Abstract
Originally designed to account for the main phenomena of symmetry-breaking morphogenesis, the well-known Rashevsky-Turing theory is a prototype model of many different synergetic systems in nature. The simplest version of Turing's model can be realized by a two-cellular symmetrical reaction-diffusion system, consisting of two cross-inhibitorily coupled, potentially oscillating two-variable subsystems (4-D flow). We present numerical evidence of symmetry-breaking nonequilibrium phase transitions from “phase-locked” coherent to “phase-lagged” differentiated behavior of the two subsystems. We further investigate the structural change of the system flow from stable morphogenesis to boiling-type turbulence. Finally, we present experimental evidence that the spatiotemporal nonlinear behavior of impurity-impact-ionization-induced avalanche breakdown in semiconducting germanium can be described qualitatively by the present 4-D reaction-diffusion model.
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Röhricht, B., Parisi, J., Peinke, J. et al. A simple morphogenetic reaction-diffusion model describing nonlinear transport phenomena in semiconductors. Z. Physik B - Condensed Matter 65, 259–266 (1986). https://doi.org/10.1007/BF01303850
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DOI: https://doi.org/10.1007/BF01303850