Robust equilibrated a posteriori error estimators for the Reissner-Mindlin system

We consider a conforming finite element approximation of the Reissner-Mindlin system. We propose a new robust a posteriori error estimator based on H(div) conforming finite elements and equilibrated fluxes. It is shown that this estimator gives rise to an upper bound where the constant is one up to higher order terms. Lower bounds can also be established with constants depending on the shape regularity of the mesh. The reliability and efficiency of the proposed estimator are confirmed by some numerical tests

Ergodic properties of Poissonian ID processes

We show that a stationary IDp process (i.e., an infinitely divisible stationary process without Gaussian part) can be written as the independent sum of four stationary IDp processes, each of them belonging to a different class characterized by its L\'{e}vy measure. The ergodic properties of each class are, respectively, nonergodicity, weak mixing, mixing of all order and Bernoullicity. To obtain these results, we use the representation of an IDp process as an integral with respect to a Poisson measure, which, more generally, has led us to study basic ergodic properties of these objects.Comment: Published at http://dx.doi.org/10.1214/009117906000000692 in the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org

Technology diffusion in a differentiated industry

This paper investigates the adoption timing pattern of a cost-reducing innovation in a differentiated oligopolistic industry. It compares price and quantity market competition with the second-best optimal adoption rule. The diffusion pattern typically depends on the degree of product differentiation, and on the ability of firms to precommit, or not, to a certain adoption date. When goods are imperfect substitutes, market competition leads always to later adoption dates than it is socially optimal. When goods are sufficiently close substitutesı the last adoption occurs always earlier than in the optimum; the first adoption might also occur earlier but only if preemption is a credible threat

Conjugacy class of homeomorphisms and distortion elements in groups of homeomorphisms

Let S be a compact connected surface and let f be an element of the group Homeo\_0(S) of homeomorphisms of S isotopic to the identity. Denote by \tilde{f} a lift of f to the universal cover of S. Fix a fundamental domain D of this universal cover. The homeomorphism f is said to be non-spreading if the sequence (d\_{n}/n) converges to 0, where d\_{n} is the diameter of \tilde{f}^{n}(D). Let us suppose now that the surface S is orientable with a nonempty boundary. We prove that, if S is different from the annulus and from the disc, a homeomorphism is non-spreading if and only if it has conjugates in Homeo\_{0}(S) arbitrarily close to the identity. In the case where the surface S is the annulus, we prove that a homeomorphism is non-spreading if and only if it has conjugates in Homeo\_{0}(S) arbitrarily close to a rotation (this was already known in most cases by a theorem by B{\'e}guin, Crovisier, Le Roux and Patou). We deduce that, for such surfaces S, an element of Homeo\_{0}(S) is distorted if and only if it is non-spreading

Competition between stable equilibria in reaction-diffusion systems: the influence of mobility on dominance

This paper is concerned with reaction-diffusion systems of two symmetric species in spatial dimension one, having two stable symmetric equilibria connected by a symmetric standing front. The first order variation of the speed of this front when the symmetry is broken through a small perturbation of the diffusion coefficients is computed. This elementary computation relates to the question, arising from population dynamics, of the influence of mobility on dominance, in reaction-diffusion systems modelling the interaction of two competing species. It is applied to two examples. First a toy example, where it is shown that, depending on the value of a parameter, an increase of the mobility of one of the species may be either advantageous or disadvantageous for this species. Then the Lotka-Volterra competition model, in the bistable regime close to the onset of bistability, where it is shown that an increase of mobility is advantageous. Geometric interpretations of these results are given.Comment: 43 pages, 10 figure