We present a percolation process in which the classical Erdo¨s–Re′nyi(ER) random evolutionary network is intervened by the product rule(PR) from some moment t0. The parameter t0is continuously tunable over the real interval [0, 1].This model becomes the random network under the Achlioptas process at t0= 0 and the ER network at t0= 1. For the percolation process at t0≤ 1, we introduce a relatively slow-growing point, after which the largest cluster begins growing faster than that in the ER model. A weakly discontinuous transition is generated in the percolation process at t0≤ 0.5.We take the relatively slow-growing point as the lower pseudotransition point and the maximum gap point of the order parameter as the upper pseudotransition point. The critical point can be approximately predicted by each fitting function of the two points about t0. This contributes to understanding the rapid mergence of the large clusters at the critical point.The numerical simulations indicate that the lower pseudotransition point and the upper pseudotransition point are equal in the thermodynamic limit. When t0> 0.5, the percolation processes generate a continuous transition. The scaling analyses of several quantities are presented, including the relatively slow-growing point, the duration of the relatively slow-growing process, as well as the relatively maximum strength between the percolation percolation at t0< 1 and the ER network about different t0. The presented mechanism can be viewed as a two-stage percolation process that has many potential applications in the growth processes of real networks.
A broadband negative refractive index metamaterial based on a windmill-like structure is proposed, and investigated numerically and experimentally at the microwave frequency range. From the numerical and experimental results, effect media parameters are retrieved, which clearly show that two broad frequency bands exist in which the permittivity and permeability are negative. The two negative bands are from 9.1 GHz to 10.5 GHz and from 12.05 GHz to 14.65 GHz respectively, and the negative bandwidth is 4 GHz. Due to the good bandwidth performance, the metallic cell with double negative property obtained in this paper is suitable for use in the design of multiband or broadband microwave devices.
A low absorptivity broadband negative refractive index metamaterial with a multi-gap split-ring and metallic cross (MSMC) structure is proposed and investigated numerically and experimentally in the microwave frequency range. The effective media parameters were retrieved from the numerical and experimental results, which clearly show that there exists a very wide frequency band where the permittivity and permeability are negative. The influence of the structure parameters on the magnetic response and the cut-off frequency of the negative permittivity are studied in detail. This metamaterial would have potential application in designing broadband microwave devices.
