Self-organization processes in continuous media
Self-organization processes in continuous media
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DOI：
10.1080/00018738500101721
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发表时间：
1985
影响因子：
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通讯作者：
A. Hasegawa
中科院分区：
文献类型：
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作者：
A. Hasegawa
摘要 本文考虑了耗散连续介质的动力学行为，在没有耗散的情况下，该介质可以通过具有两个以上非平凡守恒量的非线性偏微分方程来描述。即使从最初的湍流状态或由随机场驱动的状态开始，这种介质通常也会表现出特定物理量到特定波数区域的光谱凝聚，从而导致有序结构的形成。这里讨论的例子包括二维不可压缩流体、二维和三维磁流体动力流体、旋转行星的大气、不均匀磁化等离子体中的静电势以及科特韦格-德弗里斯方程描述的孤离气体。还讨论了孤子系统以及一些局部涡旋解中混沌开始与自组织之间的关系。
Abstract This review considers the dynamical behaviour of dissipative continuous media which can be described by nonlinear partial differential equations having more than two non-trivial conserved quantities in the absence of dissipation. Such a medium often exhibits a spectral condensation of a certain physical quantity to a specific wavenumber region resulting in the formation of an ordered structure, even when starting from an initially turbulent state or one driven by a stochastic field. Examples discussed here include two-dimensional incompressible fluids, two-and three-dimensional magnetohydrodynamic fluids, the atmospheres of rotating planets, the electrostatic potential in inhomogeneous magnetized plasmas, and the solition gas as described by the Korteweg-de Vries equation. The relationship between the onset of chaos and self-organization in a soliton system, as well as in some localized vortex solutions, is also discussed.