Search results for "Names"
showing 10 items of 6843 documents
Convergence of Markovian Stochastic Approximation with discontinuous dynamics
2016
This paper is devoted to the convergence analysis of stochastic approximation algorithms of the form $\theta_{n+1} = \theta_n + \gamma_{n+1} H_{\theta_n}({X_{n+1}})$, where ${\left\{ {\theta}_n, n \in {\mathbb{N}} \right\}}$ is an ${\mathbb{R}}^d$-valued sequence, ${\left\{ {\gamma}_n, n \in {\mathbb{N}} \right\}}$ is a deterministic stepsize sequence, and ${\left\{ {X}_n, n \in {\mathbb{N}} \right\}}$ is a controlled Markov chain. We study the convergence under weak assumptions on smoothness-in-$\theta$ of the function $\theta \mapsto H_{\theta}({x})$. It is usually assumed that this function is continuous for any $x$; in this work, we relax this condition. Our results are illustrated by c…
Probabilistic interpretation of the Calderón problem
2017
In this paper, we use the theory of symmetric Dirichlet forms to give a probabilistic interpretation of Calderon's inverse conductivity problem in terms of reflecting diffusion processes and their corresponding boundary trace processes. This probabilistic interpretation comes in three equivalent formulations which open up novel perspectives on the classical question of unique determinability of conductivities from boundary data. We aim to make this work accessible to both readers with a background in stochastic process theory as well as researchers working on deterministic methods in inverse problems.
In-situ monitoring by Raman spectroscopy of the thermal doping of graphene and MoS2 in O-2-controlled atmosphere
2017
The effects of temperature and atmosphere (air and O2) on the doping of monolayers of graphene (Gr) on SiO2 and Si substrates, and on the doping of MoS2 multilayer flakes transferred on the same substrates have been investigated. The investigations were carried out by in situ micro-Raman spectroscopy during thermal treatments up to 430 °C, and by atomic force microscopy (AFM). The spectral positions of the G and 2D Raman bands of Gr undergo only minor changes during treatment, while their amplitude and full width at half maximum (FWHM) vary as a function of the temperature and the used atmosphere. The thermal treatments in oxygen atmosphere show, in addition to a thermal effect, an effect a…
Analysis of thermally induced flows in the laboratory by geoelectrical 3-D tomography
2010
[1] Many natural bodies as well as materials inside industrial installations, such as the Earth's mantle and the glass inside melting furnaces, exchange matter through convection. These processes result from differences in temperature, density, and chemical concentration. In this analysis, we focus on the visualization of thermally driven flows in the laboratory. In nature and in industrial installations, it is difficult to measure the temperature inside the object of interest directly. We benchmark a new DC-geoelectrical 3-D tomography method for temperature measurements that allows obtaining temperature values without influencing the flow pattern. For verification of the method, we use di…
Charged colloidal particles in a charged wedge: do they go in or out?
2008
Using real-space microscopy experiments, theory and computer simulation, we study the behaviour of highly charged colloidal particles which are confined between two highly charged plates forming a wedge geometry. Under low salt conditions it is experimentally observed that colloidal particles accumulate in the cusp of a wedge to form dense fluid or crystalline ordered structures. This behaviour is found for various cell geometries, salt concentrations and gravitational strengths, and even stays stable when additional convection is present in the system. An effort is made to understand this effect qualitatively on the basis of linear screening theory. For a single macro-ion, linear screening…
Variable exponent p(x)-Kirchhoff type problem with convection
2022
Abstract We study a nonlinear p ( x ) -Kirchhoff type problem with Dirichlet boundary condition, in the case of a reaction term depending also on the gradient (convection). Using a topological approach based on the Galerkin method, we discuss the existence of two notions of solutions: strong generalized solution and weak solution. Strengthening the bound on the Kirchhoff type term (positivity condition), we establish existence of weak solution, this time using the theory of operators of monotone type.
Onset of convection in a vertical porous cylinder with a permeable and conducting side boundary
2015
Abstract The onset of natural convection in a vertical porous cylinder saturated by a fluid is studied. The lateral confinement of the porous cylinder is due to an external porous medium having a permeability much smaller than that of the cylinder. Thus, the vertical side boundary of the cylinder is permeable and constrained by given pressure and temperature distributions. The lower and upper plane boundaries of the cylinder are impermeable walls. The lower wall is subject to a uniform heat flux, while the upper wall has a uniform temperature. The basic motionless state displays a uniform and vertical temperature gradient oriented downward. The linear stability analysis is carried out by us…
Generalization of a finite-difference numerical method for the steady-state and transient solutions of the nernst—planck flux equations
1985
Abstract A generalization of the numerical method of Brumleve and Buck for the solution of Nernst—Planck equations when convective flux and electric current are involved has been developed. The simulation procedure was applied to a specific case: transport of strong electrolytes in a wide-pore membrane with simultaneous diffusion, convection and electric current. Good agreement was found between experimental data and computed results.
A study of hydrothermal convection in saturated porous media
1993
Abstract Because of its relevance to many geological and technical problems, hydrothermal convection is investigated here mainly with the aid of numerical models by a systematic analysis of the properties of this type of convection for a range of super-critical Rayleigh numbers. Calculations were performed for two-dimensional models with constant properties in a region of aspect ratio 2. The principal results in the case of temperature fixed at the impermeable top and bottom are the following for the Nusselt number Nu, the cell aspect ratio a, and the boundary layer thickness δ: Nu ≈ 1.7 R0.5, a ≈ 1.3 R−0.4, δc ≈ 0.4 R−0.4 for 2.5 R = R f /R f ∗ and Rf and R f ∗ are the ambient and critical…
Quasilinear Dirichlet Problems with Degenerated p-Laplacian and Convection Term
2021
The paper develops a sub-supersolution approach for quasilinear elliptic equations driven by degenerated p-Laplacian and containing a convection term. The presence of the degenerated operator forces a substantial change to the functional setting of previous works. The existence and location of solutions through a sub-supersolution is established. The abstract result is applied to find nontrivial, nonnegative and bounded solutions.