Basic research for systematization of self-organization paradigm

这项研究旨在解决一个具有挑战性的问题，即“什么是非线性性创造了秩序，什么普遍规则支配着这个过程。”我们已经对开放的非线性系统进行了几次大规模的计算机仿真，得到了以下结果。事实证明，我们关于秩序形成的工作假设得到了更多的证实。也就是说，当能量从外部连续供应给开放的局部系统时，能量松弛被间歇地重复，并以间歇的方式产生新的有组织的结构。间歇响应是系统非线性的一种反映。一旦从外部提供能量，系统就会变得不稳定，无法将所提供的能量释放成其他形式的能量。然而，由于不稳定模的增长率不一定与能量供应的速率相匹配，因此系统中积累了过剩能量。系统的非线性发展最终导致结构突变，从而释放累积的过剩能量。也就是说，开放的非线性系统在外界持续能量供应的作用下，暂时实现了过饱和(能量最大)状态，系统经历了向新的局部最小能量状态的结构转变。通过在等离子体流源和非线性反馈系统之间放置一层粘性薄层的模拟，得到了关于自组织情景的新发现。也就是说，划分外部能源和自组织系统的边界层起到了“膜”的作用，它自调节地控制来自外部的能量流入的量。通过对模拟结果的仔细考察，我们得出结论：作为一种“膜”的粘性薄层在自组织中显示出两个重要的功能，即a)自然选择和b)自组织结构的稳定。

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.