81 research outputs found
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
Numerical simulations of aggregate breakup in bounded and unbounded turbulent flows
Breakup of small aggregates in fully developed turbulence is studied by means of direct numerical simulations in a series of typical bounded and unbounded flow configurations, such as a turbulent channel flow, a developing boundary layer, and homogeneous isotropic turbulence. Aggregate breakup occurs when the local hydrodynamic stress , where is the energy dissipation at the position of the aggregate, overcomes a given threshold , characteristic for a given type of aggregates. Results show that the breakup rate decreases with increasing threshold. For small thresholds, it develops a universal scaling among the different flows. For high thresholds, the breakup rates show strong differences among the different flow configurations, highlighting the importance of non-universal mean-flow properties. To further assess the effects of flow inhomogeneity and turbulent fluctuations, results are compared with those obtained in a smooth stochastic flow. Furthermore, we discuss limitations and applicability of a set of independent proxies
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 , an ensemble of trajectories with zero current at t=0 yields a nonzero
finite current as . 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
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