PHYS96008 - Complexity and Networks. (incl. rice-pile modeling & BA Network Model)
Ricepiles were investigated using the Oslo Model as an example of a system with self-organised criticality, where the model’s characteristics were analysed. Key results include: a0 = 1.737 and ω1 = 0.548 for height scaling using chi-square minimisation. D = 2.2149 and τs = 1.5549 for avalanche size scaling from moment analysis.
Relationships of h ∝ t0.506 and σh ∝ L0.253 where found. Data collapses for height, height probability and avalanche size probability were completed, where the latter required log-binning. Scaling corrections were investigated for height, cross-over time, standard deviation of height and moments of avalanche size. Sites were found to tend to identical, but not independent behaviour.
Additional scaling correction constants were found for avalanche size moments, indicating possible power law dependencies on k.
The Barabasi-Albert Model was investigated with three attachment models: preferential attachment, random attachment, and random walk with preferential attach- ment. Theoretical derivations with experimental tests were carried out for the degree distribution and largest degree for random and preferential attachment. A two-sample Kolmogorov–Smirnov test was used to test goodness of fits, with log-binning used to remedy fat-tails.
Additionally, a data collapse of varying N was done for preferential attachment. For random walk, different q values were tested to show the progression of the degree distribution from random to preferential attachment. It was found for N = 1000, m = 2 with no repeats, the distribution transitioned to random at q = 0.30 ± 0.02 and transitioned to preferential at q = 0.76 ± 0.02.
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| Complexity Report | Networks Report |