Continuum Percolation in Stochastic Homogenization and the Effective Viscosity Problem

This contribution is concerned with the effective viscosity problem, that is, the homogenization of the steady Stokes system with a random array of rigid particles, for which the main difficulty is the treatment of close particles. Standard approaches in the literature have addressed this issue by m...

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Bibliographic Details
Published in:Archive for rational mechanics and analysis Vol. 247; no. 2; p. 26
Main Authors: Duerinckx, Mitia, Gloria, Antoine
Format: Journal Article
Language:English
Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.04.2023
Springer Nature B.V
Subjects:
Classical Mechanics
Clustering
Complex Systems
Compressibility
Digital Object Identifier
Fluid- and Aerodynamics
Homogenization
Mathematical and Computational Physics
Percolation
Physics
Physics and Astronomy
Stiffness
Theoretical
Viscosity
ISSN:0003-9527, 1432-0673
Online Access:Get full text
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Summary:This contribution is concerned with the effective viscosity problem, that is, the homogenization of the steady Stokes system with a random array of rigid particles, for which the main difficulty is the treatment of close particles. Standard approaches in the literature have addressed this issue by making moment assumptions on interparticle distances . Such assumptions, however, prevent clustering of particles, which is not compatible with physically-relevant particle distributions. In this contribution, we take a different perspective and consider moment bounds on the size of clusters of close particles . On the one hand, assuming such bounds, we construct correctors and prove homogenization. On the other hand, based on subcritical percolation techniques, these bounds are shown to hold for various mixing particle distributions with nontrivial clustering. As a by-product of the analysis, we also obtain similar homogenization results for compressible and incompressible linear elasticity with unbounded random stiffness.
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ISSN:0003-9527
1432-0673
DOI:10.1007/s00205-023-01857-w