Convex Sobolev inequalities and spectral gap

This Note is devoted to the proof of convex Sobolev (or generalized Poincaré) inequalities which interpolate between spectral gap (or Poincaré) inequalities and logarithmic Sobolev inequalities. We extend to the whole family of convex Sobolev inequalities results which have recently been obtained by Cattiaux, and Carlen and Loss for logarithmic Sobolev inequalities. Under local conditions on the density of the measure with respect to a reference measure, we prove that spectral gap inequalities imply all convex Sobolev inequalities including in the limit case corresponding to the logarithmic Sobolev inequalities. To cite this article: J.-P. Bartier, J. Dolbeault, C. R. Acad. Sci. Paris, Ser. I 342 (2006).     

Design and FPGA-realization of a self-synchronizing chaotic decoder in the presence of noise

This paper describes requirement for wireless transmission of Chaotic Code Division Multiplexed Access (Chaotic CDMA) and it focuses on real-time synchronization algorithm embedded into electronic programmable device. CDMA with quasi-orthogonal codes is used to allow multi-users to transmit simultaneously in the same channel. Since the channel is shared between all users, the receiver system has to cope with channel noise and overall with interference from other users. As a result, one of the main problems of communication with quasi-orthogonal chaotic codes is to implement a real time decoder in presence of noise. Even if set-membership algorithm are efficient in real time synchronization of chaotic discrete generators in the presence of noise, these algorithms require a large memory resource. In this paper, we propose an evolution of set-membership algorithm toward genetic algorithm to be implemented into electronic programmable device. The advantage of genetic algorithm compared with set-membership algorithm is that they require a fixed size of memory.     

Rigorous computation of smooth branches of equilibria for the three dimensional Cahn–Hilliard equation

In this paper, we propose a new general method to compute rigorously global smooth branches of equilibria of higher-dimensional partial differential equations. The theoretical framework is based on a combination of the theory introduced in Global smooth solution curves using rigorous branch following (van den Berg et al., Math. Comput. 79(271):1565–1584, 2010) and in Analytic estimates and rigorous continuation for equilibria of higher-dimensional PDEs (Gameiro and Lessard, J. Diff. Equ. 249(9):2237–2268, 2010). Using this method, one can obtain proofs of existence of global smooth solution curves of equilibria for large (continuous) parameter ranges and about local uniqueness of the solutions on the curve. As an application, we compute several smooth branches of equilibria for the three-dimensional Cahn–Hilliard equation.     

A policy iteration algorithm for fixed point problems with nonexpansive operators

The aim of this paper is to solve the fixed point problems:

Relaxation of variational problems in two-dimensional nonlinear elasticity

Consider a plate occupying in a reference configuration a bounded open set Ω ⊂ ℝ ² , and let be its stored-energy function. In this paper we are concerned with relaxation of variational problems of type:

Thermodynamics of a continuous medium with electric and magnetic dipoles

The thermodynamics of an electrically charged, multicomponent fluid with spontaneous electric and magnetic dipoles is analysed in the presence of electromagnetic fields. Taking into account the chemical composition of the current densities and stress tensors leads to three types of irreversible terms: scalars, vectors and pseudo-vectors. The scalar terms account for chemical reactivities, the vectorial terms account for transport and the pseudo-vectorial terms account for relaxation. The linear phenomenological relations, derived from the irreversible evolution, describe notably the Lehmann and electric Lehmann effects, the Debye relaxation of polar molecules and the Landau-Lifshitz relaxation of the magnetisation. This formalism accounts for the thermal and electric magnetisation accumulations and magnetisation waves. It also predicts that a temperature gradient affects the dynamics of magnetic vortices and drives magnetisation waves.     

Time-dependent density functional theory molecular dynamics simulation of doubly charged uracil in gas phase

We use time-dependent density functional theory and Born-Oppenheimer molecular dynamics methods to investigate the fragmentation of doubly ionized uracil in gas phase. Different initial electronic excited states of the dication are obtained by removing electrons from different inner-shell orbitals of the neutral species. We show that shape-equivalent orbitals lead to very different fragmentation patterns revealing the importance of the intramolecular chemical environment. The results are in good agreement with ionion coincidence measurements of uracil collision with 100 keV protons.     

Testing Gravity on Astrophysical Scales

We summarize a series of observational tests of the law of gravity on large astrophysical scales. These tests account for testing both the Poisson equation (inverse square law) using weak lensing and the Einstein equivalence principle through the test of the constancy of the constants of Nature. We emphasize the need to test general relativity on cosmological scales in light of the cosmological constant problem and of recent observational claims concerning the variation of fine structure constant.     

Specific influence of univalent cations on the ionization of alumina-coated TiO2 particles and on the adsorption of poly(acrylic)acid

A surface counterion titration method was used to monitor the interaction of monovalents cations (Li(+), Na(+), TMA(+)) with the surface of alumina-coated TiO(2) particles in concentrated media at different pH and electrolyte concentrations. This method allows measuring separately the negative and positive contribution to the surface charge. It showed that Cl(-) and TMA(+) are indifferent ions, but Li(+) and Na(+) specifically adsorb on the non-ionized alumina surface sites. The binding sequence of cations is Li(+)>Na(+)>TMA(+) at all ionic strengths investigated and is consistent with the structure-making and structure-breaking model developed a few decades ago. Polyacrylic acid (PAA) previously neutralized with the corresponding hydroxide (LiOH, NaOH, TMAOH) has been adsorbed on the alumina surface at different pH. The polymer counterion has a significant influence on the polymer adsorption. The sequence of the surface coverage as a function of the polymer counterion follows the order Li-PAA > Na-PAA > TMA-PAA. The much higher surface coverage with Li-PAA and Na-PAA compared to TMA-PAA is explained by the specific adsorption of Li-PAA and Na-PAA on the nonionized alumina surface sites, the same way LiCl and NaCl do.