Several aspects of the Bénard instability are approached in this work. After having described the principle of the experiments by underlining the role of the two driving forces of instability, namely surface tension and buoyancy, we show first of all, for configurations of large horizontal extension, various types of convective patterns, all made of 2D pavements of convective cells (hexagonal, square). The narrow similarity between these 2D patterns and the 2D polycristals (presence of grains, dislocations, grain boundaries) is shown. Structural order may be studied with the traditional tools (optical or mathematical Fourier transform, radial and angular correlation functions). A comparison between this (partial) disorder and mathematical models built independently of the physical phenomenon is established (minimal spanning tree, Aboav-Weaire, Lewis laws...) The agreement is surprisingly good. A study of the structural disorder can be presented as a function of Marangoni number until reaching spatio-temporal chaos. Dimensions of the attractors are calculated

Dans cet article le modèle de Darcy et l’approximation de Boussinesq sont utilisés pour étudier la convection naturelle dans un milieu poreux saturé par un fluide binaire. La géométrie considérée est celle d’une cavité partiellement chauffée par le bas et refroidie par le haut. Les forces solutales résultent de l’imposition de concentrations constantes imposées sur les surfaces horizontales de la cavité. L’existence de solutions multiples pour ce type de configuration est démontrée numériquement.

We present in this paper a method for optimizing the design of CMOS bandgap voltage reference. The purpose of this work is to provide an optimal devices sizing, to reach the bandgap reference desired performances. This is achieved by using a simple mathematic calculations, basic layout design rules and simulation analyses. The proposed method is applied to design a voltage reference using CMOS 0.35uM process, featuring low temperature coefficient over the range of 105 °C, low noise, good power supply rejection in the range: 2.9 to 3.6 V, and keep an acceptable variation of the nominal value for a different process corners.