Surface modification of gadolinium oxide thin films and nanoparticles using poly(ethylene glycol)-phosphate

The performance of nanomaterials for biomedical applications is highly dependent on the nature and the quality of surface coatings. In particular, the development of functionalized nanoparticles for magnetic resonance imaging (MRI) requires the grafting of hydrophilic, nonimmunogenic, and biocompatible polymers such as poly(ethylene glycol) (PEG). Attached at the surface of nanoparticles, this polymer enhances the steric repulsion and therefore the stability of the colloids. In this study, phosphate molecules were used as an alternative to silanes or carboxylic acids, to graft PEG at the surface of ultrasmall gadolinium oxide nanoparticles (US-Gd(2)O(3), 2-3 nm diameter). This emerging, high-sensitivity "positive" contrast agent is used for signal enhancement in T(1)-weighted molecular and cellular MRI. Comparative grafting assays were performed on Gd(2)O(3) thin films, which demonstrated the strong reaction of phosphate with Gd(2)O(3) compared to silane and carboxyl groups. Therefore, PEG-phosphate was preferentially used to coat US-Gd(2)O(3) nanoparticles. The grafting of this polymer on the particles was confirmed by XPS and FTIR. These analyses also demonstrated the strong attachment of PEG-phosphate at the surface of Gd(2)O(3), forming a protective layer on the nanoparticles. The stability in aqueous solution, the relaxometric properties, and the MRI signal of PEG-phosphate-covered Gd(2)O(3) particles were also better than those from non-PEGylated nanoparticles. As a result, reacting PEG-phosphate with Gd(2)O(3) particles is a promising, rapid, one-step procedure to PEGylate US-Gd(2)O(3) nanoparticles, an emerging "positive" contrast agent for preclinical molecular and cellular applications.     

Photovoltaic effect and optical absorption in MoS2

An investigation of the Schottky barriers of a number of metals on natural P-type MoS₂ was undertaken. The spectral dependence of the photovoltaic effect of all the metal barriers show two distinct features at 1.38 and 1.68 eV below the direct bandgap at 1.8 eV. A low energy edge at 1.2 eV is invariably observed for metal barriers on MoS₂. Absorption measurements performed over the same energy range indicate that the features observed in the photoresponse spectra are related to indirect transitions in MoS₂, in agreement with recent band calculations. Preliminary data indicate that MoS₂ based Schottky barrier solar cells may be of interest.     

Picosecond nonlinearity of GeO2–Bi2O3–PbO–TiO2 glasses at 532 and 1,064 nm

The third-order optical properties of GeO₂–Bi₂O₃–PbO–TiO₂ glasses at 532 nm and 1,064 nm were studied to evaluate their potential for optical limiting and all-optical switching. The Z-scan technique was used to determine the nonlinear (NL) refractive index, n ₂, and the NL absorption coefficient, α ₂, of samples with different amounts of the constituent oxides. Values of n ₂ ≈ + 0.7 × 10^?14 cm²/W at 1,064 nm and ≈+1.5 × 10^?14 cm²/W at 532 nm were measured. The NL absorption coefficient, α ₂, was smaller than the minimum that our apparatus can measure (α ₂ < 0.01 cm/GW) in the near-infrared (1,064 nm); in the visible region (532 nm), we obtained α ₂ ≈ 4.4 cm/GW. The set of NL parameters measured indicates the potential usefulness of the GeO₂–Bi₂O₃–PbO–TiO₂ glasses for all-optical switching at 1,064 nm and for optical limiting at 532 nm.     

Large-scale computational fluid dynamics by the finite element method

Solution methods are presented for the large systems of linear equations resulting from the implicit, coupled solution of the Navier-Stokes equations in three dimensions. Two classes of methods for such solution have been studied: direct and iterative methods. For direct methods, sparse matrix algorithms have been investigated and a Gauss elimination, optimized for vector-parallel processing, has been developed. Sparse matrix results indicate that reordering algorithms deteriorate for rectangular, i.e. M × M × N, grids in three dimensions as N gets larger than M. A new local nested dissection reordering scheme that does not suffer from these difficulties, at least in two dimensions, is presented. The vector-parallel Gauss elimination is very efficient for processing on today's supercomputers, achieving execution rates exceeding 2.3 Gflops the Cray YMP-8 and 9.2 Gflops on the NEC on SX3. For iterative methods, two approaches are developed. First, conjugate-gradient-like methods are studied and good results are achieved with a preconditioned conjugate gradient squared algorithm. Convergence of such a method being sensitive to the preconditioning, a hybrid viscosity method is adopted whereby the preconditioner has an artificial viscosity that is gradually lowered, but frozen at a level higher than the dissipation introduced in the physical equations. The second approach is a domain decomposition one in which overlapping domain and side-by-side methods are tested. For the latter, a Lagrange multiplier technique achieves reasonable rates of convergence.     

A finite element procedure for viscoelastic flows

A finite element method for the simulation of viscoelastic flows has been developed. It uses a weak formulation of the method of characteristics to treat the viscoelastic constitutive law. Numerical results in a 4:1 contraction are presented and are discussed with respect to previous computations. New phenomena are put in evidence and new questions are opened in this already controversial problem.     

Stability analysis of discrete generalized Stokes problems

In the mixed finite element approximation of Stokes-like problems, stability considerations normally restrict the choice of the finite element subspaces to families satisfying the so-called inf-sup condition. However, in the case of the generalized Stokes problems that one encounters when solving either the nonstationary compressible or incompressible Navier–Stokes equations by means of some operator splitting, the contribution of the time derivative is adding a term in the continuity equations which, at least theoretically, leads to a problem that is always stable. On the other hand, the numerical solution of the discrete problems built with approximations not satisfying the inf-sup condition are generally plagued with oscillations that look pretty much like the checkerboard phenomenon occurring in the classical context. To clarify this apparent contradiction, we undertook a theoretical study of the condition number of the linear problem involving the sensitive variable, which for such a saddle point problem is the dual problem. In the course of this study, we have exhibited the relationship between that condition number and the inf-sup constant, thus providing a different point of view on the results of Brezzi and Babuska. Finally, we conducted a parametric study of the behavior of that condition number with respect to the mesh size, the viscosity, and the time step. That study showed that, even in this context, the use of “stable element” was adding to the quality of the approximation by reducing the condition number to an acceptable level.     

Dual hybrid methods for the elasticity and the Stokes problems: a unified approach

Summary. A unified approach to construct finite elements based on a dual-hybrid formulation of the linear elasticity problem is given. In this formulation the stress tensor is considered but its symmetry is relaxed by a Lagrange multiplier which is nothing else than the rotation. This construction is linked to the approximations of the Stokes problem in the primitive variables and it leads to a new interpretation of known elements and to new finite elements. Moreover all estimates are valid uniformly with respect to compressibility and apply in the incompressible case which is close to the Stokes problem. Received June 20, 1994 / Revised version received February 16, 1996