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Spatially extended physical, chemical, biological and other nonlinear dissipative systems exhibit rather robust well-localized self-organized solitary patterns with particle like behaviour. These objects are referred to as dissipative solitons (DSs). It can be demonstrated that DSs behave similar in very different dissipative systems therefore attracting considerable interest in natural sciences and application. The present talk deals with the observation of such objects in electrical transport systems.
In the first part of the talk we present experimental results on the observation of DSs in planar gas-discharge systems, planar semiconductor devices and electrical networks. Among other things we report on single stationary and travelling DSs, their interaction including scattering, the formation of molecules and the generation and annihilation of DSs. We also present results on dense arrangements of DSs as there are chains, nets, and "gas"-, "liquid"- and "solid"-like patterns. We then describe a simple reaction-diffusion model that takes account of most of the fundamental experimental observations. In this way some understanding of the mechanisms of formation, stabilization, propagation and interaction of DSs becomes possible. In addition quantitative models being based on the drift diffusion approximation are discussed for gas-discharge and semiconductor systems. These models allow to relate the observed mesoscopic and macroscopic patterns to microscopic properties of the systems under consideration. Finally, starting from the reaction-diffusion model near to the drift-bifurcation we give a mathematical foundation for the particle picture of DSs by reducing the model equations to a set of ordinary differential equations containing the centre coordinates of the DSs. |
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