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The KdV equation under periodic boundary conditions and its perturbations
No full textInternational audienceIn this paper we discuss properties of the Korteweg–de Vries (KdV) equation under periodic boundary conditions, especially those which are important for studying perturbations of the equation. We then review what is known about the long-time behaviour of solutions for perturbed KdV equations
L'évaluation économique du risque nécléaire
No full textLa production d'électricité au moyen de l'énergie nucléaire est une activité dont on ne peut ignorer les risques et elle doit faire lobjet d'un calcul économique approprié. Les spécificités du risque nucléaire justifient que le décideur public incorpore une valorisation adéquate de ces risques dans la balance des coûts et des bénéfices : il sagit d'un risque qui n'est que partiellement mutualisable, qui a une dimension systémique, dont les aléas sous-jacents sont imparfaitement probabilisables, et qui peut conduire à des conséquences de nature catastrophique sur le très long terme. Ces différentes caractéristiques donnent au risque nucléaire une dimension spécifique qui l'éloigne des principes usuels du calcul économique public et chacune d'entre-elles justifie une valorisation spécifique de ce risque dont la probabilité est faible ou très faible, mais dont les conséquences potentielles sont de très forte intensité
Volume Viscosity and Internal Energy Relaxation : Symmetrization and Chapman-Enskog Expansion
No full textWe analyze a mathematical model for the relaxation of translational and internal temperatures in a nonequilibrium gas. The system of partial differential equations---derived from the kinetic theory of gases---is recast in its natural entropic symmetric form as well as in a convenient hyperbolic-parabolic symmetric form. We investigate the Chapman-Enskog expansion in the fast relaxation limit and establish that the temperature difference become asymptotically proportional to the divergence of the velocity field. This asymptotic behavior yields the volume viscosity term of the limiting one-temperature fluid model
2-Substituted vs 4-substituted-9,9′-spirobifluorene host materials for green and blue phosphorescent OLEDs: a structure-property relationship study
No full textNanotek for organic synthesis, and organic synthesis for nanotekInternational audienceWe report a structure-property relationship study of four 9,9′-spirobifluorene (SBF) derivatives (4-5Pm-SBF, 2-5Pm-SBF, 4-Ph-SBF and 2-Ph-SBF), substituted with either phenyl or pyrimidine at the \C2\ or \C4\ position of the \SBF\ core. Structural, thermal, electrochemical and photophysical properties have been examined and correlated to theoretical calculations in order to study the influence of the nature and the position of the substituent. The emission properties of 4- versus 2-substituted \SBFs\ are noticeably different highlighting, in the excited state, the remarkable effect of substitution in ortho position of SBF. All compounds have been used as host material for green dopant in PhOLEDs with very high performances (2-5Pm-SBF: CE>58 cd/A, PE>35 lm/W, EQE>14%). More importantly, the two 4-substituted \SBFs\ have been used as host materials in blue PhOLEDs, displaying high performance and a decrease of \VTH\ for 4-5Pm-SBF due to the incorporation of the electron-withdrawing pyrimidine
Formes automorphes et voisins de Kneser des réseaux de Niemeier
No full textIn this memoir, we study the even unimodular lattices of rank at most 24, as well as a related collection of automorphic forms of the orthogonal and symplectic groups of small rank. Our guide is the question of determining the number of p-neighborhoods, in the sense of M. Kneser, between two isometry classes of such lattices. We prove a formula for this number, in which occur certain Siegel modular forms of genus 1 and 2. It has several applications, such as the proof of a conjecture of G. Nebe and B. Venkov about the linear span of the higher genus theta series of the Niemeier lattices, the computation of the p-neighborhoods graphs of the Niemeier lattices (the case p = 2 being due to Borcherds), or the proof of a congruence conjectured by G. Harder. Classical arguments reduce the problem to the description of the automorphic representations of a suitable integral form of the euclidean orthogonal group of R^24 which are unramified at each finite prime and trivial at the archimedean prime. The recent results of J. Arthur suggest several new approaches to this type of questions. This is the other main theme that we develop in this memoir. We give a number of other applications, for instance to the classification of Siegel modular cuspforms of weight at most 12 for the full Siegel modular group
Une coupe très intéressante dans le complément de l'éponge de Menger -itération 4-
No full textAn interesting cross-section inside the complement of the Menger sponge -iteration 4- (Une coupe très intéressante dans le complément de l'éponge de Menger -itération 4-
Une coupe très intéressante dans le complément de l'éponge de Menger -itération 2-
No full textAn interesting cross-section inside the complement of the Menger sponge -iteration 2- (Une coupe très intéressante dans le complément de l'éponge de Menger -itération 2-
Le complément de l'éponge de Menger -itération 2-
No full textThe complement of the Menger sponge -iteration 2- (Le complément de l'éponge de Menger -itération 2-