Partenaires

MSC
Logo CNRS Logo Université Paris Diderot
Logo tutelle Logo tutelle



Search

On this website

On the whole CNRS Web


Home page > Séminaires > Archives séminaires > Séminaires 2016 > Séminaire MSC. Lundi 4 avril 2016. Jean Baptiste Delfau (CSIC-UIB, Espagne) : "Pattern forming instabilities leading to the formation of hexagonal clusters." .

Séminaire MSC. Lundi 4 avril 2016. Jean Baptiste Delfau (CSIC-UIB, Espagne) : "Pattern forming instabilities leading to the formation of hexagonal clusters."

Sauf mention contraire, les séminaires et les soutenances se déroulent à 11h30 en salle 454A du bâtiment Condorcet.


Pattern forming instabilities leading to the formation of hexagonal clusters

Jean-Baptiste Delfau

Instituto de Física Interdisciplinar y Sistemas Complejos (CSIC-UIB) Campus Universitat de les Illes Balears Palma de Mallorca, Spain

Abstract : It is well known amongst physicists that seemingly distinct systems can sometimes exhibit strikingly similar behaviors under some circumstances. Here, we draw a parallel between two comparable cases of clustering observed in very different models : on the one hand, Brownian particles interacting via a \soft potential", purely repulsive but allowing overlaps between particles (two characteristics typical of various types of polymeric macromolecules like polymer chains or dendrimers for example). On the other hand, a model of population dynamics with neighborhood dependent birth and death rates, accounting for the spatial heterogeneity of the competition between individuals. Both of these systems exhibit a similar phase transition leading to a segregation of their particles into clusters arranged in hexagonal patterns. Macroscopic equations can be derived for the two models and their structures are quite comparable, despite the fact that the number of particles is not conserved in the second case. Their linear stability analysis shows that this clustering is induced by an instability of the homogeneous state, triggered by the non-local mutual interactions.

Work in collaboration with : H. Ollivier, E. Hernandez-Garcia, C. Lopez, and B. Blasius.

Top Hexagonal clustering : numerical integration of the Dean-Kawasaki equation for a system of Brownian particles interacting via a purely repulsive soft potential.

Top Hexagonal clustering : particles simulation showing the onset of hexagonal clusters in a system of Brownian particles with neigh- borhood dependent birth and death rates.


Contact : Équipe séminaires / Seminar team - Published on / Publié le 24 février 2016


Dans la même rubrique :