We theoretically investigate quantum entanglement and coherence in a hybrid Laguerre–Gaussian rotating cavity optomechanical system with two-level atoms, where cavity and mechanical modes are coupled through the exchange of orbital angular momentum. Our study shows that the injection of atoms with a suitable choice of the physical parameters can significantly improve the degree of optomechanical entanglement in all aspects. In the study of quantum coherence research, we show more comprehensively the negative and positive effects of atoms on the coherence. The result obtained is that only when the atom is significantly off-resonant to driving field, the coupling strength in between the atoms and light field increases and the quantum coherence can be enhanced, otherwise it will reduce quantum coherence. In addition, the atomic decay suppresses quantum coherence phenomenon.

A micro-mechanical model was developed to describe the electrical percolation and effective electrical conductivity of nanocomposites containing fillers with different shapes such as graphene nanoplatelets, carbon black, and carbon nanotubes. The fillers are considered to be an oblate or short cylindrical shape for graphene nanoplatelets, a spherical or spheroidal shape for carbon blacks, and a prolate or long cylindrical shape for carbon nanotubes. The effects of the filler shape, filler size, filler aspect ratios, the thickness of the interphase layer, the conductivity of the filler, the conductivity of the interphase layer, the conductivity of the matrix, volume fractions, quantum tunneling distance, and tunneling barrier height have been examined. This modified mean field model well describes the electrical properties of nanocomposites in the whole range of volume fractions for a variety of experimental results with various reinforcements. Also, it reproduces the very sharp behavior of the percolation transition well around the percolation threshold. The results show that nanocomposites containing fillers with an aspect ratio of 10⁻² < M < 10² and a volume fraction of ϕ_f < 0.3 show an insulating behavior while exhibiting a metallic behavior in the ranges M < 10⁻² and M > 10². This model produces variations in the percolation threshold in terms of the aspect ratio as a parabolic curve that can be used to predict the percolation threshold of nanocomposites with various fillers. The present general model can provide a new insight to design conductive polymer nanocomposites with the desired features and specific applications.