Heat flux localization and abnormal size effect induced by multi-body vibration in complex networks

Heat conduction in real physical networks such as nanotube/nanowire networks has been attracting more and more attention, but its theoretical understanding is far behind. To open a way to this problem, we present a multi-body vibration model to study heat conduction in complex networks, where nodes’ degrees satisfy a random distribution, and links consist of 1D atom chains with nonlinear springs. Based on this model, we find two interesting phenomenons: (1) The main heat fluxes of a network always localize in a skeleton subnetwork, which may have potential applications in thermal management and thermal concentrators, and (2) there exists an abnormal size effect of heat conduction in complex networks, i.e., the total heat flux of a network will enlarge with the increase of atoms on links, which is in contrast to the previous result on a 1D chain. Furthermore, we introduce a transmission diagram to characterize the skeleton of localized heat fluxes and then discover a jumping transition of total heat flux in the process of removing links, implying that the control of heat flux can be effective only when the change in a network topology focuses on the links within the skeleton. A brief theory is introduced to explain the abnormal size effect.