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AKSOE: Arbeitskreis Physik sozio-ökonomischer Systeme

AKSOE 4: Dynamics of Groups and Organizations II

AKSOE 4.3: Vortrag

Montag, 25. Februar 2008, 15:00–15:30, EW 203

Surrounding of clusters in a one-dimensional system — •Julian Sienkiewicz and Janusz Holyst — Faculty of Physics, Warsaw University of Technology, Poland

We investigate evolution of a system consisting of randomly added two-state objects e.g. spins or group members having one of the two opinions. Our numercial and analytical calculations show that even a simple one-dimensional model (a chain of N nodes) provides interesting results. The system’s dynamics is described as follows: in each time step we add a spin with opposite value at a random, not occupied node in the chain until there is no space left in the chain. If after the addition of a new spin, there is a cluster (n consecutive spins with the same sign) surrounded by two spins of the opposite sign - the spins in the cluster are turned inactive. Those nodes no longer interact with the rest of the chain. In the investigated system the critical density - the moment at which the first blocked spin appears vanishes in the termodynamical limit (N goes to infinity). The rescaled number of the blocked nodes Z / N increases with the rescaled time t / N as (Z / N) ∼ (t / N)^γ with γ exponent close to 3. We believe that the future generalization on other structures (2D, 3D and arbitrary complex network) can be used to model the process of one community being surrounded by another one.