Institute for Mathematics and Its Applications
H.G. Purwins, Universitat Münster
Lateral DC and AC gas-discharge-systems exhibit a large variety of self-organized current density patterns. These patterns are experimentally observed in one- and two-dimensional systems and can be stationary or nonstationary and spatially extended or well localized. Examples are domains, hexagons, stripes, spirals, targets, zigzag-patterns, strings, filaments, and clusters of filaments. In this talk the main emphasis is layed on filaments that behave experimentally like quasiparticles.
The experimental results are discussed qualitatively in terms of a three-component reaction-diffusion-model. Numerical solutions of the corresponding partial differential equation are discussed, in particular those representing well-localized solitary filaments that again can be referred to as quasiparticles. These particles can undergo interactions thereby being generated, annihilated, captured, reflected or scattered. The interaction of quasiparticles can also lead to the formation of quasimolecules and large clusters. The experimental work suggests that lateral gas discharge devices can serve as model systems for the investigation of pattern formation in dissipative systems of reaction-diffusion type. The model equation is complex enough to exhibit a rich variety of fundamental patterns at the same time the structure is sufficiently simple to obtain deep insight into the mechanisms that lead to patterns in reaction-diffusion-systems.