Compression différentielle de transitoires bruités

The analysis and compression of noisy transient signals are handled via methods stemming from elementary differential algebra, noncommutative algebra and operational calculus. The efficiency of our approach is illustrated by an academic example and a more concrete case-study which is a musical signal. To cite this article: M. Fliess et al., C. R. Acad. Sci. Paris, Ser. I 339 (2004).     

Generalized Besicovitch spaces and applications to deterministic homogenization

The purpose of the present work is to introduce a framework which enables us to study nonlinear homogenization problems. The starting point is the theory of algebras with mean value. Very often in physics, from very simple experimental data, one gets complicated structure phenomena. These phenomena are represented by functions which are permanent in mean, but complicated in detail. In addition the functions are subject to the verification of a functional equation which in general is nonlinear. The problem is therefore to give an interpretation of these phenomena using functions having the following qualitative properties: they are functions that represent a phenomenon on a large scale, and which vary irregularly, undergoing nonperiodic oscillations on a fine scale. In this work we study the qualitative properties of spaces of such functions, which we call generalized Besicovitch spaces, and we prove general compactness results related to these spaces. We then apply these results in order to study some new homogenization problems. One important achievement of this work is the resolution of the generalized weakly almost periodic homogenization problem for a nonlinear pseudo-monotone parabolic-type operator. We also give the answer to the question raised by Frid and Silva in their paper [35] [H. Frid, J. Silva, Homogenization of nonlinear pde’s in the Fourier-Stieltjes algebras, SIAM J. Math. Anal, 41 (4) (2009) 1589-1620] as regards whether there exist or do not exist ergodic algebras that are not subalgebras of the Fourier-Stieltjes algebra.     

Strain-induced reversal of charge transfer in contact electrification

We have contact! Material strain can have a dominating effect on contact electrification. When a deflated (relaxed) balloon is rubbed against teflon, the teflon surface charges positively, but when the same balloon is inflated (strained), the teflon surface charges negatively. This result illustrates that material strain can control contact electrification and alter the driving force of some (yet unknown) charge-transfer species.     

Numerical differentiation with annihilators in noisy environment

Numerical differentiation in noisy environment is revised through an algebraic approach. For each given order, an explicit formula yielding a pointwise derivative estimation is derived, using elementary differential algebraic operations. These expressions are composed of iterated integrals of the noisy observation signal. We show in particular that the introduction of delayed estimates affords significant improvement. An implementation in terms of a classical finite impulse response (FIR) digital filter is given. Several simulation results are presented.      

Hydration of copper(II): new insights from density functional theory and the COSMO solvation model

The hydrated structure of the Cu(II) ion has been a subject of ongoing debate in the literature. In this article, we use density functional theory (B3LYP) and the COSMO continuum solvent model to characterize the structure and stability of [Cu(H2O)n](2+) clusters as a function of coordination number (4, 5, and 6) and cluster size (n = 4-18). We find that the most thermodynamically favored Cu(II) complexes in the gas phase have a very open four-coordinate structure. They are formed from a stable square-planar [Cu(H2O)8](2+) core stabilized by an unpaired electron in the Cu(II) ion d(x(2)-y(2)) orbital. This is consistent with cluster geometries suggested by recent mass-spectrometric experiments. In the aqueous phase, we find that the more compact five-coordinate square-pyramidal geometry is more stable than either the four-coordinate or six-coordinate clusters in agreement with recent combined EXAFS and XANES studies of aqueous solutions of Cu(II). However, a small energetic difference (approximately 1.4 kcal/mol) between the five- and six-coordinate models with two full hydration shells around the metal ion suggests that both forms may coexist in solution.     

Two-electron three-centered bond in side-on (eta2) uranyl(V) superoxo complexes

Theoretical calculations suggest a novel two-electron three-atom bonding scheme for complexation of O 2 with U(V) compounds, leading to the stabilization of superoxo complexes in the side-on (eta (2)) configuration. This binding motif is likely to play an important role in the oxidative processes involving trans-uranium compounds having valence 5f phi electrons.     

Nanomaterials and Water Purification: Opportunities and Challenges

Advances in nanoscale science and engineering suggest that many of the current problems involving water quality could be resolved or greatly ameliorated using nanosorbents, nanocatalysts, bioactive nanoparticles, nanostructured catalytic membranes and nanoparticle enhanced filtration among other products and processes resulting from the development of nanotechnology. Innovations in the development of novel technologies to desalinate water are among the most exciting and promising. Additionally, nanotechnology-derived products that reduce the concentrations of toxic compounds to sub-ppb levels can assist in the attainment of water quality standards and health advisories. This article gives an overview of the use of nanomaterials in water purification. We highlight recent advances on the development of novel nanoscale materials and processes for treatment of surface water, groundwater and industrial wastewater contaminated by toxic metal ions, radionuclides, organic and inorganic solutes, bacteria and viruses. In addition, we discuss some challenges associated with the development of cost effective and environmentally acceptable functional nanomaterials for water purification.     

Magnetohydrodynamic turbulent flows: Existence results

In this paper we provide a detailed investigation of the problem of existence of solutions to the stochastic magnetohydrodynamic equations which describe the motion of turbulent particles of fluids in a magnetic field. The results are proved through a delicate combination of Galerkin approximation scheme with some deep compactness results of analytic and probabilistic nature.