The Criticality Of Non-conservative Earthquake Models On Random Local Area Networks

The concept of self-organized criticality(SOC)play an important role in physics.Earthquakes may be the most dramatic example of SOC that can be observed by humans on earth.Then Olami,Feder,and Christensen(OFC)introduced a nonconservative model on a lattice that displayed SOC in 1992.The distribution of avalanche sizes is followed by a power-law function,and the power-law exponent depends on the dissipation parameter in the OFC model.Since then,the model has attracted wide attention.And several extended models are proposed according to the model.The main research of this paper is to make some changes in the OFC model to be closer to the reality and consists of two chapters as follows:First,we investigate the critical behavior on a modified anisotropic OFC model.Two situations are considered in this paper.One situation is that the energy of the unstable site is redistributed to its nearest neighbors randomly not averagely and keeps itself to zero.The other situation is that the energy of the unstable site is redistributed to its nearest neighbors randomly and keeps some energy for itself instead of reset to zero.Different boundary conditions were considered as well.By analyzing the distribution of earthquake sizes,we found that self-organized criticality can be excited only in the conservative case or the approximate conservative case in the above situations.Some evidence indicated that the critical exponent of both above situations and the original OFC model tend to the same result in the conservative case.The only difference is that the avalanche size in the original model is bigger.This result may be closer to the real world,after all,every crust plate size is different.Than we study the nonconservative earthquake model on a random spatial network.The spatial networks are composed by sites on a 2D plane which are connected locally.Different from the regular lattice,the randomness of sites is modelled in the way that sites are randomly placed on the plane.Use the same connectivity degree as the 2D lattice,however,the spatial network cannot exhibit critical earthquake behavior.Mimicking the long-range energy transfer,the connection radius is increased and the connectivity degree of the spatial network is increased.Then we show that the model exhibits self-organized criticality.The mechanism of the structural effect is presented.The spatial network includes many modules when connectivity degree is very small.The effect of modular structure on the avalanche dynamics is to limit the spreading of avalanches in the whole network.When the connectivity degree is larger,the long-range energy transfer can overcome the effect of local modularity and the criticality can be reached.We believe that these results provide a new theoretical understanding of the role of coupled structures in earthquake self organized criticality behavior.