ONE-DIMENSIONAL SHORT-RANGE NEAREST-NEIGHBOR INTERACTION AND ITS NONLINEAR DIFFUSION LIMIT - Archive ouverte HAL Accéder directement au contenu
Article Dans Une Revue SIAM Journal on Applied Mathematics Année : 2024

ONE-DIMENSIONAL SHORT-RANGE NEAREST-NEIGHBOR INTERACTION AND ITS NONLINEAR DIFFUSION LIMIT

Résumé

Repulsion between individuals within a finite radius is encountered in numerous applications, including cell exclusion, i.e. an overlap of cells to be avoided, bird flocks, or microscopic pedestrian models. We define such individual based particle dynamics in one spatial dimension with minimal assumptions of the repulsion force f and prove their characteristic properties. Moreover, we are able to perform a rigorous limit from the microscopic-to the macroscopic scale, where we could recover the finite interaction radius as a density threshold. Specific choices for the repulsion force f lead to well known nonlinear diffusion equations on the macroscopic scale, as e.g. the porous medium equation. At both scaling levels numerical simulations are presented and compared to underline the analytical results. We discuss the possible applications of this new diffusion term.
Fichier principal
Vignette du fichier
FKS.pdf (1.24 Mo) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)

Dates et versions

hal-04002707 , version 1 (23-02-2023)
hal-04002707 , version 2 (04-10-2023)

Identifiants

Citer

Michael Fischer, Laura Kanzler, Christian Schmeiser. ONE-DIMENSIONAL SHORT-RANGE NEAREST-NEIGHBOR INTERACTION AND ITS NONLINEAR DIFFUSION LIMIT. SIAM Journal on Applied Mathematics, 2024, 84 (1), pp.1-18. ⟨10.1137/23M155520X⟩. ⟨hal-04002707v2⟩
46 Consultations
20 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More