R. Dohmen

Observation of solitary filaments and spatially periodic patterns in a dc gas-discharge system

Abstract In a planar gas-discharge system consisting of a metal and a high ohmic semiconductor electrode we observe experimentally the generation of stationary current density filaments, a discontinuous device characteristic with hysteresis and the bifurcation from a homogeneous discharge into a spatially periodic discharge pattern.

Spatio-temporal oscillations during filament splitting in gas discharge systems

Abstract The process of generation of current density filaments has been investigated in a dc driven gas discharge systems consisting of a metal and a high ohmic semiconductor electrode and in an ac driven gas discharge system between two dielectrically covered electrodes. By means of a streak camera system we find that the generation process is accompanied by spatio-temporal filament oscillations.

Application of the activator inhibitor principle to physical systems

Abstract The transition from a spatially homogeneous state into a spatially periodic state and the development of solitary filaments are observed experimentally in an electrical network and in a dc-gas discharge system, respectively. The explanation for these phenomena is done in terms of the biomathematical activator inhibitor principle with the help of a recently proposed model.

Transition from pulsating to rocking localized structures in nonlinear dissipative distributive media with global inhibition

Abstract We consider localized structures generated in a certain of two component reaction-diffusion system. Four different electric systems, namely reverse-biased p-n diodes, p-n-p transistors, a gas-discharge system, and an electrical network are recapitulated and it is shown that, in spite of the existence of different underlying physical mechanisms, in all cases an activator-inhibitor system is realized. If these systems are driven by an external voltage source via a load resistor, the equation for the external circuit leads to the appearance of an integral term in the reaction terms causing a nonlocal additional inhibiting component. Numerical calculations of the equations system with the simplest reaction terms show exemplarily that there is a critical value of the load resistor in such systems: While below this critical value besides static only pulsating localized structures appear, for values larger than the critical one instead of pulsating only rocking localized structures can be stabilized. Near the critical resistor value we observe patterns composed of pulsating and rocking modes.

Pattern Formation in Nonlinear Physical Systems with Characteristic Electric Properties

Systems are considered which consist of two layers, one of them characterized by a high ohmic, approximately linear and one by an S-shaped current-voltage characteristic. We describe such systems mathematically in terms of two-component reaction-diffusion equations. Analytical and numerical investigations of these equations reveal that the systems can self-organize different stable stationary inhomogeneous nonequilibrium structures as well as spatio-temporal irregular behaviour. These results are in good qualitative agreement with the current density patterns in two experimentally investigated systems, namely a one-dimensional npnp-semiconductor structure and a one-dimensional gas discharge system.

Stable multifilament structures in semiconductor materials based on a kinetic model

A new model for pattern formation in semiconductor materials is proposed based essentially on kinetic processes of charge carriers. This model leads to a set of coupled nonlinear reaction‐diffusion equations with two components: the electron density in the conduction band and the occupation density of a trap level. The model possesses a variety of stable solutions including stable multifilament structures.

Analytical approach to stationary wall solutions in bistable reaction−diffusion systems

Abstract Stationary wall solutions of a two-component nonlinear reaction-diffusion system are developed by means of an analytical approach consisting mainly in replacing the nonlinearity by a piecewise linear approximation. The analytically determined solutions are in good accordance to numerically calculated solutions. The analytical description also explains qualitatively the transition to another kind of solutions, namely solitary filament structures of a special width, for approximately chosen system parameters.