Institut de Physique Théorique
Direction de la Recherche Fondamentale  -  Saclay
UMR 3681 - INP
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Mardi 24 avril 2018

Publication : t17/162


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

Carra G. (CEA, IPhT (Institut de Physique Théorique), F-91191 Gif-sur-Yvette, France)
Mallick K. (CEA, IPhT (Institut de Physique Théorique), F-91191 Gif-sur-Yvette, France)
Barthélémy M. (CEA, IPhT (Institut de Physique Théorique), F-91191 Gif-sur-Yvette, France)
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) θ where θ>0 , we derive the mean-field equations governing the dynamics of the primary colony, calculate the scaling exponents versus θ 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 (θ=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.
Année de publication : 2017
Preprint : arXiv:1709.08628
Langue : Anglais

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