Physique mésoscopique

Résumé

La physique mésoscopique est un domaine de la physique de la matière condensée qui étudie les systèmes ayant des dimensions intermédiaires entre celles de la physique quantique et de la physique classique. L'échelle des distances en cause s'étend des dimensions de l'atome jusqu'au micromètre. La dimension mésoscopique est une dimension intermédiaire entre la dimension macroscopique et la dimension microscopique. Elle permet des études statistiques du système étudié. Description Si les systèmes mésoscopiques et macroscopiques comprennent tous les deux plusieurs atomes, les systèmes macroscopiques sont bien décrits par les propriétés moyennes dérivées des lois de la mécanique classique, alors que les systèmes mésoscopiques sont affectés par les fluctuations autour de la moyenne et doivent être décrits par la mécanique quantique. Un système est dit de dimensions mésoscopiques lorsqu'il commence à montrer des propriétés quantiques. Par exemple, alors que la conductance d'un fi

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We construct a non-equilibrium steady state and calculate the corresponding current for a mesoscopic Fermi system in the partition-free setting. To this end we study a small sample coupled to a finite number of semi-infinite leads. Initially, the whole system of quasi-free fermions is in a grand canonical equilibrium state. At t = 0 we turn on a potential bias on the leads and let the system evolve. We study how the charge current behaves in time and how it stabilizes itself around a steady state value, which is given by a Landauer-type formula.

2010

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Hot tearing is a major defect of solidification processes and welding. It occurs in metallic alloys while they are in the semi-solid state and is caused by a lack of liquid feeding in the mushy zone to compensate solid network openings due to tensile and shear strains. These strains are localized in the thin liquid films that remain at grain boundaries. Therefore, it is important to know when the solid grains coalesce and percolate to form a fully coherent solid, i.e., when the material can transmit stresses and strains but also withstand thermal contraction without rupture. Coalescence is defined as the disappearance of a liquid film in between two distinct grains, forming a solid grain boundary, while percolation is defined as the gradual transition of isolated grains or clusters surrounded by a continuous liquid film to a continuous solid network across a domain, even if some liquid regions remain. If the simulation of hot tearing has to account for localization of strains and liquid feeding, it is mandatory to use a granular approach. Two previous theses done recently at EPFL have developed such granular models of hot tearing, first in 2D (PhD of S. Vernède) and then in 3D (PhD of M. Sistaninia). However, these models have used a Voronoi tessellation for the description of globular microstructures in which equiaxed grains were approximated by polygons and polyhedra, respectively. From the experimental point of view, an innovative method, based on the Bridgman furnace principle, has been developed. The standard Bridgman furnace has been substantially modified in order to obtain the desired globular-equiaxed grain structure and reduce macrosegregation in the quenched sample. This modified furnace has been characterized then in terms of thermal measurements and observed final grain size. The samples obtained with the modified Bridgman furnace were then observed post-mortem by ex situ X-ray tomography. In addition, X-ray tomography experiments under similar conditions have been performed in situ with the laser-heated furnace installed on the TOMCAT synchrotron beam line at PSI. A postprocessing analysis of the principal curvature distribution (ISD plots) was performed on both ex situ and in situ observations for various compositions of inoculated Al-Cu alloys. The ISD plots of the X-ray tomography observations indicated the formation of liquid cylinders along triple line and, at a more advanced solidification stage, the formation of liquid pocket at quadruple vertices. From the modeling point of view, a new mesoscopic model has been developed both for 2D and 3D simulations. This model was inspired by the granular model developed by Phillon et al. that considers polyhedral grains based on a Voronoi tessellation of space, but allow to obtain smoother grain shapes and more progressive coalescence. After its validation with multiphase-field simulations, the mesoscopic model has been used to predict the various percolation transitions of the solid phase. In addition, by estimating the solid moment at which the liquid starts to form isolated pockets, it was possible to predict the temperature and solid fractions for which the mushy zone is most vulnerable to hot tearing. The simulations have been performed for various conditions and copper compositions, indicating the nominal compositions that are more sensitive to hot tearing. Finally, the 3D mesoscopic model predictions were compared with the X-ray tomography observations.

EPFL2015

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Tensor-Based Numerical Method For Stochastic Homogenization

This paper addresses the complexity reduction of stochastic homogenization of a class of random materials for a stationary diffusion equation. A cost-efficient approximation of the correctors is obtained using a method designed to exploit quasi-periodicity. Accuracy and cost reduction are investigated for local perturbations or small transformations of periodic materials as well as for materials with no periodicity but a mesoscopic structure, for which the limitations of the method are shown. Finally, for materials outside the scope of this method, we propose to use the approximation of homogenized quantities as control variates for variance reduction of a more accurate and costly Monte Carlo estimator (using a multifidelity Monte Carlo method). The resulting cost reduction is illustrated in a numerical experiment and compared with a control variate method from weakly stochastic homogenization. The limits of this variance reduction technique are tested on materials without periodicity or mesoscopic structure.

SIAM PUBLICATIONS2022

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EPFL2015