The Phase Transition Of Ising Model On Complex Networks And The Dynamics Of Network Transportation

Complex network is an important method to study complex system. On the basis of complex network theory, the phase transition of a one-dimensional Ising model with distance-dependent connections, network opinion evolution and the statistical properties of the dynamics of particle transportation are studied in this thesis.1. The work about one-dimensional Ising model with distance-dependent connections:To study the impact of the long-range connections, critical behavior of the Ising model on a one-dimensional network, which has long-range connections at distances l > 1 with the probabilityθ(l)～l^-m is studied. With the finite-size scaling analysis of the Binder cumulant U_N, the susceptibility X, the specific heat C_v and the order-parameter M, it is observed that in the whole range of 0 < m < 2, a finite-temperature phase transition exists, and the critical exponents show consistence with mean-field values, which indicates a mean-field nature of the phase transition.2. The work about network opinion evolution:In the first work about network opinion evolution, a multi-agent modeling environment is constructed to simulate the process of how media influences a population of agents' ranking of the importance of a set of issues. With the study of agents' prioritization of new issue and the average impact of different resource allocation strategies, the results indicate that, different allocation strategies result in similar trends of the evolution of the average prioritization of the new issue. The greater the resources invested in order to obtain coverage from the large media, the greater the average impact over the population. What's more, the average impact is higher the less connected the agents in the network.In the second work about network opinion evolution, we go further to study the evolution of one single opinion under the influence of the interaction among agents and the external field. Here, a model without the bounded confidence is proposed. The macro-behavior of the average opinion and it's relative change rate after the canceling of the external field are studied. The results show that the external field and the underlying network both play important role in making the opinion balance or increase. Without the influence of the external field, the relative change rate shows a nonlinear increasing behavior which is independent of the initial condition, the strength of the external field and the time that we cancel the external field. And that, the time when the opinion gets extreme value has a power-law relationship with the power of the external field.3. The work about particle transportation:Limited node capacity of holding particles is proposed for the first time to study congestion from the local point of view. The time-dependent activity of each node captures the network transportation system's dynamics from a different angle, so that these parallel time series can increasingly complete the information about the systems's collective behavior. In the first work about particle transportation, one abstract method is proposed by interpolating the properties of the edges that constitute network into the two leading parameters of the nodes. What's more, one new criterion parameter, congestion time T_c, is defined. Then this abstract method is applied to the traffic problem in the process of city expansion. The observation of the relationship between T_c and network size N reveals that the width and distance from one crossroad to another can be designed properly to enlarge the tolerance size of the city, consequently avoid frequent reconstruction or over-estimated building of city roads.In the second work about particle congestion, with the algorithm of avoiding congestion, the statistical property of the number of over-capacity nodes is studied. During the simulation, the particles are delivered according to the shortest-path algorithm and the smallest-degree algorithm. The shortest-path algorithm is the most rapid transportation algorithm while the smallest-degree algorithm is the most efficient transportation algorithm to avoid congestion. During the simulation, the evolution of the number of over-capacity nodes A(t) and the cumulative particle life-time L_c(t) are studied. The results show that, the interaction of the two algorithm results in the punctuated equilibrium behavior of the number of the over-capacity nodes, and the average number of the over-capacity nodes under different punctuated interval has similar relationship with the punctuated point. The study of the cumulative particle-life time reveals that the smallest-degree algorithm improves network transportation at the cost of prolonging the delivering time.Real-life network transportation system has pseudo-congestion. Pseudo-congestion prolongs the transportation time but do not cause the collapse the transportation system. So that it is very important to find the second-order phase transition of the dynamics of network transportation. In the third work about particle transportation, the self-adaptive algorithm to avoid congestion is going be added so as to seek for proper order-parameter to study this second-order phase transition so as to make the study of network congestion closer to real-life.