On passage through resonances in volume-preserving systems |
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Authors: | Vainchtein D L Neishtadt A I Mezic I |
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Institution: | School of Physics, Georgia Institute of Technology, Atlanta, Georgia 30332, USA. |
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Abstract: | Resonance processes are common phenomena in multiscale (slow-fast) systems. In the present paper we consider capture into resonance and scattering on resonance in 3D volume-preserving multiscale systems. We propose a general theory of those processes and apply it to a class of kinematic models inspired by viscous Taylor-Couette flows between two counter-rotating cylinders. We describe the phenomena during a single passage through resonance and show that multiple passages lead to the chaotic advection and mixing. We calculate the width of the mixing domain and estimate a characteristic time of mixing. We show that the resultant mixing can be described using a diffusion equation with a diffusion coefficient depending on the averaged effect of the passages through resonances. |
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