Ensemble averageability in network spectra

The extreme eigenvalues of connectivity matrices govern the influence of the network structure on a number of network dynamical processes. A fundamental open question is whether the eigenvalues of large networks are well represented by ensemble averages. Here we investigate this question explicitly and validate the concept of ensemble averageability in random scale-free networks by showing that the ensemble distributions of extreme eigenvalues converge to peaked distributions as the system size increases. We discuss the significance of this result using synchronization and epidemic spreading as example processes.Comment: 4 pages, 4 figure

Absorption cross section and Hawking radiation in two-dimensional AdS black hole

We calculate the absorption coefficient of scalar field on the background of the two-dimensional AdS black hole, which is of relevance to Hawking radiation. For the massless scalar field, we find that there does not exist any massless radiation.Comment: 6 pages, revtex, no figure

A Review of Double-Walled and Triple-Walled Carbon Nanotube Synthesis and Applications

Double- and triple-walled carbon nanotubes (DWNTs and TWNTs) consist of coaxially-nested two and three single-walled carbon nanotubes (SWNTs). They act as the geometrical bridge between SWNTs and multi-walled carbon nanotubes (MWNTs), providing an ideal model for studying the coupling interactions between different shells in MWNTs. Within this context, this article comprehensively reviews various synthetic routes of DWNTs’ and TWNTs’ production, such as arc discharge, catalytic chemical vapor deposition and thermal annealing of pea pods (i.e., SWNTs encapsulating fullerenes). Their structural features, as well as promising applications and future perspectives are also discussed. Keywords: carbon nanotubes; double-walled carbon nanotubes; triple-walled carbon nanotubes; synthesis; catalytic chemical vapor deposition; arc discharge; fullerenes; pea pod