Improved error estimates for mixed finite-element approximations for nonlinear parabolic equations: The discrete-time case

This article treats mixed finite-element methods for second-order quasilinear parabolic equations. A fully discrete scheme is presented and L₂-error estimates are established. The convergence of both the function value and the flux is demonstrated. In a previous paper, Part I the author introduced powerful numerical methods for dealing with parabolic problems. The technique used here is an extension of the continuous-time results for the discrete-time case. © 1994 John Wiley & Sons, Inc.     

Some existence results for quasilinear elliptic equations in a finite cylinder

We study the existence of solutionsu in the finite cylinderS _a=(?a, a)×ω of the quasilinear elliptic equation $$\sum\limits_{i,j = 1}^n {a_{i,j} (x)\partial _{i,j} u + f(x,u,\nabla u) = 0} $$ with Dirichlet boundary condition on flat parts of σS _a and Neumann condition on the curved parts. In this paper, we focus on the technicality caused by the “corners” ofS _a. We prove the existence of such solutions provided that suitable sub and super solutions are known and under the condition that the coefficientsa _1,i,i#1 vanish on the corners. We also prove a more general result in ?².     

First application of the real space linear muffin-tin orbital atomic sphere approximation method for calculating Fermi contact hyperfine fields

In this work we apply the recently developed first-principles real space linear muffin-tin orbital atomic sphere approximation (RS-LMTO-ASA) scheme to calculate the hyperfine field for 3d impurities (V, Cr, Mn andFe) in Cu. We obtain the Fermi contact term at the impurities andat four shells of host atoms around the impurities. We compare our results with theoretical values obtained using the KKR-Green-function method andwith NMR measurements. The overall agreement is excellent, confirming the reliability of the RS-LMTO-ASA approach as means of obtaining information on hyperfine fields.     

Evolution of the correlation between orthogonal polarization patterns in broad-area lasers

We measure polarization-resolved instantaneous patterns in a large-aspect ratio quasi-isotropic Nd:YAG laser. High correlation between the instantaneous orthogonal polarization patterns recorded at the earlier stages of the laser pulse has been found due to the strong cross saturation between both polarization modes.     

In vitro evaluation of cytotoxic and inflammatory properties of silica nanoparticles of different sizes in murine RAW 264.7 macrophages

The biological response to four well-characterized amorphous silica nanoparticles was investigated in RAW 264.7 macrophages in view of their potential application as drug carriers to sites of inflammation. All silica nanoparticles-induced cell membrane damage, reduced metabolic activity, generated ROS and released various cytokines, but to different extents. Two silica nanoparticles of 34 nm (A and B) with different zetapotentials were more cytotoxic than (aggregated) 11 and 248 nm nanoparticles, while cytokines were mostly induced by the (aggregated) 11 nm and only one of the 34 nm nanoparticles (34A). The results indicate that specific silica nanoparticles may have counterproductive effects, for example when used as carriers of anti-inflammatory drugs. The physicochemical properties determining the response of nanoparticles vary for different responses, implying that a screening approach for the safe development of nanoparticles needs to consider the role of combinations of (dynamic) physicochemical properties and needs to include multiple toxicity endpoints.     

Wave propagation in locally perturbed periodic media (case with absorption): Numerical aspects

We are interested in the numerical simulation of wave propagation in media which are a local perturbation of an infinite periodic one. The question of finding artificial boundary conditions to reduce the actual numerical computations to a neighborhood of the perturbation via a DtN operator was already developed in [1] at the continuous level. We deal in this article with the numerical aspects associated to the discretization of the problem. In particular, we describe the construction of discrete DtN operators that relies on the numerical solution of local cell problems, non stationary Ricatti equations and the discretization of non standard integral equations in Floquet variables.     

Chernoff approximations of Feller semigroups in Riemannian manifolds

Chernoff approximations of Feller semigroups and the associated diffusion processes in Riemannian manifolds are studied. The manifolds are assumed to be of bounded geometry, thus including all compact manifolds and also a wide range of non-compact manifolds. Sufficient conditions are established for a class of second order elliptic operators to generate a Feller semigroup on a (generally non-compact) manifold of bounded geometry. A construction of Chernoff approximations is presented for these Feller semigroups in terms of shift operators. This provides approximations of solutions to initial value problems for parabolic equations with variable coefficients on the manifold. It also yields weak convergence of a sequence of random walks on the manifolds to the diffusion processes associated with the elliptic generator. For parallelizable manifolds this result is applied in particular to the representation of Brownian motion on the manifolds as limits of the corresponding random walks.     

Preparation of cholesterol oxidase nanoparticles and their application in amperometric determination of cholesterol

Highly dispersed platinum nanoparticles were deposited on gram quantities of non-functionalized multiwalled carbon nanotubes (MWCNTs) by atomic layer deposition (ALD) in a fluidized bed reactor at 300 °C. (Methylcyclopentadienyl) trimethylplatinum and oxygen were used as precursors. The results of TEM analysis showed that ~1.3 nm Pt nanoparticles were highly dispersed on non-functionalized MWCNTs. The porous structures of MWCNTs did not change with the deposition of Pt nanoparticles. For comparison, the commercial 3 wt% Pt/C catalyst was also characterized. The ALD-prepared Pt/MWCNT was used for the hydrogenation of xylose to xylitol. The ALD-prepared Pt/MWCNT showed the best catalytic performance with 100 % conversion of xylose and 99.3 % selectivity to xylitol, compared to commercially available Pt/C, Ru/C, and Raney Ni catalysts. The stability of ALD produced Pt/MWCNT catalyst was higher than that of the commercial Pt/C, due to the presence of surface defects on the MWCNTs and the strong metal–support interaction for the ALD-prepared Pt/MWCNT catalyst.