Blowout bifurcation and spatial mode excitation in the bubbling transition to turbulence

The transition to turbulence (spatio-temporal chaos) in a wide class of spatially extended dynamical system is due to the loss of transversal stability of a chaotic attractor lying on a homogeneous manifold (in the Fourier phase space of the system) causing spatial mode excitation Since the latter manifests as intermittent spikes this has been called a bubbling transition We present numerical evidences that this transition occurs due to the so called blowout bifurcation whereby the attractor as a whole loses transversal stability and becomes a chaotic saddle We used a nonlinear three-wave interacting model with spatial diffusion as an example of this transition (C) 2010 Elsevier B V All rights reserved

Robust tori in a double-waved Hamiltonian model

A Hamiltonian system perturbed by two waves with particular wave numbers can present robust tori, which are barriers created by the vanishing of the perturbed Hamiltonian at some defined positions. When robust tori exist, any trajectory in phase space passing close to them is blocked by emergent invariant curves that prevent the chaotic transport. Our results indicate that the considered particular solution for the two waves Hamiltonian model shows plenty of robust tori blocking radial transport. (C) 2010 Elsevier B.V. All rights reserved.

Periodic window arising in the parameter space of an impact oscillator

In the bi-dimensional parameter space of an impact-pair system, shrimp-shaped periodic windows are embedded in chaotic regions. We show that a weak periodic forcing generates new periodic windows near the unperturbed one with its shape and periodicity. Thus, the new periodic windows are parameter range extensions for which the controlled periodic oscillations substitute the chaotic oscillations. We identify periodic and chaotic attractors by their largest Lyapunov exponents. (C) 2010 Elsevier B.V. All rights reserved.

Clustering and diffusion in a symplectic map lattice with non-local coupling

We study a symplectic chain with a non-local form of coupling by means of a standard map lattice where the interaction strength decreases with the lattice distance as a power-law, in Such a way that one can pass continuously from a local (nearest-neighbor) to a global (mean-field) type of coupling. We investigate the formation of map clusters, or spatially coherent structures generated by the system dynamics. Such clusters are found to be related to stickiness of chaotic phase-space trajectories near periodic island remnants, and also to the behavior of the diffusion coefficient. An approximate two-dimensional map is derived to explain some of the features of this connection. (C) 2008 Elsevier Ltd. All rights reserved.

Transport control in fusion plasmas by changing electric and magnetic field spatial profiles

For magnetically confined plasmas in tokamaks, we have numerically investigated how Lagrangian chaos at the plasma edge affects the plasma confinement. Initially, we have considered the chaotic motion of particles in an equilibrium electric field with a monotonic radial profile perturbed by drift waves. We have showed that an effective transport barrier may be created at the plasma edge by modifying the electric field radial profile. In the second place, we have obtained escape patterns and magnetic footprints of chaotic magnetic field lines in the region near a tokamak wall with resonant modes due to the action of an ergodic magnetic limiter. For monotonic plasma current density profiles we have obtained distributions of field line connections to the wall and line escape channels with the same spatial pattern as the magnetic footprints on the tokamak walls. (c) 2008 Elsevier B.V. All rights reserved.

A scenario for torus T(2) destruction via a global bifurcation

We show a scenario of a two-frequeney torus breakdown, in which a global bifurcation occurs due to the collision of a quasi-periodic torus T(2) with saddle points, creating a heteroclinic saddle connection. We analyze the geometry of this torus-saddle collision by showing the local dynamics and the invariant manifolds (global dynamics) of the saddle points. Moreover, we present detailed evidences of a heteroclinic saddle-focus orbit responsible for the type-if intermittency induced by this global bifurcation. We also characterize this transition to chaos by measuring the Lyapunov exponents and the scaling laws. (C) 2007 Elsevier Ltd. All rights reserved.

Bubbling transition to spatial mode excitation in an extended dynamical system

We investigated the transition to spatio-temporal chaos in spatially extended nonlinear dynamical systems possessing an invariant subspace with a low-dimensional attractor. When the latter is chaotic and the subspace is transversely stable we have a spatially homogeneous state only. The onset of spatio-temporal chaos, i.e. the excitation of spatially inhomogeneous modes, occur through the loss of transversal stability of some unstable periodic orbit embedded in the chaotic attractor lying in the invariant subspace. This is a bubbling transition, since there is a switching between spatially homogeneous and nonhomogeneous states with statistical properties of on-off intermittency. Hence the onset of spatio-temporal chaos depends critically both on the existence of a chaotic attractor in the invariant subspace and its being transversely stable or unstable. (C) 2008 Elsevier B.V. All rights reserved.

Chaotic transport in reversed shear tokamaks

For tokamak models using simplified geometries and reversed shear plasma profiles, we have numerically investigated how the onset of Lagrangian chaos at the plasma edge may affect the plasma confinement in two distinct but closely related problems. Firstly, we have considered the motion of particles in drift waves in the presence of an equilibrium radial electric field with shear. We have shown that the radial particle transport caused by this motion is selective in phase space, being determined by the resonant drift waves and depending on the parameters of both the resonant waves and the electric field profile. Moreover, we have shown that an additional transport barrier may be created at the plasma edge by increasing the electric field. In the second place, we have studied escape patterns and magnetic footprints of chaotic magnetic field lines in the region near a tokamak wall, when there are resonant modes due to the action of an ergodic magnetic limiter. A non-monotonic safety factor profile has been used in the analysis of field line topology in a region of negative magnetic shear. We have observed that, if internal modes are perturbed, the distributions of field line connection lengths and magnetic footprints exhibit spatially localized escape channels. For typical physical parameters of a fusion plasma, the two Lagrangian chaotic processes considered in this work can be effective in usual conditions so as to influence plasma confinement. The reversed shear effects discussed in this work may also contribute to evaluate the transport barrier relevance in advanced confinement scenarios in future tokamak experiments.

Plasma confinement in tokamaks with robust torus

We present a non-linear symplectic map that describes the alterations of the magnetic field lines inside the tokamak plasma due to the presence of a robust torus (RT) at the plasma edge. This RT prevents the magnetic field lines from reaching the tokamak wall and reduces, in its vicinity, the islands and invariant curve destruction due to resonant perturbations. The map describes the equilibrium magnetic field lines perturbed by resonances created by ergodic magnetic limiters (EMLs). We present the results obtained for twist and non-twist mappings derived for monotonic and non-monotonic plasma current density radial profiles, respectively. Our results indicate that the RT implementation would decrease the field line transport at the tokamak plasma edge. (C) 2010 Elsevier B.V. All rights reserved.

CRITICAL BEHAVIOR AND THRESHOLD OF COEXISTENCE OF A PREDATOR-PREY STOCHASTIC MODEL IN A 2D LATTICE

We investigate the critical behavior of a stochastic lattice model describing a predator-prey system. By means of Monte Carlo procedure we simulate the model defined on a regular square lattice and determine the threshold of species coexistence, that is, the critical phase boundaries related to the transition between an active state, where both species coexist and an absorbing state where one of the species is extinct. A finite size scaling analysis is employed to determine the order parameter, order parameter fluctuations, correlation length and the critical exponents. Our numerical results for the critical exponents agree with those of the directed percolation universality class. We also check the validity of the hyperscaling relation and present the data collapse curves.

Experimental identification of chaotic fibers

In a 2D parameter space, by using nine experimental time series of a Clitia`s circuit, we characterized three codimension-1 chaotic fibers parallel to a period-3 window. To show the local preservation of the properties of the chaotic attractors in each fiber, we applied the closed return technique and two distinct topological methods. With the first topological method we calculated the linking, numbers in the sets of unstable periodic orbits, and with the second one we obtained the symbolic planes and the topological entropies by applying symbolic dynamic analysis. (C) 2007 Elsevier Ltd. All rights reserved.

Numerical test of Born-Oppenheimer approximation in chaotic systems

We study the validity of the Born-Oppenheimer approximation in chaotic dynamics. Using numerical solutions of autonomous Fermi accelerators. we show that the general adiabatic conditions can be interpreted as the narrowness of the chaotic region in phase space. (C) 2009 Elsevier B.V. All rights reserved.

Perturbation treatment of symmetry breaking within random matrix theory

We discuss the applicability, within the random matrix theory, of perturbative treatment of symmetry breaking to the experimental data on the flip symmetry breaking in quartz crystal. We found that the values of the parameter that measures this breaking are different for the spacing distribution as compared to those for the spectral rigidity. We consider both two-fold and three-fold symmetries. The latter was found to account better for the spectral rigidity than the former. Both cases, however, underestimate the experimental spectral rigidity at large L. This discrepancy can be resolved if an appropriate number of eigenfrequencies is considered to be missing in the sample. Our findings are relevant for symmetry violation studies in general. (C) 2008 Elsevier B.V. All rights reserved.

An analytical relation between entropy production and quantum Lyapunov exponents for Gaussian bipartite systems

We study and compare the information loss of a large class of Gaussian bipartite systems. It includes the usual Caldeira-Leggett-type model as well as Anosov models ( parametric oscillators, the inverted oscillator environment, etc), which exhibit instability, one of the most important characteristics of chaotic systems. We establish a rigorous connection between the quantum Lyapunov exponents and coherence loss, and show that in the case of unstable environments coherence loss is completely determined by the upper quantum Lyapunov exponent, a behavior which is more universal than that of the Caldeira-Leggett-type model.

Velocity-dependent KAM islands

We revisit the non-dissipative time-dependent annular billiard and we consider the chaotic dynamics in two planes of conjugate variables in order to describe the behavior of the growth, or saturation, of the mean velocity of an ensemble of particles. We observed that the changes in the 4-d phase space occur without changing any parameter. They occur depending on where the initial conditions start. The emerging KAM islands interfere in the behavior of the particle dynamics especially in the Fermi acceleration mechanism. We show that Fermi acceleration can be suppressed, without dissipation, even considering the non-dissipative energy context. (C) 2011 Published by Elsevier Ltd.