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FROM TEMPORAL TO SPATIO-TEMPORAL CHAOS

机译:从时空到时空混沌

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The "nature" of turbulence is discussed in relation with the strength of confinement effects. Examples from Rayleigh-Benard convection are given. For strongly confined systems, the framework of low-dimensional dynamical systems is fully adapted and the classical scenarios of transition to temporal chaos are obtained. In weakly confined systems, the degrees of freedom gain a functional nature, i.e., envelopes describing modulated patterns. The dynamics of textures can then be expressed using generalized phase variables and structural defects and the emerging spatio-temporal chaos can be interpreted in terms of phase and/or topological turbulence, at least as long as no subcritical instability is involved. A different scenario can develop when an inverse bifurcation takes place, with domains of different local regime coexisting ill physical space separated by fronts. The transition can then occur via spatio-temporal intermittency, a contamination process akin to directed percolation. The critical nature of the process and its universal content are discussed using coupled map lattices and their reduction in terms of cellular automata.
机译:讨论了湍流的“性质”与约束作用的强度。给出了瑞利-贝纳德对流的例子。对于高度受限的系统,完全适应了低维动力系统的框架,并获得了过渡到时间混沌的经典方案。在弱约束系统中,自由度具有功能性,即描述调制模式的包络。然后,可以使用广义的相位变量和结构缺陷来表达纹理的动态,并且只要不涉及亚临界不稳定性,就可以根据相位和/或拓扑湍流来解释出现的时空混乱。当发生反向分叉时,可能会出现不同的情况,其中不同的局部区域的域共存病态的物理空间,并由前沿分开。然后可以通过时空间断发生过渡,这是类似于定向渗滤的污染过程。使用耦合图格子及其在细胞自动机方面的减少,讨论了该过程的关键性质及其通用内容。

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