Speaker
Description
Multiscale systems are widely present in both biological structures and technological applications. The ability to account not only for the macroscopic behavior of an elastic medium, but also for its microscopic arrangement, allows for a more complete and realistic description. Recently, I studied two problems in which a non-trivial interaction
arises between two contributions coming from different scales of a structure.
In the first problem [1, 2], we prove the existence and geometric properties of an equilibrium configuration for a nematic film with surface tension using the Calculus of Variations. The key aspect is the non-trivial competition between the Frank energy of the crystal and the area functional.
In the second case [3], we derive the equations of Biot’s poroelasticity from the microstructure under the assumption of incompressibility of both an isotropic linear-elastic solid and a low-Reynolds-number Newtonian fluid flowing through its pores. By using the asymptotic homogenization technique, we obtain a macroscale system of PDEs, with corresponding cell problems at the pore-scale; moreover, we recover the equivalence between the change in volume of the porous solid and the volume of fluid exchanged.
References
[1] G. Bevilacqua, C. Lonati, L. Lussardi, A. Marzocchi, A variational analysis of axisymmetric nematic films: the covariant derivative case, arXiv:2405.20154, Calculus of Variations and Partial Differential Equations, 2026.
[2] G. Bevilacqua, C. Lonati, L. Lussardi, A. Marzocchi, Existence and uniqueness of minimizers for axisymmetric nematic films, arXiv:2601.09348, submitted.
[3] R. Penta, C. Lonati, L. Miller, A. Marzocchi, Poroelasticity derived from the microstructure for intrinsically incompressible constituents, Zeitschrift f¨ur angewandte Mathematik und Physik, 2026.