Crisis and unstable dimension variability in the bailout embedding map |
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Authors: | N Nirmal Thyagu Neelima Gupte |
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Institution: | (1) Department of Physics, Indian Institute of Technology Madras, Chennai, 600 036, India |
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Abstract: | The dynamics of inertial particles in 2-d incompressible flows can be modeled by 4-d bailout embedding maps. The density of
the inertial particles, relative to the density of the fluid, is a crucial parameter which controls the dynamical behaviour
of the particles. We study here the dynamical behaviour of aerosols, i.e. particles heavier than the flow. An attractor widening
and merging crisis is seen in the phase space in the aerosol case. Crisis-induced intermittency is seen in the time series
and the laminar length distribution of times before bursts give rise to a power law with the exponent β = −1/3. The maximum Lyapunov exponent near the crisis fluctuates around zero indicating unstable dimension variability (UDV)
in the system. The presence of unstable dimension variability is confirmed by the behaviour of the probability distributions
of the finite time Lyapunov exponents.
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Keywords: | Bailout embedding map crisis unstable dimension variability Lyapunov exponents |
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