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Einladung zum Vortrag (Zoom) von Herrn Prof. François Willot (Université PSL, Paris) am 02.07.2024 - 14:30 Uhr im Rahmen des Forschungsseminars Analysis
[02.07.2024]Im Rahmen des Forschungsseminars Analysis hält am Dienstag, den 2. Juli 2024, um 14:30 Uhr,
Herr Prof. François Willot (Université PSL, Paris) einen Vortrag zum Thema
Homogenized metrics in planar, multiscale random sets
Abstract: We derive new bounds for the length of minimal paths spanning a class of heterogeneous media in two dimensions, based on random set theory. These bounds provide insights into homogenization problems studied in theoretical mechanics, involving perfectly-plastic materials or related to fracture. Here we consider media containing randomly-distributed particles embedded in a matrix. Two types of particles are examined: "porous" inclusions that can be crossed at no cost and "rigid'" obstacles that can not be crossed. The metric in the embedding matrix is the Euclidean distance.
Our main interest is on the effect of a multiscale random dispersion of particles, simulated by hierachical Boolean random sets and random sequential adsorption models. The bounds are derived in the case of a vanishingly small particle density, and are compared with numerical computations, performed by means of specialized, discretization-free algorithms. Comparisons are also made with other known bounds and exact results predicted by nonlinear homogenization theories.
Der Vortrag findet im Rahmen eines Zoom-Meetings statt. Bei Interesse an den Zugangsdaten bitte bei Herrn Prof. Mugnolo (delio.mugnolo) melden.
