Percolation

Percolation originally means that “to filter” or “trickle through”. Here, in statistical physics, it often refers to a simple model and the corresponding profound theoretical system, which touches many concepts of statistical physics and nonlinear physics, such as scaling, renormalization, phase transition, critical phenomena and fractal. Due to the complexity involved in obtaining exact results from analytical models of percolation, computer simulations are typically used. So computational methods is also involved in the study of percolation model. Now, percolation model is often taken as the typical model to study computational physics with Ising model.

Our reasearch interests include the critical phenomena of the percolation transition on various networked systems, as well as some extended models. Besides, we also study the applications of percolation theory on some real problems, especially for network structure analysis.

Please refer to Percolation Theory in Wikipedia for the details of the percolation model.

Complex networks

In recent years, much researches have been carried out to explore the structural properties and dynamics of complex networks. Why so much focus on complex networks? Firstly, networks are ubiquitous in almost every aspect of our lives, such as communication networks, Internet, relationship networks, neural networks and metabolic networks. Understanding how these networks work is highly meaningful for improving the qualities of our lives, that’s exactly what the scientists like to do. Secondly, in modern physics and other related disciplines, networks with simple topologies can no longer meet the requirements of describing the structural relationships among the components of a system. Therefore, complex networks must be studied to give a new tool to deal with these problems.

There are many networks of interest to scientists that are composed of individual parts or components linked together in some way. For example, the Internet is a collection of computers linked by data connections. As also noted, human societies are collections of people linked by acquaintance or social interaction. In a concept of complex networks, they all can be presented as a network, the components of the system being the network nodes and the connections or interactions the links. In this way, the systems can be studied mathematically. In another perspective, these networks are all many-body systems, which can be studied using statistical mechanics. Facing the gigantic network information, the physics approach may be the most advantageous for the understanding of the structures and dynamics of networks. Actually, many approaches used today in complex networks are a directed generalization of the classical methods in statistical mechanics, such as ensemble theory, phase transition theory, mean field method, Ising model and percolation model. Besides, the complex network also present challenges to physics, such as dynamics in a strong heterogeneous system, and phase transition in the infinite dimension systems.

All these are things that we’re interested in.

Please refer to Network Science in Wikipedia for the more information of complex networks.

Nonlinear dynamics

We also study nonlinear dynamics in complex systems, including evolutionary game, epidemic spreading, and traffic flow.