A posteriori error estimation with finite element methods of lines for one-dimensional parabolic systems

Summary Consider the solution of one-dimensional linear initial-boundary value problems by a finite element method of lines using a piecewiseP ^th -degree polynomial basis. A posteriori estimates of the discretization error are obtained as the solutions of either local parabolic or local elliptic finite element problems using piecewise polynomial corrections of degreep+1 that vanish at element ends. Error estimates computed in this manner are shown to converge in energy under mesh refinement to the exact finite element discretization error. Computational results indicate that the error estimates are robust over a wide range of mesh spacings and polynomial degrees and are, furthermore, applicable in situations that are not supported by the analysis.This research was partially supported by the U.S. Air Force Office of Scientific Research, Air Force Systems Command, USAF, under Grant Number AFOSR 90-0194; by the U.S. Army Research Office under Contract Number DAAL03-91-G-0215; and by the National Science Foundation under Institutional Infrastructure Grant Number CDA-8805910     

Mixed formulations for a class of variational inequalitiesFormulations mixtes pour une classe d'inéquations variationnelles

This Note is an attempt to extend the mixed finite element method to a class of variational inequalities including the problems of Signorini and of unilateral contact in elasticity with or without friction. Existence and uniqueness for the continuous and the discrete problems as well as error estimates are established in a general abstract framework. As a result, the mixed approximation of the Signorini problem is proved to converge with an error bound in h^3/4. To cite this article: L. Slimane et al., C. R. Acad. Sci. Paris, Ser. I 334 (2002) 87–92     

Synthesis and characterization of active ester-functionalized polypyrrole-silica nanoparticles: application to the covalent attachment of proteins

Novel ester-functionalized polypyrrole-silica nanocomposite particles were prepared by oxidative copolymerization of pyrrole and N-succinimidyl ester pyrrole (50/50% initial concentrations), using FeCl3 in the presence of ultrafine silica nanoparticles (20 nm diameter). The N-succinimidyl ester pyrrole monomer was prepared in aqueous solution using 1-(2-carboxyethylpyrrole) and N-hydroxysuccinimide in the presence of 1-ethyl-3-(3-dimethylaminopropyl) carbodiimide. The resulting nanocomposites (N-succinimidyl ester polypyrrole-silica) are raspberry-shaped agglomerates of silica sol particles "glued" together by the insoluble poly(pyrrole-co-N-succinimidyl pyrrole). The N-succinimidyl ester polypyrrole-silica particles were characterized in terms of their size, density, copolymer content, and polydispersity. Scanning electron microscopy and disk centrifuge sedimentometry confirmed that the nanocomposite particles had narrow size distributions. X-ray photoelectron spectroscopy analysis indicated a silica-rich surface and a high surface concentration of N-succinimidyl ester groups. These nanoparticles exhibited good long-term dispersion stability. The chemical stability of the ester functions in aqueous media after several weeks of storage was monitored by FTIR spectroscopy. The functionalized nanocomposites were tested as bioadsorbents of human serum albumin (HSA). The very high amount of immobilized HSA determined by UV-visible spectroscopy is believed to be due to covalent binding. Incubation of the HSA-grafted nanocomposite with anti-HSA resulted in immediate flocculation, an indication that they are alternative candidates for visual diagnostic assays.     

Low-temperature formation and characterization of Cu2O nanoparticles in the binary gold alloys

Thermal analyses, using differential scanning calorimetry (DSC) and dilatometry, reveal an important anomaly at low temperature for Au-25 wt.% Cu composition after homogenization at 700°C during 2 hours under vacuum followed by heating up to 160°C before water quenching. This anomaly has been already observed and not explained. Surface characterization, using scanning electron microscopy (SEM), atomic force microscopy (AFM), and scanning tunneling microscopy (STM), exhibits a specific topography, consisting of a nanostructured surface. The precipitates of nanostructured particles are homogeneously scattered all over the surface for this 18-carat gold alloy. Moreover, X-ray photoelectron spectroscopy (XPS) shows that the composition of the observed particles corresponds to cuprous oxide phase (Cu₂O). The formation of such material can be explained by the diffusion of copper atoms from the lattice to the surface at 160°C. Pulsed radio-frequency glow discharge optical emission spectroscopy (RF GD-OES) further proves the proposed Cu₂O formation through a diffusion process. The appearance of such cuprous oxide nanoparticles on the Au-Cu alloy surface explains the low-temperature DSC and dilatometry anomaly and affects directly the surface electrical resistance at low temperature. These results might open a large gate for new ideas to investigate in catalytic, electronic, and antimicrobial activities.     

Complex Surface Chemistry of an Otherwise Inert Solvent Molecule: Tetrahydrofuran on Si(001)

The reaction of tetrahydrofuran (THF), an otherwise inert solvent molecule, on Si(001) was experimentally studied in ultra‐high vacuum. Using scanning tunneling microscopy (STM) and photoelectron spectroscopy at variable temperature, we could both isolate a datively bound intermediate state of THF on Si(001), as well as the final configuration that bridges two dimer rows of the Si(001) surface after ether cleavage. The latter configuration implies splitting of the O?C bond, which is typically kinetically suppressed. THF thus exhibits a hitherto unknown reactivity on Si(001).     

Multi-Fractal Formalism for Quasi-Self-Similar Functions

The study of multi-fractal functions has proved important in several domains of physics. Some physical phenomena such as fully developed turbulence or diffusion limited aggregates seem to exhibit some sort of self-similarity. The validity of the multi-fractal formalism has been proved to be valid for self-similar functions. But, multi-fractals encountered in physics or image processing are not exactly self-similar. For this reason, we extend the validity of the multi-fractal formalism for a class of some non-self-similar functions. Our functions are written as the superposition of similar structures at different scales, reminiscent of some possible modelization of turbulence or cascade models. Their expressions look also like wavelet decompositions. For the computation of their spectrum of singularities, it is unknown how to construct Gibbs measures. However, it suffices to use measures constructed according the Frostman's method. Besides, we compute the box dimension of the graphs.     

catena‐Poly[[aqua­barium(II)]‐μ‐aqua‐bis­(μ‐2′‐carboxy­biphenyl‐2‐carboxyl­ato)]

In the title compound, [Ba{HOOC(C₆H₄)₂CO₂}₂(H₂O)₂] or [Ba(C₁₄H₉O₄)₂(H₂O)₂], the Ba atoms are coordinated by nine O atoms, six from two 2′‐carboxy­biphenyl‐2‐carboxyl­ate (Hbpdc⁻) ligands and three from three coordinated water mol­ecules, resulting in the formation of face‐sharing distorted monocapped square anti­prisms. The Hbpdc⁻ ligands bridge the Ba atoms to form a one‐dimensional helical polymer, with a Ba⋯Ba distance across the chain of 4.1386 (17) Å. Adjacent chains are parallel to each other. The two independent ligands are tetra­dentate and have the same coordination mode, exhibiting μ‐oxo bridges and η⁸‐chelation. The crystal structure is further stabilized by hydrogen bonds within each chain.     

Angular Multiplexing Gratings Characterization in Dichromated Gelatin and Thoughts on Diffractive Optical Memory

We were mainly concerned here with multiple exposure gratings that allow interactions and coupling between gratings. We started the study of interactions and coupling with five gratings recorded in dichromated gelatin (DCG). Having determined experimentally the characteristic parameters of these five gratings, we used a method developed by Oxford University to synthesize the modulation profile. Entering these parameters of each grating into our computing programs (based on the alternative theory of diffraction in modulated media) and by varying the amplitude modulation, the latter was deduced by adjusting the numerical curve to the experimental one. We then extended the study to nine multiplexed gratings. This study allowed us to know the range of the amplitude modulation such that a certain number of angular multiplexing can be done in DCG. Several undesirable effects which we had experimentally observed appeared then during the reconstruction of any one of the multiplexed images, such as cross-talk effect. We noted the good concordance between experimental and theoretical results. We finally illustrated cross-talk effect in a diffractive memory where, if the amplitude modulation was first calculated, the number of multiplexing for an angular range could then be determined and the angular separation achieved to avoid cross-talk.     

Phase transition in ammonium hexafluorovanadate (III)

Heat capacity of ammonium hexafluorovanadate (NH₄)₃ [VF₆] has been measured with a miniaturized adiabatic calorimeter from 20 to 300 K. A phase transition was found at 280.44 ± 0.05 K with the associated entropy change Δ_trs S = 24.9 ± 0.5 JK^?1 mol^?1. The entropy transition is accounted for by the orientational order-disorder changes of hexafluorovanadate ion and ammonium ion occupying respective octahedral sites, as in the cases of (NH₄)₃AlF₆ and (NH₄)₃FeF₆ crystals. Changes in infrared spectra relative to v₃ vibrational mode of [VF₆]^3? ion can be explained by an orientational disorder of the anions in the high-temperature phase (HTP). The dependence of cubic root of the unit-cell volume of a family of ammonium cryolites on their transition temperatures is discussed in relation to the nature of interactions which induce the phase transition.     

Multi-layer model of correlated energy prices

In this article we develop an extension of the affine jump-diffusion modeling framework and use it to build an intuitive and tractable model of an energy price complex. The development is motivated by the need to model prices of electricity while capturing their dependence on the price of other energy commodities. Such a model is essential for valuing a range of typical derivatives traded in the electricity markets: cross-commodity spread options, cross-location spread options, fuel-switching powerplants, etc. We give an approximate pricing method for these derivatives together with precise error bound estimates.