Géométrie sacrée

thumb|Cube de Metatron, réunissant les 5 Solides de Platon La géométrie sacrée est un type de design architectural, industriel et artistique basé sur la répétition de certaines formes géometriques que l'on retrouve souvent dans un lieu sacré, par exemple dans une mosquée, un temple, une synagogue ou une église. Selon certaines religions et courants spirituels, Dieu a créé le monde selon un plan géométrique que l'on peut vérifier à la fois sur un plan microsomique et macrocosmique. Plutarque a attribué cette découverte a Platon, écrivant que "Platon a dit que Dieu crée de façon géométrique constamment et continuellement" (Convivialium disputationum, liber 8,2). Durant les temps modernes, le mathématicien Carl Friedrich Gauss a adapté ce dicton de Platon en disant "Dieu arithmetise". Bibliographie *

Nigel Pennick, Sacred Geometry: Symbolism and Purpose in Religious Structures
, Celtic Art: The Methods of Construction, Dover, 1973
, Sacred Geometry: Philosophy and

Additive Fabrication of Silicon Pillars on Monocrystalline Silicon by Direct Laser Melting

Marie Camille Laëtitia Le Dantec

Additive Manufacturing (AM) is an emerging part production technology that offers many ad-vantages such as high degree of customization, material savings and design of 3D highly complex structures. However, AM is a complex multiphysics process. Therefore, only a limited number of materials can already be commercially used to produce parts and a handful of others are being studied or developed for such process. Consequently, limited knowledge on this process is available, especially concerning materials that present thermomechanical challenges such as brittle materials. The present research focuses on additive fabrication of silicon pillars on a monocrystalline silicon wafer by Direct Laser Melting (DLM) with a pulsed 1064 nm laser beam. The simple geometry of pillars allowed for the first determining steps into process understanding. Several results were achieved through this PhD work. First, crack-free silicon pillars were successfully built onto monocrystalline silicon wafers. With the help of in-situ process monitoring and sample characterization, wafer substrate temperature and laser repetition rate were found to be the main influential parameters to obtain crack-free samples, as minimum substrate temperature of 730°C and a minimum repetition rate of 100 Hz were necessary to reach this goal (for a feed rate of 15 g/min and a pulse duration of 1 ms). The influence of secondary process parameters such as feed rate and energy per pulse were also discussed. A simple Finite Element Modeling (FEM) model validated by the experiments was used to explain crack propagation in the samples. Then, process monitoring of the DLM process was realized. High-speed camera image analysis re-vealed that vertical stage speed and powder feed rate should match to obtain a constant pillar building rate. As all pillars presented necking at their base, estimations of the thermal characteristics of the pillar during growth were carried out by FEM simulations. They were additionally used to explain the pillar final shape. Finally, the microstructure of the pillars built was characterized by the Electron Back-Scattering Dif-fraction (EBSD) technique. In the conditions presented in this work, the microstructure of the pillar was found to be in the columnar growth mode. The feed rate was identified as the most influential parameter on the microstructure, followed by the stage speed, the impurity content of the powder and the crystallographic orientation of the substrate. Epitaxial growth was achieved on more than 1 mm with a feed rate of 1.0 g/min, a stage speed of 0.1 mm/s, a powder with purity of 4N and a oriented wafer substrate. This work could be further continued by making improvements to the DLM setup, studying the influence of additional process parameters on the thermomechanical behavior and the microstructure control of the pillars, and/or using these results to realize more complicated shapes, either with this setup or by using a powder bed technique.

EPFL2018

Simulation of viscoelastic fluids in a 2D abrupt contraction by spectral element method

Michel Deville, Nicolas Fietier, Azadeh Jafari

This study presents the vortex structure and numerical instability increase occurring when the level of elasticity is enhanced in inertial flows in planar contraction configuration for finitely extensible nonlinear elastic model by Peterlin (FENE-P) fluid . The re-entrant corner effect on corner vortices is also considered. The calculations are performed using extended matrix logarithm formulation described in a previous paper: A. Jafari et al. A new extended matrix logarithm formulation for the simulation of viscoelastic fluids by spectral elements. Computer & Fluids 2010; 39(9):1425-1438. In that reference, the proposed algorithm has been tested for simple geometry such as Poiseuille flow. In this study, we are interested in the capability of this algorithm for more complex geometry. This formulation helps to reach higher values of the Weissenberg number when compared with the classical one. Copyright (c) 2015John Wiley & Sons, Ltd.

Wiley-Blackwell2015

Additive Fabrication of Silicon Pillars on Monocrystalline Silicon by Direct Laser Melting

Marie Camille Laëtitia Le Dantec

EPFL2018

A geographical study of (M)over-bar(2)(P-2, 4)(main)

Additive Fabrication of Silicon Pillars on Monocrystalline Silicon by Direct Laser Melting

Simulation of viscoelastic fluids in a 2D abrupt contraction by spectral element method

Simulation of viscoelastic fluids in a 2D abrupt contraction by spectral element method

Additive Fabrication of Silicon Pillars on Monocrystalline Silicon by Direct Laser Melting

A geographical study of (M)over-bar(2)(P-2, 4)(main)