Investigations On Dynamics Of Particle Condensation And Its Application On Complex Networks

The condensation is an intriguing phenomenon observed in nonequilibrium systems. In interacting particle systems, a finite fraction of particles may be con-densed onto a single site. The condensation has been studied mostly on regular lattices. On the other hand, particularly, many real-world networks are found to be scale-free. Noh et al. has studied the condensation phenomenon in a zero range process (ZRP) on scale-free networks. They show that the stationary state depends only on the degree distribution of underlying networks. The model displays a stationary state phase transition between a condensed phase and an uncondensed phase. Enlightened by this work, we focus on condensation phe-nomenon on complex networks:ZRP condensation, the fluctuation of particles and particle diffusion in condensed phase, traffic congestion, and their applica-tions in epidemic spreading.1. We study the condensation phenomenon in a ZRP on weighted scale-free networks in order to show how the weighted transport influences the particle condensation. Instead of the approach of grand canonical ensemble which is generally used in a ZRP, we introduce an alternate approach of the mean-field equations to study the dynamics of particle transport. We find that the stationary state of particle is determined by the strength distribution, in contrary to the case of the same weight on the edge where the stationary state is determined by the degree distribution. Moreover, we find that there is a hierarchical relaxation dy-namics in the evolution. We also show that the relaxation time follows a power law with the network size in the condensed phase and depends on both the net-work topology and the jumping exponent.2. We here investigate the fluctuation of particles on each individual node and particle diffusion at equilibrium status. For the former, we find that the par- ticle distributions can be normalized to the same Gaussian distribution, which is independent of the nodes and network structures. By the approach of detrended fluctuation analysis we reveal that the correlation exponents of particle fluctua-tions may reflect the information of particle condensation and be useful in explor-ing the network structure. For the latter, we show that the statistical quantities of diffusion can be significantly reduced by the condensation and can be figured out by the time delay of a particle staying at a node.3. Revealing the mechanism of the traffic congestion and enhancing the per-formance of a network to avoid congestion are very valuable problems in trans-portation networks. We consider three different traffic models: stationary traffic, time-varying traffic, and the limited bandwidth. For the different traffic models, we propose some effective routing strategies to enhance the congestion thresh-old and reduce travel times in scale-free networks. Our study can provide some valuable suggestions for routing in real systems.4. We investigate the influences of two characteristic features of condesation phenomenon on epidemic spreading in scale-free networks. For the first one, we investigate how the condensation of moving bosonic particles influences the epi-demic spreading in scale-free metapopulation networks. Our mean-field theory shows that condensation can significantly enhance the effect of epidemic spread-ing and reduce the threshold for epidemic to survive. For the second one, we present a reaction-traveling model to study how the objective traveling influences the epidemic spreading. Through a SIS model we theoretically prove that near the threshold of epidemic outbreak, the objective traveling can significantly enhance the final infected population and the infected fraction at a node is proportional to its betweenness for the traveling agents and approximately proportional to its degree for the non-traveling agents.