Hysteresis of dynamos in rotating spherical shell convection

Bifurcations of dynamos in rotating and buoyancy-driven spherical Rayleigh-Bénard convection in an electrically conducting fluid are investigated numerically. Both nonmagnetic and magnetic solution branches comprised of rotating waves are traced by path-following techniques, and their bifurcations and interconnections for different Ekman numbers are determined. In particular, the question of whether the dynamo branches bifurcate super- or subcritically and whether a direct link to the primary pure convective states exists is answered

Hysteresis of dynamos in rotating spherical shell convection

Bifurcations of dynamos in rotating and buoyancy-driven spherical Rayleigh-Bénard convection in an electrically conducting fluid are investigated numerically. Both nonmagnetic and magnetic solution branches comprised of rotating waves are traced by path-following techniques, and their bifurcations and interconnections for different Ekman numbers are determined. In particular, the question of whether the dynamo branches bifurcate super- or subcritically and whether a direct link to the primary pure convective states exists is answered

Collective Phase Locked States in a Chain of Coupled Chaotic Oscillators

We discuss the emergence of a collective phase locked state in an open chain of N unidirectionally weakly coupled nonidentical chaotic oscillators. Such a regime is characterized by a Lyapunov spectrum where N21 exponents that were zero in the uncoupled regime assume negative values as the coupling strength increases. The dynamics of such collective state is studied, and a comparison is drawn with the case of phase synchronization of a pair of coupled chaotic oscillators. In particular, it is shown that a full phase synchronized state cannot be constructed without at least partial correlation in the chaotic amplitudes

Dissipative chaotic scattering

We show that weak dissipation, typical in realistic situations, can have a metamorphic consequence on nonhyperbolic chaotic scattering in the sense that the physically important particle-decay law is altered, no matter how small the amount of dissipation. As a result, the previous conclusion about the unity of the fractal dimension of the set of singularities in scattering functions, a major claim about nonhyperbolic chaotic scattering, may not be observable.Comment: 4 pages, 2 figures, revte

Fractalization of Torus Revisited as a Strange Nonchaotic Attractor

Fractalization of torus and its transition to chaos in a quasi-periodically forced logistic map is re-investigated in relation with a strange nonchaotic attractor, with the aid of functional equation for the invariant curve. Existence of fractal torus in an interval in parameter space is confirmed by the length and the number of extrema of the torus attractor, as well as the Fourier mode analysis. Mechanisms of the onset of fractal torus and the transition to chaos are studied in connection with the intermittency.Comment: Latex file ( figures will be sent electronically upon request):submitted to Phys.Rev. E (1996

Shallow BF2 implants in Xe-bombardment-preamorphized Si: the interaction between Xe and F

Si(100) samples, preamorphized to a depth of ~30 nm using 20 keV Xe ions to a nominal fluence of 2×1014 cm-2 were implanted with 1 and 3 keV BF2 ions to fluences of 7×1014 cm-2. Following annealing over a range of temperatures (from 600 to 1130 °C) and times the implant redistribution was investigated using medium-energy ion scattering (MEIS), secondary ion mass spectrometry (SIMS), and energy filtered transmission electron microscopy (EFTEM). MEIS studies showed that for all annealing conditions leading to solid phase epitaxial regrowth, approximately half of the Xe had accumulated at depths of 7 nm for the 1 keV and at 13 nm for the 3 keV BF2 implant. These depths correspond to the end of range of the B and F within the amorphous Si. SIMS showed that in the preamorphized samples, approximately 10% of the F migrates into the bulk and is trapped at the same depths in a ~1:1 ratio to Xe. These observations indicate an interaction between the Xe and F implants and a damage structure that becomes a trapping site. A small fraction of the implanted B is also trapped at this depth. EXTEM micrographs suggest the development of Xe agglomerates at the depths determined by MEIS. The effect is interpreted in terms of the formation of a volume defect structure within the amorphized Si, leading to F stabilized Xe agglomerates or XeF precipitates

Order-of-magnitude speedup for steady states and traveling waves via Stokes preconditioning in Channelflow and Openpipeflow

Steady states and traveling waves play a fundamental role in understanding hydrodynamic problems. Even when unstable, these states provide the bifurcation-theoretic explanation for the origin of the observed states. In turbulent wall-bounded shear flows, these states have been hypothesized to be saddle points organizing the trajectories within a chaotic attractor. These states must be computed with Newton's method or one of its generalizations, since time-integration cannot converge to unstable equilibria. The bottleneck is the solution of linear systems involving the Jacobian of the Navier-Stokes or Boussinesq equations. Originally such computations were carried out by constructing and directly inverting the Jacobian, but this is unfeasible for the matrices arising from three-dimensional hydrodynamic configurations in large domains. A popular method is to seek states that are invariant under numerical time integration. Surprisingly, equilibria may also be found by seeking flows that are invariant under a single very large Backwards-Euler Forwards-Euler timestep. We show that this method, called Stokes preconditioning, is 10 to 50 times faster at computing steady states in plane Couette flow and traveling waves in pipe flow. Moreover, it can be carried out using Channelflow (by Gibson) and Openpipeflow (by Willis) without any changes to these popular spectral codes. We explain the convergence rate as a function of the integration period and Reynolds number by computing the full spectra of the operators corresponding to the Jacobians of both methods.Comment: in Computational Modelling of Bifurcations and Instabilities in Fluid Dynamics, ed. Alexander Gelfgat (Springer, 2018

Directed current due to broken time-space symmetry

We consider the classical dynamics of a particle in a one-dimensional space-periodic potential U(X) = U(X+2\pi) under the influence of a time-periodic space-homogeneous external field E(t)=E(t+T). If E(t) is neither symmetric function of t nor antisymmetric under time shifts $E(t \pm T/2) \neq -E(t)$, an ensemble of trajectories with zero current at t=0 yields a nonzero finite current as $t\to \infty$. We explain this effect using symmetry considerations and perturbation theory. Finally we add dissipation (friction) and demonstrate that the resulting set of attractors keeps the broken symmetry property in the basins of attraction and leads to directed currents as well.Comment: 2 figure

Simple nonlinear models suggest variable star universality

Dramatically improved data from observatories like the CoRoT and Kepler spacecraft have recently facilitated nonlinear time series analysis and phenomenological modeling of variable stars, including the search for strange (aka fractal) or chaotic dynamics. We recently argued [Lindner et al., Phys. Rev. Lett. 114 (2015) 054101] that the Kepler data includes "golden" stars, whose luminosities vary quasiperiodically with two frequencies nearly in the golden ratio, and whose secondary frequencies exhibit power-law scaling with exponent near -1.5, suggesting strange nonchaotic dynamics and singular spectra. Here we use a series of phenomenological models to make plausible the connection between golden stars and fractal spectra. We thereby suggest that at least some features of variable star dynamics reflect universal nonlinear phenomena common to even simple systems.Comment: 9 pages, 9 figures, accepted for publication in Physica