A macroscopic structure was analyzed for a system comprising multiple elements in which the dynamics is affected by their distribution. First, a nonlinear Boltzmann equation, which has an integration term with respect to the distribution of the elements, was derived. Next, the moment vector equation (MVE) for the Boltzmann equation was derived. The average probability density function (pdf) in a steady state was derived using eigen analysis of the coefficient matrix of the MVE. The macroscopic structure of the system and the mechanism that provides the average pdf and the transient response were then analyzed using eigen analysis. Evaluation of the average pdf and transient response showed that using eigen analysis is effective for analyzing not only the transient and stationary properties of the system but also the macroscopic structure and the mechanism providing the properties.

We formulated the excitation rate of VUV and emitted visible light from rare gas on PDP by using the Boltzmann equation with electron-atom collision integral term and obtained the excitation rate as the function of Temperature and Mass. This form of excitation rate was firstly derived in PDP area. In addition we showed the Pressure dependence of intensity ratio of Ne/VUV as the application of our excitation rate formulae.

A first-order investigation of the transport and energy-loss processes in silicon dioxide is worked out in the frame of the Spherical-Harmonics solution of the Boltzmann Transport Equation. The SiO2 conduction band is treated as a single-valley spherical and parabolic band. The relevant scattering mechanisms are modeled consistently: both the polar and nonpolar electron-phonon scattering mechanisms are considered. The scattering rates for each contribution are analyzed in comparison with Monte Carlo data. A number of macroscopic transport properties of electrons in SiO2 are worked out in the steady-state regime for a homogeneous bulk structure. The investigation shows a good agreement in comparison with experiments in the low-field regime and for different temperatures.