Mines ParisTech

About: Mines ParisTech is a education organization based out in Paris, France. It is known for research contribution in the topics: Finite element method & Microstructure. The organization has 6564 authors who have published 11676 publications receiving 359898 citations. The organization is also known as: École nationale supérieure des mines de Paris & École des mines de Paris.

Fixed-rank matrix factorizations and Riemannian low-rank optimization

Abstract: Motivated by the problem of learning a linear regression model whose parameter is a large fixed-rank non-symmetric matrix, we consider the optimization of a smooth cost function defined on the set of fixed-rank matrices. We adopt the geometric framework of optimization on Riemannian quotient manifolds. We study the underlying geometries of several well-known fixed-rank matrix factorizations and then exploit the Riemannian quotient geometry of the search space in the design of a class of gradient descent and trust-region algorithms. The proposed algorithms generalize our previous results on fixed-rank symmetric positive semidefinite matrices, apply to a broad range of applications, scale to high-dimensional problems, and confer a geometric basis to recent contributions on the learning of fixed-rank non-symmetric matrices. We make connections with existing algorithms in the context of low-rank matrix completion and discuss the usefulness of the proposed framework. Numerical experiments suggest that the proposed algorithms compete with state-of-the-art algorithms and that manifold optimization offers an effective and versatile framework for the design of machine learning algorithms that learn a fixed-rank matrix.

Oil–water two‐phase flow in microchannels: Flow patterns and pressure drop measurements

Abstract: This paper investigates oil–water two-phase flows in microchannels of 793 and 667 µm hydraulic diameters made of quartz and glass, respectively. By injecting one fluid at a constant flow rate and the second at variable flow rate, different flow patterns were identified and mapped and the corresponding two-phase pressure drops were measured. Measurements of the pressure drops were interpreted using the homogeneous and Lockhart–Martinelli models developed for two-phase flows in pipes. The results show similarity to both liquid–liquid flow in pipes and to gas–liquid flow in microchannels. We find a strong dependence of pressure drop on flow rates, microchannel material, and the first fluid injected into the microchannel.

Mullite Based Oxidation Protection for SiC-C/C Composites in Air at Temperatures up to 1900 K

Abstract: For an industrial Si-SiC coated C/C material (reference material) the temperature dependence of the linear rate of mass loss is interpreted in the temperature range 773 < T < 1973 K. The Arrhenius plot of the thermogravimetrically determined oxidation rate shows four typical regimes. Only in the temperature range 1323 < T < 1823 K is the oxidation rate close to or lower than the limit for long-term application. Pulsed Laser Deposition (PLD) allows the ablation of nonconductive and high melting targets and the preparation of films with complex composition. High energy impact CO 2 laser pulses (j= 3.10 7 W cm -2 ) lead to melting and evaporation of the target material in a single step. Therefore the flux of the metal components is stoichiometric. Deposited green layers did not show IR peaks typical for mullite. After a short oxidation treatment (15 min at 1673K) the formation of mullite in the coating was completed as was confirmed by IR spectroscopy and XRD investigations. Thin PLD-mullite layers (900 nm) did not markedly improve the oxidation resistance of the reference material in the high temperature range 1473 < T < 1973 K. However, a preoxidation treatment of the substrate material and mullite coatings with a thickness of 2.5 μm improved the oxidation behaviour significantly. Because of SiO 2 formation at the mullite-SiC interface all samples exhibited a mass increase on oxidation. The inward diffusion of oxygen across the outer mullite-containing layer controlled the kinetics of the reaction as was deduced from 18 O diffusivity measurements in PLD mullite layers. The calculated oxidation rates resulting from the diffusion parameters in SiO 2 and mullite are close to the thermogravimetric data. For oxidation durations of three days only amorphous SiO 2 is formed at the mullite-SiC interface.