Pré-Publication, Document De Travail Année : 2025

The Spear and the Ring: Emergent Structures in Magnetic Colloidal Suspensions

Résumé

We study from a mathematical point of view the nanoparticle model of a magnetic colloid, presented by G. Klughertz. Our objective is to obtain properties of stable stationary structures that arise in the long-time limit for the magnetic nanoparticles dynamics following this model. In this article, we present a detailed study of two specific structures using techniques from the calculus of variations. The first, called the spear, consists of a chain of aligned particles interacting via a Lennard-Jones potential. We establish existence and uniqueness results, derive bounds on the distances between neighboring particles, and provide a sharp asymptotic description as the number of particles tends to infinity. The second structure, the ring, features particles uniformly distributed along a circle. We prove its existence and uniqueness and derive an explicit formula for its radius.

Fichier principal
Vignette du fichier
main.pdf (775.48 Ko) Télécharger le fichier
Origine Fichiers produits par l'(les) auteur(s)
Licence

Dates et versions

hal-05016866 , version 1 (02-04-2025)

Licence

Identifiants

  • HAL Id : hal-05016866 , version 1

Citer

Raphaël Côte, Clémentine Courtès, Guillaume Ferriere, Ludovic Godard-Cadillac, Yannick Privat. The Spear and the Ring: Emergent Structures in Magnetic Colloidal Suspensions. 2025. ⟨hal-05016866⟩
287 Consultations
198 Téléchargements

Partager

  • More