated activity. The quality of the parameters De and α was tested by using them as input parameters in the equation of flux. Moreover, the diffusion parameters of HTO and 22 Na+ …