Explicit minimizers for a class of nonlocal interaction energies | Vidéo | Carmin.tv

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Explicit minimizers for a class of nonlocal interaction energies

De Maria-Giovanna Mora

Apparaît dans la collection : Beyond Elasticity: Advances and Research Challenges / Au-delà de l'élasticité : avancées dans la recherche et prochains défis

Nonlocal interaction energies are continuum models for large systems of particles, where typically each particle interacts not only with its immediate neighbors, but also with particles that are far away. Examples of these energies arise in many different applications, such as biology (population dynamics), physics (Ginzburg-Landau vortices), and material science (dislocation theory). A fundamental question is understanding the optimal arrangement of particles at equilibrium, which are described, at least in average, by minimizers of the energy. In this talk I will focus on a class of nonlocal energies that are perturbations of the Coulomb energy and I will show how their minimizers can be explicitly characterized. This is based on joint works with J. Mateu, L. Rondi, L. Scardia, and J. Verdera.

Informations sur la vidéo

Date de captation 17/05/2022
Date de publication 17/06/2022
Institut CIRM
Licence CC BY NC ND
Langue Anglais
Audience Chercheurs, Doctorants
Réalisateur(s) Guillaume Hennenfent
Format MP4

Données de citation

DOI 10.24350/CIRM.V.19918603
Citer cette vidéo Mora, Maria-Giovanna (17/05/2022). Explicit minimizers for a class of nonlocal interaction energies. CIRM. Audiovisual resource. DOI: 10.24350/CIRM.V.19918603
URL https://dx.doi.org/10.24350/CIRM.V.19918603

Domaine(s)

Equations aux dérivées partielles

Bibliographie

MORA, Maria Giovanna, RONDI, Luca, et SCARDIA, Lucia. The equilibrium measure for a nonlocal dislocation energy. Communications on Pure and Applied Mathematics, 2019, vol. 72, no 1, p. 136-158. - https://doi.org/10.1002/cpa.21762
MATEU, Jоan, MORA, Maria Giovanna, RONDI, Luca, et al. Explicit minimizers of some non-local anisotropic energies: a short proof. Izvestiya: Mathematics, 2021, vol. 85, no 3, p. 468. - https://doi.org/10.1070/IM9048

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