1,720,983 research outputs found
Adiabatic ac-drive as a tool for acceleration of diffusion in spatially periodic structures and of reset process in threshold devices
No full textDrastic facilitation of the onset of global chaos due to an extremum in the dependence of eigenfrequency on energy
No full textTheory for the drastic facilitation of the onset of global chaos between separatrices of a Hamiltonian system
No full textWidth of the chaotic layer associated with a separatrix of a one-dimensional Hamiltonian system subjected to a low-frequency time-periodic perturbation
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Matching of separatrix map and resonant dynamics, with application to global chaos onset between separatrices
No full textWe have developed a general method for the description of separatrix chaos, based on the analysis of the separatrix map dynamics. Matching it with the resonant Hamiltonian analysis, we show that, for a given amplitude of perturbation, the maximum width of the chaotic layer in energy may be much larger than it was assumed before. We use the above method to explain the drastic facilitation of global chaos onset in time-periodically perturbed Hamiltonian systems possessing two or more separatrices, previously discovered [S. M. Soskin, O. M. Yevtushenko, and R. Mannella, Phys. Rev. Lett. 90, 174101 (2003)]. The theory well agrees with simulations. We also discuss generalizations and applications. The method may be generalized for single-separatrix cases. The facilitation of global chaos onset may be relevant to a variety of systems, e. g., optical lattices, magnetic and semiconductor superlattices, meandering flows in the ocean, and spinning pendulums. Apart from dynamical transport, it may facilitate noise-induced transitions and the stochastic web formation
Acceleration of the chaotic and noise-induced transport in adiabatically driven spatially periodic systems
No full textAdiabatic divergence of the chaotic layer width and acceleration of chaotic and noise-induced transport
Full text linkSUMMARY We show that, in spatially periodic Hamiltonian systems driven by a time-periodic coordinate-independent (AC) force, the upper energy of the chaotic layer grows unlimitedly as the frequency of the force goes to zero. This remarkable effect is absent in any other physically significant systems. It gives rise to the divergence of the rate of the spatial chaotic transport. We also generalize this phenomenon for the presence of a weak noise and weak dissipation. We demonstrate for the latter case that the adiabatic AC force may greatly accelerate the spatial diffusion and the reset rate at a given threshold
A new approach to the treatment of separatrix chaos
Full text linkWe review an approach to separatrix chaos that has allowed us to solve some significant problems by: (i) finding analytically the maximum width of the chaotic layer, a problem that lay unsolved for 40 years, and showing that the maximum may be much larger than had previously been assumed; (ii) describing the drastic facilitation of the onset of global chaos between neighboring separatrices, a phenomenon discovered eight years ago
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