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.     

Analysis of phase transitions by photothermal probe beam deflection

A recent photothermal technique has been used to study the smectic A-nematic and nematic-isotropic phase transitions in 4-n-octyl-4prime;-cyanobiphenyl and in binary mixtures of 4-n-octyl- and 4-n-octyloxy-4prime;-cyanobiphenyl. A numerical analysis shows that both amplitude and phase of the photothermal signal are sensitive to the change of certain thermal parameters for the sample.     

An oracle based method to compute a coupled equilibrium in a model of international climate policy

This paper proposes a computational game-theoretic model for the international negotiations that should take place at the end of the period covered by the Kyoto protocol. These negotiations could lead to a self-enforcing agreement on a burden sharing scheme given the necessary global emissions limit that will be imposed when the real extent of climate change is known. The model assumes a non-cooperative behavior of the parties except for the fact that they will be collectively committed to reach a target on total cumulative emissions by the year 2050. The concept of normalized equilibrium, introduced by J.B. Rosen for concave games with coupled constraints, is used to characterize a family of dynamic equilibrium solutions in an m-player game where the agents are (groups of) countries and the payoffs are the welfare gains obtained from a Computable General Equilibrium (CGE) model. The model deals with the uncertainty about climate sensitivity by computing an S-adapted equilibrium. These equilibria are computed using an oracle-based method permitting an implicit definition of the payoffs to the different players, obtained through simulations performed with the global CGE model GEMINI-E3. Partly supported by GICC (French Ministry of Ecology), TOCSIN (EU-044287) and the Swiss-NSF NCCR-Climate program of the Swiss NSF. For helpful comments and discussions, we thank A. Bernard, P. Thalmann, and the anonymous referee.     

Convex hull: A new method to determine the separation space used and to optimize operating conditions for comprehensive two-dimensional gas chromatography

It is important to develop methods of optimizing the selection of column sets and operating conditions for comprehensive two-dimensional gas chromatography. A new method for the calculation of the percentage of separation space used was developed using Delaunay's triangulation algorithms (convex hull). This approach was compared with an existing method and showed better precision and accuracy. It was successfully applied to the selection of the most convenient column set and the geometrical parameters of second column for the analysis of 49 target compounds in wastewater.     

Computation of Smooth Manifolds Via Rigorous Multi-parameter Continuation in Infinite Dimensions

In this paper, we introduce a constructive rigorous numerical method to compute smooth manifolds implicitly defined by infinite-dimensional nonlinear operators. We compute a simplicial triangulation of the manifold using a multi-parameter continuation method on a finite-dimensional projection. The triangulation is then used to construct local charts and an atlas of the manifold in the infinite-dimensional domain of the operator. The idea behind the construction of the smooth charts is to use the radii polynomial approach to verify the hypotheses of the uniform contraction principle over a simplex. The construction of the manifold is globalized by proving smoothness along the edge of adjacent simplices. We apply the method to compute portions of a two-dimensional manifold of equilibria of the Cahn–Hilliard equation.