196,209 research outputs found
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
Maximal width of the separatrix chaotic layer
No full textSUMMARY The main goal of the paper is to find the {\it absolute maximum} of the width
of the separatrix chaotic layer as function of the frequency of the
time-periodic perturbation of a one-dimensional Hamiltonian system possessing a
separatrix, which is one of the major unsolved problems in the theory of
separatrix chaos. For a given small amplitude of the perturbation, the width is
shown to possess sharp peaks in the range from logarithmically small to
moderate frequencies. These peaks are universal, being the consequence of the
involvement of the nonlinear resonance dynamics into the separatrix chaotic
motion. Developing further the approach introduced in the recent paper by
Soskin et al. ({\it PRE} {\bf 77}, 036221 (2008)), we derive leading-order
asymptotic expressions for the shape of the low-frequency peaks. The maxima of
the peaks, including in particular the {\it absolute maximum} of the width, are
proportional to the perturbation amplitude times either a logarithmically large
factor or a numerical, still typically large, factor, depending on the type of
system. Thus, our theory predicts that the maximal width of the chaotic layer
may be much larger than that predicted by former theories. The theory is
verified in simulations. An application to the facilitation of global chaos
onset is discussed
Stochastic webs and quantum transport in superlattices : an introductory review.
No full textStochastic webs were discovered, first by Arnold for multi-dimensional Hamiltonian systems, and later byChernikov et al. for the low-dimensional case. Generated by weak perturbations, they consist of thread-like regions of chaotic dynamics in phase space. Their importance is that, in principle, they enable transport from small energies to high energies. In this introductory review, we concentrate on low-dimensional stochastic webs and on their applications to quantum transport in semiconductor superlattices subject to electric and magnetic fields. We also describe a recently-suggested modification of the stochastic web to enhance chaotic transport through it and we discuss its possible applications to superlattices
A new approach to the treatment of separatrix chaos
No full textWe 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
Adiabatic divergence of the chaotic layer width and acceleration of chaotic and noise-induced transport
No full textSUMMARY 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
Theory for the drastic facilitation of the onset of global chaos between separatrices of a Hamiltonian system
No full textDrastic facilitation of the onset of global chaos due to an extremum in the dependence of eigenfrequency on energy
No full textCharles Péguy
No full textAu-delà de l’apologie circonstancielle du bergsonisme contre ses adversaires rationalistes et thomistes, les deux textes testamentaires de Charles Péguy constituent l’une des traversées les plus éloquentes, inséparable d’une reprise originale, de la philosophie de Bergson. Le gérant des Cahiers de la Quinzaine y renouvelle la métaphysique du temps depuis une analyse critique de la société de son temps. Avec cet engagement du bergsonisme, c’est le legs philosophique de Péguy lui-même que la Note sur M. Bergson et la Note conjointe sur M. Descartes recueillent en dernière instance. De là qu’elles demeurent sans équivalent pour aborder ou méditer cet auteur insaisissable. Socialiste utopiste, dreyfusard militant, poète chrétien, nationaliste enragé : les ultimes écrits de Péguy invitent à déposer ce kaléidoscope pour découvrir un penseur à la hauteur de son époque de crise, peut-être aussi de la nôtre. Plus profondément que deux philosophes français, c’est une réflexion métaphysique sur la scission radicale de la durée incarnée et une critique sociale de sa dénégation qui sont ici conjointes. Si bien qu’au seuil du désastre on ne trouve pas, sous la plume de ce va-t-en-guerre mélancolique, une théorie du déclin glorifiant le passé national, mais une ode à la « mouvance » du présent et une dénonciation de son gel catastrophique sous les règnes complices de l’argent et du positivisme. Péguy articule par-là, à une interprétation hardie de la métaphysique bergsonienne qui annonce les philosophies de l’événement, une étonnante contribution aux critiques marxistes de la modernité capitaliste et du mythe du progrès. Versant bergsonien d’un réquisitoire antimoderne, les Notes en sont aussi bien le pendant : un plaidoyer pour l’assomption de cet éternel passage du temps que refoulent tous les cultes de l’habitude et de la mémoire. De quoi rendre possible une réappréciation de Charles Péguy et de sa position singulière, entre diagnostic de la crise et affirmation de l’espérance
Acceleration of the chaotic and noise-induced transport in adiabatically driven spatially periodic systems
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