I review recent results and unsolved problems concerning the hard-core lattice gas and the q-coloring model (antiferromagnetic Potts model at zero temperature). For each model, I consider its equilibrium properties (uniqueness/nonuniqueness of the infinite-volume Gibbs measure, complex zeros of the partition function) and the dynamics of local and nonlocal Monte Carlo algorithms (ergodicity, ra...

The problem of partial exact boundary controllability and exponential stability for the higher-dimensional linear system of thermoelasticity is considered. By introducing a velocity feedback on part of the boundary of the thermoelastic body, which is clamped along the rest of its boundary, to increase the loss of energy, we prove that the energy in the system of thermoelasticity decays to zero ...

We consider the numerical approximation of a flrst order stationary hyperbolic équation by the method of characteristics with pseudo time step k using discontinuous finite éléments on a mesh Th. For this method, we exhibit a "natural" norm || \\h,k for which we show that the discrete variational problem P^ is welî posed and we obtain an error estimate. We show that when k goes to zero problem (...

Dans cet article, nous démontrons des variantes du théorème d’Ax–Lindemann–Weierstrass (ALW) pour fonctions analytiques satisfaisant équations différentielles de type « Schwarzienne ». travaux antérieurs, avons prouvé le ALW les uniformisantes groupes fuchsiens genre zéro. ce travail, généralisons résultat plusieurs manières en utilisant techniques variées provenant la théorie modèles, Galois d...

We develop a polarised variant of Curien and Herbelin’s λ̄μμ̃ calculus suitable for sequent calculi that admit a focalising cut elimination (i.e. whose proofs are focalised when cut-free), such as Girard’s classical logic LC or linear logic. This gives a setting in which Krivine’s classical realisability extends naturally (in particular to callby-value), with a presentation in terms of orthogonal...

The purpose of this paper is to investigate the limit of some kinetic equations with a strong force. Due to friction, the solution concentrates to a monokinetic distribution so as to keep the total of force bounded and in the limit we recover a macroscopic system. This kind of asymptotics is a natural question when the mass of the particles is very small or their inertia is neglected. After tha...