Physical Mechanism Underlying Opinion Spreading. Jia Shao Shlomo Havlin, H. Eugene Stanley. J. Shao, S. Havlin, and H. E. Stanley, Phys. Rev. Lett. 103 , 018701 (2009). Questions. How can we understand, and model the coexistence of two mutually exclusive opinions?
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Shlomo Havlin, H. Eugene Stanley
J. Shao, S. Havlin, and H. E. Stanley, Phys. Rev. Lett. 103, 018701 (2009).
Example: US presidential elections
Example:the Amish people
to demonstrate both.
(no one in local
stable state : =1:4
stable state : =1:1
size of the second
critical initial fraction fc=0.5
Preferential Attachment2 classes of network: differ in degree k distribution
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?
Example: Inject water into layer containing oil
not be invaded.
A: Injection Point
D. Wilkinson and J. F. Willemsen, J. Phys. A 16, 3365 (1983).
Trapped Region of size s
P(s) ~ s-1.89
Fractal dimension: 1.84
S. Schwarzer et al., Phys. Rev. E. 59, 3262 (1999).
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.