Physical Mechanism Underlying Opinion Spreading. Jia Shao Advisor: H. Eugene Stanley. J. Shao, S. Havlin, and H. E. Stanley, Phys. Rev. Lett. 103 , 018701 (2009). Questions. How do different opinions influence each other in human society? Why minority opinion can persistently exist?.
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Physical Mechanism Underlying Opinion Spreading
Advisor: H. Eugene Stanley
J. Shao, S. Havlin, and H. E. Stanley, Phys. Rev. Lett. 103, 018701 (2009).
US presidential elections
Instead of using individual level
network, we propose a community
level network to study opinion
We study counties with f>fT
Vote for Obama
County network of f>fT=0.6
Number of counties:17
Size of largest cluster: 10
Counties of fObama>fT
Counties of fMcCain>fT
Fractal dimension: dl=1.56
The phase transition in county network is
different from randomized county network.
What class of percolation does this phase transition
Example: Inject water into earth layer containing oil
not be invaded.
A: Injection Point
P. G. de Gennes and E. Guyon, J.Mech. 17, 403(1978).
D. Wilkinson and J. F. Willemsen, J. Phys. A 16, 3365 (1983).
Trapped Region of size s
P(s) ~ s-1.89
Fractal dimension: 1.51
S. Schwarzer et al., Phys. Rev. E. 59, 3262 (1999).
(no one in local
stable state : =1:4
stable state : =1:1
size of the second
critical initial fraction fc=0.5
Edges connect randomly
Poisson distribution: Power-law distribution:
Q1: At fc , what is the distribution of cluster size“s”?
Q2: What is the average distance“r” between nodes belonging to the same cluster?
Cumulative distribution function
P(s’>s) ~ s-0.89
s ~ r1.84
PDF P(s) ~ s-1.89
Conclusion: “Phase transition” of opinion model belongs to the
same universality class of invasion percolation.