Date/heure
3 octobre 2025
11:00 - 12:00
Oratrice ou orateur
Dominik Stantejsky (IECL)
Catégorie d'évènement Séminaire EDP, Analyse et Applications (Metz)
Résumé
In this talk, I will present an asymptotic expansion for the minimal Dirichlet energy of $\mathbb{S}^2$-valued maps outside a finite number of particles of size $\rho$ in $\mathbb{R}^3$ under general anchoring conditions at the particle boundaries as $\rho\to 0$. The first two terms of this expansion consist of the minimal energy after zooming in at scale $\rho$ around each particle and a Coulomb-like interaction that agrees with the electrostatics analogy depending on the far-field behavior of the corresponding single-particle minimizer. This approximation is commonly used in the physics literature for colloid interactions in nematic liquid crystals and for the first time a precise estimate of the energy error introduced by that linearization is derived, by developing new tools that address the lack of convergence rate when zooming in at scale $\rho$.
The talk is based on joint work with L. Bronsard, X. Lamy and R. Venkatraman.