Dimensionality of Local Minimizers of the Interaction Energy

By D. Balagué, José Antonio Carrillo, Thomas Laurent, Gaël Raoul. 2012

165 citations recorded by the source corpus.

In this work we consider local minimizers (in the topology of transport distances) of the interaction energy associated with a repulsive–attractive potential. We show how the dimensionality of the support of local minimizers is related to the repulsive strength of the potential at the origin.

Subfields: Applied Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/45d998057bdd16f7a6bfd9485d8b8ae23b9abf87

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Applied Mathematics

1. Razvan C. Fetecau
2. Theodore Kolokolnikov
3. Andrea L. Bertozzi
4. Rustum Choksi
5. Ihsan Topaloglu
6. Thomas Laurent
7. José Antonio Carrillo
8. Dong Li

In Mathematical Physics

1. Andrea L. Bertozzi
2. James von Brecht
3. José Antonio Carrillo

Citations in the corpus

• Ring patterns and their bifurcations in a nonlocal model of biological swarms (2015, background): “Recently, it was shown in [1] that the Hausdorff dimension of the steady state in two dimensions is at least 1−p provided that −1≤p≤1, which is consistent with our analysis of the high-mode perturbations.”
• On minimizers of interaction functionals with competing attractive and repulsive potentials (2015, methodology): “The repulsion exponent p in [4] is restricted to be above the Newtonian singularity, i.”