8 papers
Homogenization of the 2D Euler system: lakes and porous media
Mitia Duerinckx, Antoine Gloria
This work is devoted to the long-standing open problem of homogenization of 2D perfect incompressible fluid flows, such as the 2D Euler equations with impermeable inclusions modeli…
The Clausius-Mossotti formula
Mitia Duerinckx, Antoine Gloria
In this note, we provide a short and robust proof of the Clausius-Mossotti formula for the effective conductivity in the dilute regime, together with an optimal error estimate. The…
Quantitative homogenization theory for random suspensions in steady Stokes flow
Mitia Duerinckx, Antoine Gloria
This work develops a quantitative homogenization theory for random suspensions of rigid particles in a steady Stokes flow, and completes recent qualitative results. More precisely,…
Sedimentation of random suspensions and the effect of hyperuniformity
Mitia Duerinckx, Antoine Gloria
This work is concerned with the mathematical analysis of the bulk rheology of random suspensions of rigid particles settling under gravity in viscous fluids. Each particle generate…
Corrector equations in fluid mechanics: Effective viscosity of colloidal suspensions
Mitia Duerinckx, Antoine Gloria
Consider a colloidal suspension of rigid particles in a steady Stokes flow. In a celebrated work, Einstein argued that in the regime of dilute particles the system behaves at leadi…
A remark on a surprising result by Bourgain in homogenization
Mitia Duerinckx, Antoine Gloria, Marius Lemm
In a recent work, Bourgain gave a fine description of the expectation of solutions of discrete linear elliptic equations on with random coefficients in a perturbative…