A deterministic model of competitive cluster growth: glassy dynamics, metastability and pattern formation
Service de Physique Théorique (URA 2306 of CNRS) ,
CEA Saclay, 91191 Gif-sur-Yvette Cedex, France
2 S.N. Bose National Centre for Basic Sciences, Block JD, Sector 3, Salt Lake, Calcutta 700098, India
Published online: 16 April 2005
We investigate a model of interacting clusters which compete for growth. For a finite assembly of coupled clusters, the largest one always wins, so that all but this one die out in a finite time. This scenario of `survival of the biggest' still holds in the mean-field limit, where the model exhibits glassy dynamics, with two well separated time scales, corresponding to individual and collective behaviour. The survival probability of a cluster eventually falls off according to the universal law . Beyond mean field, the dynamics exhibits both aging and metastability, with a finite fraction of the clusters surviving forever and forming a non-trivial spatial pattern.
PACS: 05.45.-a – Nonlinear dynamics and nonlinear dynamical systems / 47.54.+r – Pattern selection; pattern formation / 89.75.-k – Complex systems / 64.60.My – Metastable phases
© EDP Sciences, Società Italiana di Fisica, Springer-Verlag, 2005