2020/02/12 by David Gérard‐Varet, Gérard-Varet, David, Richard M. Höfer +1
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Point processes and geometric inequalities #Stochastic processes and statistical mechanics
paper · pdf · doi:10.48550/arxiv.2002.04846
openalex publication_date 2020/02/12 · openalex created_date 2020/12/07 · openalex updated_date 2026/08/04
We provide a rigorous derivation of Einstein's formula for the effective\nviscosity of dilute suspensions of n rigid balls, n \≫ 1, set in a volume\nof size 1. So far, most justifications were carried under a strong assumption\non the minimal distance between the balls: dmin \≥ c n-\(1)/(3), c\n> 0. We relax this assumption into a set of two much weaker conditions: one\nexpresses essentially that the balls do not overlap, while the other one gives\na control of the number of balls that are close to one another. In particular,\nour analysis covers the case of suspensions modelled by standard Poisson\nprocesses with almost minimal hardcore condition.\n