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A numerical simulation method using a one-dimensional fluid model under the local field approximation is presented in order to understand pulsed-dc discharge in He–Xe gas mixture in a cell of a full-color plasma display panel. Spatiotemporal behaviors of the electric field and number densities of twelve independent particles, including electrons and four kinds of ions, were calculated self-consistently at a gas pressure of 200 Torr (27 kPa) and an electrode distance of 0.02 cm. The imprisonment of 147-nm-resonance radiation, the excitation source of phosphors, was also taken into account. Calculated results of the discharge current and voltage are consistent with those of experiment. The waveform of 147-nm-resonance radiation agreed well with experiment, although that of the discharge current showed some difference, probably due to the local field approximation.

A theory of the hollow cathode glow discharge based on the two-temperature electron model is developed. The following two interdependent mechanisms are consistently taken into account: the creation of ions and excited atoms due to electron collisions in the discharge and the emission of secondary electrons on the cathode surface due to ions and ultraviolet photons. Trapped electrons in the hollow are also considered. Numerical calculations are made for helium gas in a cylindrical hollow cathode whose inner diameter and length are 10 and 32 mm, respectively, on the basis of a onedimensional steady state model. Voltage-current relations are obtained at gas pressures of 0.13, 0.27 and 0.40 kPa. Population densities of 64 excited atomic levels are determined as a function of the radial distance r as well as the densities of the ions and electrons.

We study the level spacing distribution p(s) in the spectrum of random networks. According to our numerical results, the shape of p(s) in the Erdős-Rényi (E-R) random graph is determined by the average degree k and p(s) undergoes a dramatic change when k is varied around the critical point of the percolation transition, k = 1. When k 1, the p(s) is described by the statistics of the Gaussian orthogonal ensemble (GOE), one of the major statistical ensembles in Random Matrix Theory, whereas at k = 1 it follows the Poisson level spacing distribution. Closely above the critical point, p(s) can be described in terms of an intermediate distribution between Poisson and the GOE, the Brodydistribution. Furthermore, below the critical point p(s) can be given with the help of the regularized Gamma-function. Motivated by these results, we analyse the behaviour of p(s) in real networks such as the internet, a word association network and a protein-protein interaction network as well. When the giant component of these networks is destroyed in a node deletion process simulating the networks subjected to intentional attack, their level spacing distribution undergoes a similar transition to that of the E-R graph.