Basic research for systematization of self-organization paradigm

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This research is aiming at attacking a challenging problem of "what nonlineality creates order, and what universal rule governs the process." We have done several large scale computer simulations for open nonlinear systems, and obtained the following results.1. Our working hypothesis on the formation of order turns out to be more confirmed. Namely, when energy is supplied continuously from outside to an open local system, energy relaxation is intermittently repeated, and new organized structures are created in an intermittent fashion.2. Intermittent response is a reflection of the nonlinearity of the system. Upon supply of energy from outside, the system becomes unstable to release the supplied energy into other forms of energy. However, because the growth rate of the unstable mode dose not necessarily match the rate of energy supply, a surplus energy is accumulated in the system. The nonlinear development of the system gives rise eventually to a sudden structure transition to release the accumulated surplus energy. In other words, a supersaturated (energy maximum) state is realized temporarily in the open nonlinear system by the continuous energy supply from outside, and the system undergoes a structure transition to a new local minimum energy state.3. A new findings on the scenario of self-organization is obtained by a simulation in which a viscous thin layr is placed between a plasma flow source and a nonlinear feedback system. Namely, a boundary layr demarcating the outside energy source and the self-organizing system is found to play a role of a "membrane", that controls self-adjustably the amount of the energy influx from outside. Careful examination of the simulation results has led us to a conclusion that a thin viscous layr, a "membrane", exhibits two important functions in self-organization, i.e., a) natural selection and b) stabilization of self-organized structure.