Statistical networks emerging from link-node interactions

We study a model for a statistical network formed by interactions between its nodes and links. Each node can be in one of two states (Ising spin up or down) and the node-link interaction facilitates linking between the like nodes. For high temperatures the influence of the nodes on the links can be neglected, and we get the Ising ferromagnet on the random (Erdos-Renyi) graph. For low temperatures the nodes get spontaneously ordered. Due to this, the connectivity of the network enhances and links having a common node are correlated. The emerged network is clustered. The node-link interaction shifts the percolation threshold of the random graph to much smaller values, and the very percolation transition can become of the first order: the giant cluster coexist with the unconnected phase leading to bistability and hysteresis. The model can be applied to the striction phenomena in magnets and to studying opinion formation in the sociophysical context.Comment: 4 pages, 1 figur

Electromagnetic wave propagation in spatially homogeneous yet smoothly time-varying dielectric media

We explore the propagation and transformation of electromagnetic waves through spatially homogeneous yet smoothly time-dependent media within the framework of classical electrodynamics. By modelling the smooth transition, occurring during a finite period {\tau}, as a phenomenologically realistic and sigmoidal change of the dielectric permittivity, an analytically exact solution to Maxwell's equations is derived for the electric displacement in terms of hypergeometric functions. Using this solution, we show the possibility of amplification and attenuation of waves and associate this with the decrease and increase of the time-dependent permittivity. We demonstrate, moreover, that such an energy exchange between waves and non-stationary media leads to the transformation (or conversion) of frequencies. Our results may pave the way towards controllable light-matter interaction in time-varying structures.Comment: 5 figure