5,990 research outputs found
Dynamics of the Free Surface of a Conducting Liquid in a Near-Critical Electric Field
Near-critical behavior of the free surface of an ideally conducting liquid in
an external electric field is considered. Based on an analysis of three-wave
processes using the method of integral estimations, sufficient criteria for
hard instability of a planar surface are formulated. It is shown that the
higher-order nonlinearities do not saturate the instability, for which reason
the growth of disturbances has an explosive character.Comment: 19 page
Hyperbolic chaos in self-oscillating systems based on mechanical triple linkage: Testing absence of tangencies of stable and unstable manifolds for phase trajectories
Dynamical equations are formulated and a numerical study is provided for
self-oscillatory model systems based on the triple linkage hinge mechanism of
Thurston -- Weeks -- Hunt -- MacKay. We consider systems with holonomic
mechanical constraint of three rotators as well as systems, where three
rotators interact by potential forces. We present and discuss some quantitative
characteristics of the chaotic regimes (Lyapunov exponents, power spectrum).
Chaotic dynamics of the models we consider are associated with hyperbolic
attractors, at least, at relatively small supercriticality of the
self-oscillating modes; that follows from numerical analysis of the
distribution for angles of intersection of stable and unstable manifolds of
phase trajectories on the attractors. In systems based on rotators with
interacting potential the hyperbolicity is violated starting from a certain
level of excitation.Comment: 30 pages, 18 figure
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