Journal of Statistical Mechanics: Theory and Experiment
Volume 2009
November 2009
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Andrea Baronchelli and Romualdo Pastor-Satorras J. Stat. Mech. (2009) L11001 doi:10.1088/1742-5468/2009/11/L11001
Effects of mobility on ordering dynamics
FREE ARTICLEAndrea Baronchelli and Romualdo Pastor-Satorras
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| Figure 1. (a) Density of + 1 individuals as a function of the degree in MVM and MMP on heterogeneous scale-free networks generated with the (uncorrelated) configuration model [22] with degree distribution P(k) ~ k–2.5 for different values of p = p+ 1 = p–1 (curves are shifted vertically for clarity). (b) Partial density of + 1 individuals as a function of time (p+ 1 = p–1 = 0.5) in scale-free networks. ((c), main) and (d) partial density of + 1 individuals as a function of time for the MVM in scale-free and fully connected networks, respectively. Dashed lines represent the theoretical slope |p+ 1–p–1|–1 (p–1 = 0.7). Data from single runs with homogeneous initial conditions ρ+ 1(0) = ρ–1(0) = 10, in networks of size V = 103. ((c), inset) Also in the low mobility case (p+ 1 = 0.05, p–1 = 0.1) averaged curves for fully connected (empty circles) and scale-free networks (full circles) collapse well to an exponential decay. |
Figure 2. Left: scaling of the fixation time for the MVM and MMP with mobility
p+ 1 = p–1 = p, in the limit  (top) and  (bottom), in fully connected networks. Right: rescaled fixation time for the MVM and MMP with mobility p+ 1 = p–1 = p in fully connected (FC) and scale-free (SF) networks of different sizes. Dashed lines are nonlinear fits to the functional form equation (7) for  and  . Data refer to homogeneous initial conditions. |
Figure 3. Ordering mechanisms as a function of mobility. In the limit (black curves) local order ( (t)) grows in short time, while global order (ψ(t)) emerges as a result of vertex–vertex competition. When (red curves), on the other hand, local order emerges only as a result of global ordering at late times. Data refer to a fully connected network with
V = 100 with homogeneous initial conditions ρ+ 1(0) = ρ–1(0) = 10. |
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Effects of mobility on ordering dynamics
Andrea Baronchelli and Romualdo Pastor-Satorras J. Stat. Mech. (2009) L11001
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