High field breakdown of narrow quasi uniform field gaps in vacuumThe electric-field behavior at the triple junction of metal-dielectric-vacuum is theoretically investigated. For a two-dimensional junction in which the electric-field magnitude F behaves as r Ϫ1 , is obtained as a function of the configuration geometry and the dielectric constant. It is found that varies with the dielectric portion in the field-varying region, becoming as low as 0.25 in the extreme case. The enhancement of F due to the reduction of is responsible for the field emission enhancement as well as the vacuum insulation breakdown at the triple junction.
Entropy plays a key role in statistical physics of complex systems, which in general exhibit diverse aspects of emergence on different scales. However, it still remains not fully resolved how entropy varies with the coarse-graining level and the description scale. In this paper, we consider a Yule-type growth model, where each element is characterized by its size being either continuous or discrete. Entropy is then defined directly from the probability distribution of the states of all elements as well as from the size distribution of the system. Probing in detail their relations and time evolutions, we find that heterogeneity in addition to correlations between elements could induce loss of information during the coarse-graining procedure. It is also revealed that the expansion of the size space domain depends on the description level, leading to a difference between the continuous description and the discrete one.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.