H.-G. Purwins

Interaction of dissipative solitons: particle-like behaviour of localized structures in a three-component reaction-diffusion system

We investigate the static and dynamic behaviour of well localized solitary solutions of a three-component reaction-diffusion model in two- and three-dimensional space. These solutions behave like particles under many aspects and we refer to them as dissipative solitons. These objects may interact with each other, and are influenced by boundaries and inhomogeneities of the parameters. Depending on parameters and initial conditions they may be generated or annihilated. Reflection, scattering and the formation of bound states is commonly observed and dissipative solitons essentially retain their identity under such interactions if these are sufficiently weak. For parameters near to the onset of propagation, the field equations are reduced to a set of ordinary differential equations describing rather well the dynamical behaviour of many aspects of isolated and interacting dissipative solitons using their center coordinates and amplitudes of certain propagator modes. The work demonstrates that dissipative solitons are a generic self-organized pattern of reaction-diffusion systems, that they are rather robust under interaction and in many circumstances can be considered as elementary constituents of patterns of higher complexity. The reduced description can be looked upon as a theoretical foundation of the concept of dissipative solitons exhibiting particle-like behaviour. In addition, for the first time these equations allow a numerical investigation of systems with large number of dissipative solitons as they are observed experimentally. It is pointed out that many of the described properties of dissipative solitons are observed in experimental systems of reaction-diffusion type.

Self-organized filaments in dielectric barrier glow discharges

The filamentation of a plasma created by a dielectric barrier discharge in conditions of low pd products (i.e., Townsend breakdown and not streamer breakdown) is investigated both experimentally and with a two-dimensional numerical discharge model. Complex stationary and dynamical domains and filaments are observed experimentally. Some of the properties of these systems are reproduced by the model.

Simulations of self-organized filaments in a dielectric barrier glow discharge plasma

The spontaneous filamentation of a dielectric barrier glow discharge plasma (Townsend, not streamer breakdown), i.e., an instability of the homogeneous state has been simulated and understood with the help of a self-consistent two-dimensional fluid model of the discharge. The formation of self-organized or solitary filaments observed experimentally and described in previous papers can be explained in terms of electron and ion transport coefficients only, without including gas heating, plasma chemistry or surface effects. The conditions favoring the plasma filamentation are discussed.

Plasma spots in a gas discharge system: birth, scattering and formation of molecules

Abstract Experiments on a planar gas discharge device, where formation of spatial structures is of the Turing origin, demonstrate that particle-like states of a pattern can scatter at each other, form bound (“molecular”) states that propagate over the active area of the device, and generate additional quasi-particles in the course of collisions.

Spatio-temporal pattern formation in a lateral high-frequency glow discharge system

Abstract In a two-dimensional lateral high frequency glow discharge system pattern formation has been investigated experimentally. We observe, e.g., Turing patterns, isolated solitary like filaments, filament clusters, coexisting stationary and nonstationary structures and various kinds of rotating filamentary patterns.

Pattern formation in reaction-diffusion systems—dissipative solitons in physical systems

Abstract Two-component reaction-diffusion systems are discussed. These systems may have dissipative solitions as solutions. This is demonstrated by reporting recent experimental results obtained from physical systems. Generation of dissipative solitons and their behaviour is discussed theoretically in terms of interacting fronts. Various patterns as there are stationary and moving fronts, cascades of stationary dissipative solitons and travelling, swinging and breathing solitons are the natural outcome of the theory.

HEXAGON AND STRIPE TURING STRUCTURES IN A GAS DISCHARGE SYSTEM

Abstract We report the observation of different scenarios of pattern formation in a dc driven two-dimensional semiconductor-discharge system. Transitions from the homogeneous state to stationary hexagon and stripe patterns are referred to as instabilities of Turing type. The underlying physical mechanism is discussed.

THE FORMATION OF VORONOI DIAGRAMS IN CHEMICAL AND PHYSICAL SYSTEMS: EXPERIMENTAL FINDINGS AND THEORETICAL MODELS

The work discusses the formation of Voronoi diagrams in spatially extended nonlinear systems taking experimental and theoretical results into account. Concerning experimental systems a number of chemical systems used previously as prototype chemical processors and a barrier gas-discharge system are investigated. Although the underlying microscopic processes are very different, both types of systems show self-organized Voronoi diagrams for suitable parameters. Indeed certain chemical systems exhibit Voronoi diagrams as an output state for two distinct sets of parameters one that corresponds to the interaction of stable forced trigger waves and the other that corresponds to the spontaneous initiation and interaction of waves due to point instabilities in the system. In the case of the chemical systems front initiation, propagation and interaction (annihilation) are the primary mechanisms for Voronoi diagram formation, in the case of the barrier gas-discharge system regions of vanishing electric field define the medial axes of the Voronoi diagram. On the basis of cellular automata models the general concept of the formation of Voronoi diagrams has been explained, and related mechanisms have been simulated. Another intuitive approach towards the understanding of self-organized Voronoi diagrams has been given on the basis of reaction–diffusion models explaining the formation of Voronoi diagrams as a result of the mutual interactions of trigger fronts. The variety of systems exhibiting Voronoi diagrams as stationary states indicates that Voronoi diagrams are a generic and natural pattern formation phenomenon.

Pattern formation in gas discharge systems with high impedance electrodes

Abstract A gas discharge is induced in a helium atmosphere using silicon electrodes and exhibits spatial structures of current filaments depending on the applied voltage, gas pressure and the geometry of the electrodes. These observations can be described phenomenologically by a reaction-diffusion equation. There is good qualitative agreement between solutions of the model equations and the experiment.

Speed properties of a semiconductor-discharge gap IR image converter studied with a streak camera system

Under certain experimental conditions a semiconductor‐discharge gap structure can be used as detector for spatiotemporal resolved measurements on IR radiation. With a streak camera system and a semiconductor laser diode (λ=1.3 μm), we investigate experimentally the speed properties of this kind of converter. The experimental results are compared with the predictions of a simple theoretical model.