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Cutting and shuffling a hemisphere: non-orthogonal axes. (arXiv:1810.05283v1 [math.DS])
来源于:arXiv
We examine the dynamics of cutting-and-shuffling a hemispherical shell driven
by alternate rotation about two horizontal axes using the framework of
piecewise isometry (PWI) theory. Previous restrictions on how the domain is
cut-and-shuffled are relaxed to allow for non-orthogonal rotation axes, adding
a new degree of freedom to the PWI. A new computational method for efficiently
executing the cutting-and-shuffling using parallel processing allows for
extensive parameter sweeps and investigations of mixing protocols that produce
a low degree of mixing. Non-orthogonal rotation axes break some of the
symmetries that produce poor mixing with orthogonal axes and increase the
overall degree of mixing on average. Arnold tongues arising from rational
ratios of rotation angles and their intersections, as in the orthogonal axes
case, are responsible for many protocols with low degrees of mixing in the
non-orthogonal-axes parameter space. Arnold tongue intersections along a
fundamental symmetry 查看全文>>