Influence of the degree of a complex network on heat conduction

Devices made of nanotubes and nanowires networks are of great interest for applications and have caught increasing attention in recent years. In this work, we study heat conduction in a network model with nodes being atoms and links being one-dimensional chains of atoms. It is found that heat conduction in the complex network is fundamentally different from that of regular lattices. It depends very sensitively on the average degrees of complex networks and the degrees of nodes that are attached to the two heat baths. For example, when the two heat source nodes have the same degree k_{0}, the heat flux reaches a maximum at an optimized value of k_{0} and decreases with the increase of the average degree 〈k〉. In other words, the source nodes with optimal degree k_{0} and the sparse network are more favorable to heat flux. Thermal rectification effect is found when the two heat source nodes have different degrees or the network model has multiple heat source nodes. Theoretical analysis is provided to explain the numerical results.