Search results for "Diffusion process"
showing 10 items of 44 documents
Approximation of exit times for one-dimensional linear diffusion processes
2020
International audience; In order to approximate the exit time of a one-dimensional diffusion process, we propose an algorithm based on a random walk. Such an algorithm was already introduced in both the Brownian context and the Ornstein-Uhlenbeck context, that is for particular time-homogeneous diffusion processes. Here the aim is therefore to generalize this efficient numerical approach in order to obtain an approximation of both the exit time and position for a general linear diffusion. The main challenge of such a generalization is to handle with time-inhomogeneous diffusions. The efficiency of the method is described with particular care through theoretical results and numerical example…
Solving stochastic differential equations on Homeo(S1)
2004
Abstract The Brownian motion with respect to the metric H 3/2 on Diff( S 1 ) has been constructed. It is realized on the group of homeomorphisms Homeo( S 1 ). In this work, we shall resolve the stochastic differential equations on Homeo( S 1 ) for a given drift Z .
Exact simulation of first exit times for one-dimensional diffusion processes
2019
International audience; The simulation of exit times for diffusion processes is a challenging task since it concerns many applications in different fields like mathematical finance, neuroscience, reliability horizontal ellipsis The usual procedure is to use discretization schemes which unfortunately introduce some error in the target distribution. Our aim is to present a new algorithm which simulates exactly the exit time for one-dimensional diffusions. This acceptance-rejection algorithm requires to simulate exactly the exit time of the Brownian motion on one side and the Brownian position at a given time, constrained not to have exit before, on the other side. Crucial tools in this study …
Effects of Pressure, Temperature, and Particles Size on O2 Diffusion Dynamics in Silica Nanoparticles
2013
The O2 diffusion process in silica nanoparticles is experimentally studied in samples of average radius of primary particles ranging from 3.5 to 20 nm and specific surface ranging from 50 to 380 (m2/g). The investigation is done in the temperature range from 98 to 177 °C at O2 pressure ranging from 0.2 to 66 bar by measuring the interstitial O2 concentration by Raman and photoluminescence techniques. The kinetics of diffusion can be described by the Fick’s equation with an effective diffusion coefficient depending on the temperature, O2 pressure, and particles size. In particular, the dependence of the diffusion coefficient on the pressure and nanoparticles size is more pronounced at lower …
Grain-boundary modelling of hydrogen assisted intergranular stress corrosion cracking
2018
Abstract A novel hybrid strategy for modelling intergranular hydrogen embrittlement in polycrystalline microstructures is proposed. The technique is based on a grain-boundary integral representation of the polycrystalline micro-mechanics, numerically solved by the boundary element method, coupled with an explicit finite element model of the intergranular hydrogen diffusion. The intergranular interaction between contiguous grains in the aggregate is modelled through extrinsic cohesive-frictional traction-separation laws, whose parameters depend on the concentration of intergranular hydrogen, which diffuses over the interface according to the Fick’s second law, inducing the weakening of the i…
A thermodynamic approach to nonlocal plasticity and related variational principles
1999
Elastic-plastic rate-independent materials with isotropic hardening/softening of nonlocal nature are considered in the context of small displacements and strains. A suitable thermodynamic framework is envisaged as a basis of a nonlocal associative plasticity theory in which the plastic yielding laws comply with a (nonlocal) maximum intrinsic dissipation theorem. Additionally, the rate response problem for a (continuous) set of (macroscopic) material particles, subjected to a given total strain rate field, is discussed and shown to be characterized by a minimum principle in terms of plastic coefficient. This coefficient and the relevant continuum tangent stiffness matrix are shown to admit, …
Information Exchange in Mobile Encounter Network
2007
In this paper we analyze an information exchange method based on information diffusion in mobile encounter networks, a form of mobile peer-to-peer networks. We utilize dual mobility model which provides support for more realistic simulations compared to mobility models based only one method of movement. The distribution of the mobile device encounter intervals are discussed and analyzed via simulation runs. The logistic model is suggested to provide reasonably accurate estimates of the information diffusion process.
Reversibility and Diffusion in Mandelythiamin Decarboxylation. Searching Dynamical Effects in Decarboxylation Reactions
2012
Decarboxylation of mandelylthiamin in aqueous solution is analyzed by means of quantum mechanics/molecular mechanics simulations including solvent effects. The free energy profile for the decarboxylation reaction was traced, assuming equilibrium solvation, while reaction trajectories allowed us to incorporate nonequilibrium effects due to the solvent degrees of freedom as well as to evaluate the rate of the diffusion process in competition with the backward reaction. Our calculations that reproduce the experimental rate constant show that decarboxylation takes place with a non-negligible free energy barrier for the backward reaction and that diffusion of carbon dioxide is very fast compared…
Understanding Acid Reaction and Diffusion in Chemically Amplified Photoresists: An Approach at the Molecular Level
2011
Acid diffusion in chemically amplified resist might limit the ultimate minimum half-pitch that can be achieved with high sensitivity resists unless diffusion length is reduced until new methods of sensitizing resists are found. Precise knowledge of molecular dynamics of resist materials and advanced techniques need to be developed actively for this issue. In this sense, computer simulations have become a valuable tool in terms of reducing time and costs. However, simulations are generally based on continuum or mesoscale models, which are unable to accurately predict variations at the molecular level. Deeper understanding and investigation of the coupled reaction-diffusion kinetics at the mo…
Experimental Investigations on Hair Fibers as Diffusion Bridges and Opiates as Solutes in Solution
1996
Diffusion experiments were performed using clipped hair fibers as diffusion bridges and aqueous solutions of morphine, codeine and dihydrocodeine. Natural as well as predamaged hair fibers were investigated. The test series were conducted at ambient temperature and at high humidity. After 312 or 372 hours the middle segments of the strands were clipped, washed and analyzed by GC/MS. Only when virgin hair samples were used the solutes passed along the fiber at full length resulting in a positive immunological finding at the end of the diffusion bridge. Most of the washing fluids were positive for opiates. All centerpieces had a high opiate content. The opiate concentration in damaged hair wa…