%0 Book Section %1 statphys23_0085 %A Dotenco, D. %A Paladi, F. %B Abstract Book of the XXIII IUPAP International Conference on Statistical Physics %C Genova, Italy %D 2007 %E Pietronero, Luciano %E Loreto, Vittorio %E Zapperi, Stefano %K cluster complex dynamics glassy metastable state statphys23 system topic-3 %T Clustering in Complex Systems: an Application to Nucleation and Glassy Dynamics %U http://st23.statphys23.org/webservices/abstract/preview_pop.php?ID_PAPER=85 %X A theoretical model based on the cluster theory was developed and used to simulate the dynamics of complex systems, composed of a number of interacting agents-clusters, with different sizes $M$ 1. The case of systems formed by a constant total number of agents in metastable (partial) equilibrium was considered, and the size effect on the formation of groups of agents (clusters) was particularly elucidated. \newline The results indicate the importance of a concrete mechanism by which the agents-clusters change their size, regardless of the model used to study the kinetics of random evolution. For early and late stages of cluster formation, they are expected to grow and decay mainly by gaining and losing single agents, because a relatively low cluster concentration at the early stage and an immobile, stable structure at the late stage would require a single-agent mechanism of cluster formation without a preferential attachment. The advanced stage could be characterized additionally by the merge of agents-clusters into a new bigger one, and the leading role in this coalescence process will be played by the binary contacts between them. The probability for mutual contacts between the clusters of various sizes increases at this stage, and the contacts between them begin to have an increasingly important role in size changes, because many of the initially present agents are already absorbed by the growing clusters and both the clusters concentration and their mobility are relatively high. In this way an $n $-sized cluster can become larger not only by attaching a single agent, but also by merging with other clusters. \newline We prove that the random evolution of groups of agents definitely depends on the size of the group. The average group (cluster) size problem was also solved for different values of $M $, and the process of relaxation in the system was studied. The role of attachment probability is described by comparison between this model and other kinetic models of random growing networks and herding phenomena. In order to include the effects of fluctuations, we further consider a finite-dimensional lattice model. In particular, numerical simulations are performed for a chain, square and cubic lattices, where the coordination numbers of these lattices are 2, 4 and 6, respectively. In addition to the emergence of different time scales, the model displays metastability, and the metastable states are usually called attractors or quasi-states. The number of metastable states increases exponentially with the system size and configurational entropy, or complexity. Spatial correlation between clusters, which is especially meaningful in the long-time limit, and spatial patterns of attractors, or metastable states, where every surviving cluster is isolated, are also studied.\\ 1) F.Paladi and V.Eremeev, Physica A 348 (2005) 630-640.

@incollection{statphys23_0085, abstract = {A theoretical model based on the cluster theory was developed and used to simulate the dynamics of complex systems, composed of a number of interacting agents-clusters, with different sizes $\it M$ [1]. The case of systems formed by a constant total number of agents in metastable (partial) equilibrium was considered, and the size effect on the formation of groups of agents (clusters) was particularly elucidated. \newline The results indicate the importance of a concrete mechanism by which the agents-clusters change their size, regardless of the model used to study the kinetics of random evolution. For early and late stages of cluster formation, they are expected to grow and decay mainly by gaining and losing single agents, because a relatively low cluster concentration at the early stage and an immobile, stable structure at the late stage would require a single-agent mechanism of cluster formation without a preferential attachment. The advanced stage could be characterized additionally by the merge of agents-clusters into a new bigger one, and the leading role in this coalescence process will be played by the binary contacts between them. The probability for mutual contacts between the clusters of various sizes increases at this stage, and the contacts between them begin to have an increasingly important role in size changes, because many of the initially present agents are already absorbed by the growing clusters and both the clusters concentration and their mobility are relatively high. In this way an $\it n $-sized cluster can become larger not only by attaching a single agent, but also by merging with other clusters. \newline We prove that the random evolution of groups of agents definitely depends on the size of the group. The average group (cluster) size problem was also solved for different values of $\it M $, and the process of relaxation in the system was studied. The role of attachment probability is described by comparison between this model and other kinetic models of random growing networks and herding phenomena. In order to include the effects of fluctuations, we further consider a finite-dimensional lattice model. In particular, numerical simulations are performed for a chain, square and cubic lattices, where the coordination numbers of these lattices are 2, 4 and 6, respectively. In addition to the emergence of different time scales, the model displays metastability, and the metastable states are usually called attractors or quasi-states. The number of metastable states increases exponentially with the system size and configurational entropy, or complexity. Spatial correlation between clusters, which is especially meaningful in the long-time limit, and spatial patterns of attractors, or metastable states, where every surviving cluster is isolated, are also studied.\\ 1) F.Paladi and V.Eremeev, Physica A 348 (2005) 630-640.}, added-at = {2007-06-20T10:16:09.000+0200}, address = {Genova, Italy}, author = {Dotenco, D. and Paladi, F.}, biburl = {https://www.bibsonomy.org/bibtex/2ddf8548b97df253c63d1da5468aa160b/statphys23}, booktitle = {Abstract Book of the XXIII IUPAP International Conference on Statistical Physics}, editor = {Pietronero, Luciano and Loreto, Vittorio and Zapperi, Stefano}, interhash = {4359fb8c5e44f24e1f34839936fb706b}, intrahash = {ddf8548b97df253c63d1da5468aa160b}, keywords = {cluster complex dynamics glassy metastable state statphys23 system topic-3}, month = {9-13 July}, timestamp = {2007-06-20T10:16:11.000+0200}, title = {Clustering in Complex Systems: an Application to Nucleation and Glassy Dynamics}, url = {http://st23.statphys23.org/webservices/abstract/preview_pop.php?ID_PAPER=85}, year = 2007 }