The Spear and the Ring: Emergent Structures in Magnetic Colloidal Suspensions
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| Main Authors: | , , , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866915225380323328 |
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| author | Côte, Raphaël Courtès, Clémentine Ferrière, Guillaume Godard-Cadillac, Ludovic Privat, Yannick |
| author_facet | Côte, Raphaël Courtès, Clémentine Ferrière, Guillaume Godard-Cadillac, Ludovic Privat, Yannick |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2504_02379 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The Spear and the Ring: Emergent Structures in Magnetic Colloidal Suspensions Côte, Raphaël Courtès, Clémentine Ferrière, Guillaume Godard-Cadillac, Ludovic Privat, Yannick Mathematical Physics Optimization and Control 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. |
| title | The Spear and the Ring: Emergent Structures in Magnetic Colloidal Suspensions |
| topic | Mathematical Physics Optimization and Control |
| url | https://arxiv.org/abs/2504.02379 |