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.     

Beta zeolite supported on silicon carbide for Friedel-Crafts fixed-bed reactions

Beta zeolite supported on silicon carbide, with high thermal conductivity and high mechanical strength, was successfully used as an active and stable catalyst for Friedel-Crafts reactions in a fixed bed configuration.     

Interchange of infimum and integral

We prove a new interchange theorem of infimum and integral. Its distinguishing feature is, on the one hand, to establish a general framework to deal with interchange problems for nonconvex integrands and nondecomposable sets, and, on the other hand, to link the theorems of Rockafellar and Hiai-Umegaki with the one of Bouchitté-Valadier. We give an application to relaxation of nonconvex geometric integrals of Calculus of Variations.Received: 20 March 2002, Accepted: 12 March 2003, Published online: 16 May 2003     

The acceleration of the universe and the physics behind it

Using a general classification of dark enegy models in four classes, we discuss the complementarity of cosmological observations to tackle down the physics beyond the acceleration of our universe. We discuss the tests distinguishing the four classes and then focus on the dynamics of the perturbations in the Newtonian regime. We also exhibit explicitely models that have identical predictions for a subset of observations.     

Gradient estimates for a degenerate parabolic equation with gradient absorption and applications

Qualitative properties of non-negative solutions to a quasilinear degenerate parabolic equation with an absorption term depending solely on the gradient are shown, providing information on the competition between the nonlinear diffusion and the nonlinear absorption. In particular, the limit as t→∞ of the L¹-norm of integrable solutions is identified, together with the rate of expansion of the support for compactly supported initial data. The persistence of dead cores is also shown. The proof of these results strongly relies on gradient estimates which are first established.     

Tests of general relativity on astrophysical scales

While tested to a high level of accuracy in the Solar system, general relativity is under the spotlight of both theoreticians and observers on larger scales, mainly because of the need to introduce dark matter and dark energy in the cosmological model. This text reviews the main tests of general relativity focusing on the large scale structure and more particularly weak lensing. The complementarity with other tests (including those on Solar system scales and the equivalence principle) is discussed.     

The blow-up curve of solutions of mixed problems for semilinear wave equations with exponential nonlinearities in one space dimension, I

In this paper, we consider mixed problems with a spacelike boundary derivative condition for semilinear wave equations with exponential nonlinearities in a quarter plane. Results similar to those obtained earlier by Caffarelli-Friedman for Cauchy problems and power nonlinearities are proved in the present situation, namely we show that solutions either are global or blow up on a spacelike curve. Weaker results are also obtained if the boundary vector field is tangent to the characteristic which leaves the domain in the future. Received January 7, 2000 / Accepted July 17, 2000 /Published online December 8, 2000     

Acoustic emission potentialities for characterization of Mullins effect in natural rubber materials filled with carbon black

Acoustic Emission (AE) was investigated in order to monitor in real time the Mullins effect. Cyclic uniaxial tensile tests were carried out on two different natural rubbers. Different behaviour is revealed depending on whether or not the material undergoes the Mullins effect. The acoustic emission activity is very important during the first cycle, but decreases gradually with increasing number of cycles, when the Mullins effect is observed. On the contrary, when there is no Mullins effect no significant AE activity is recorded.