The coalescing colony model: mean-field, scaling, and geometry

Abstract : We analyze the coalescing model where a 'primary' colony grows and randomly emits secondary colonies that spread and eventually coalesce with it. This model describes population proliferation in theoretical ecology, tumor growth and is also of great interest for modeling the development of cities. Assuming the primary colony to be always spherical of radius $r(t)$ and the emission rate proportional to $r(t)$$^ \theta$ where $ \theta$ > 0, we derive the mean-field equations governing the dynamics of the primary colony, calculate the scaling exponents versus $ \theta$ and compare our results with numerical simulations. We then critically test the validity of the circular approximation and show that it is sound for a constant emission rate ($ \theta$ = 0). However, when the emission rate is proportional to the perimeter, the circular approximation breaks down and the roughness of the primary colony can not be discarded, thus modifying the scaling exponents.
Type de document :
Pré-publication, Document de travail
2017
Liste complète des métadonnées

Littérature citée [4 références]  Voir  Masquer  Télécharger

https://hal-cea.archives-ouvertes.fr/cea-01626261
Contributeur : Emmanuelle De Laborderie <>
Soumis le : lundi 30 octobre 2017 - 15:23:57
Dernière modification le : jeudi 15 mars 2018 - 15:05:19
Document(s) archivé(s) le : mercredi 31 janvier 2018 - 12:53:21

Fichier

1709.08628.pdf
Fichiers produits par l'(les) auteur(s)

Identifiants

  • HAL Id : cea-01626261, version 1

Citation

Giulia Carra, Kirone Mallick, Marc Barthelemy. The coalescing colony model: mean-field, scaling, and geometry. 2017. 〈cea-01626261〉

Partager

Métriques

Consultations de la notice

37

Téléchargements de fichiers

15