Pattern formation in planar gas-discharge systems

摘要

We summarize the experimental observation of a large variety of self-organized patterns in the electrical current density of the discharge space of planar gas-discharge systems with high impedance electrodes. In the center of interest are static and dynamic well-localized solitary patterns (dissipative solitons, DSs) and their interaction leading e.g. to scattering, the formation of "molecules", generation, annihilation and the formation of patterns of higher complexity consisting of DSs. A simple 3-component reaction-diffusion system qualitatively takes account of most of the observed phenomena. In addition, we present a rigorous reduction of these equations to a set of ordinary differential equations near the transition point from a stationary to a travelling DS, giving a mathematical foundation of a description of DSs as particles.