Chaotic mixing Poincare section

Until recently, numerical tools and resources were also underdeveloped relative to the magnitude of the striation measurement problem Poincare sections and tracer dispersion simulations were the primary techniques used to characterize mixing. To reconstruct striation patterns successfully by computational methods, it is necessary to track continuous material lines (i.e., dye blobs) injected in chaotic flows. The difficulty of such a numerical experiment is hidden in one word of the previous sentence continuous. The feasibility of tracking material lines or surfaces numerically was explored by Franjione and Ottino, (Franjione and Ottino, 1987). These authors estimations of time and disk space demands... 

The helium atom is an atomic physics example of a three-body problem. On the basis of Poincare s result we have to expect that the helium atom is classically chaotic. Richter and Wintgen (1990b) showed that this is indeed the case the helium atom exhibits a mixed phase space with intermingled regular and chaotic regions (see also Wintgen et al. (1993)). Thus, conceptually, the helium atom is a close relative of the double pendulum studied in Section 3.2. Given the classical chaoticity of the helium atom we are confronted with an important question How does chaos manifest itself in the helium atom ... 

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