3,554 research outputs found
Nontwist non-Hamiltonian systems
We show that the nontwist phenomena previously observed in Hamiltonian
systems exist also in time-reversible non-Hamiltonian systems. In particular,
we study the two standard collision/reconnection scenarios and we compute the
parameter space breakup diagram of the shearless torus. Besides the Hamiltonian
routes, the breakup may occur due to the onset of attractors. We study these
phenomena in coupled phase oscillators and in non-area-preserving maps.Comment: 7 pages, 5 figure
Stickiness in mushroom billiards
We investigate dynamical properties of chaotic trajectories in mushroom
billiards. These billiards present a well-defined simple border between a
single regular region and a single chaotic component. We find that the
stickiness of chaotic trajectories near the border of the regular region occurs
through an infinite number of marginally unstable periodic orbits. These orbits
have zero measure, thus not affecting the ergodicity of the chaotic region.
Notwithstanding, they govern the main dynamical properties of the system. In
particular, we show that the marginally unstable periodic orbits explain the
periodicity and the power-law behavior with exponent observed in the
distribution of recurrence times.Comment: 7 pages, 6 figures (corrected version with a new figure
Chaotic Explosions
We investigate chaotic dynamical systems for which the intensity of
trajectories might grow unlimited in time. We show that (i) the intensity grows
exponentially in time and is distributed spatially according to a fractal
measure with an information dimension smaller than that of the phase space,(ii)
such exploding cases can be described by an operator formalism similar to the
one applied to chaotic systems with absorption (decaying intensities), but
(iii) the invariant quantities characterizing explosion and absorption are
typically not directly related to each other, e.g., the decay rate and fractal
dimensions of absorbing maps typically differ from the ones computed in the
corresponding inverse (exploding) maps. We illustrate our general results
through numerical simulation in the cardioid billiard mimicking a lasing
optical cavity, and through analytical calculations in the baker map.Comment: 7 pages, 5 figure
Characterizing Weak Chaos using Time Series of Lyapunov Exponents
We investigate chaos in mixed-phase-space Hamiltonian systems using time
series of the finite- time Lyapunov exponents. The methodology we propose uses
the number of Lyapunov exponents close to zero to define regimes of ordered
(stickiness), semi-ordered (or semi-chaotic), and strongly chaotic motion. The
dynamics is then investigated looking at the consecutive time spent in each
regime, the transition between different regimes, and the regions in the
phase-space associated to them. Applying our methodology to a chain of coupled
standard maps we obtain: (i) that it allows for an improved numerical
characterization of stickiness in high-dimensional Hamiltonian systems, when
compared to the previous analyses based on the distribution of recurrence
times; (ii) that the transition probabilities between different regimes are
determined by the phase-space volume associated to the corresponding regions;
(iii) the dependence of the Lyapunov exponents with the coupling strength.Comment: 8 pages, 6 figure
Noise-enhanced trapping in chaotic scattering
We show that noise enhances the trapping of trajectories in scattering
systems. In fully chaotic systems, the decay rate can decrease with increasing
noise due to a generic mismatch between the noiseless escape rate and the value
predicted by the Liouville measure of the exit set. In Hamiltonian systems with
mixed phase space we show that noise leads to a slower algebraic decay due to
trajectories performing a random walk inside Kolmogorov-Arnold-Moser islands.
We argue that these noise-enhanced trapping mechanisms exist in most scattering
systems and are likely to be dominant for small noise intensities, which is
confirmed through a detailed investigation in the Henon map. Our results can be
tested in fluid experiments, affect the fractal Weyl's law of quantum systems,
and modify the estimations of chemical reaction rates based on phase-space
transition state theory.Comment: 5 pages, 5 figure
Emission from dielectric cavities in terms of invariant sets of the chaotic ray dynamics
In this paper, the chaotic ray dynamics inside dielectric cavities is
described by the properties of an invariant chaotic saddle. I show that the
localization of the far field emission in specific directions is related to the
filamentary pattern of the saddle's unstable manifold, along which the energy
inside the cavity is distributed. For cavities with mixed phase space, the
chaotic saddle is divided in hyperbolic and non-hyperbolic components, related,
respectively, to the intermediate exponential (t<t_c) and the asymptotic
power-law (t>t_c) decay of the energy inside the cavity. The alignment of the
manifolds of the two components of the saddle explains why even if the energy
concentration inside the cavity dramatically changes from tt_c, the
far field emission changes only slightly. Simulations in the annular billiard
confirm and illustrate the predictions.Comment: Corrected version, as published. 9 pages, 6 figure
Non-Hamiltonian dynamics in optical microcavities resulting from wave-inspired corrections to geometric optics
We introduce and investigate billiard systems with an adjusted ray dynamics
that accounts for modifications of the conventional reflection of rays due to
universal wave effects. We show that even small modifications of the specular
reflection law have dramatic consequences on the phase space of classical
billiards. These include the creation of regions of non-Hamiltonian dynamics,
the breakdown of symmetries, and changes in the stability and morphology of
periodic orbits. Focusing on optical microcavities, we show that our adjusted
dynamics provides the missing ray counterpart to previously observed wave
phenomena and we describe how to observe its signatures in experiments. Our
findings also apply to acoustic and ultrasound waves and are important in all
situations where wavelengths are comparable to system sizes, an increasingly
likely situation considering the systematic reduction of the size of electronic
and photonic devices.Comment: 6 pages, 4 figures, final published versio
Associations between congenital malformations and childhood cancer. A register-based case-control study.
This report describes a population-based case-control study that aimed to assess and quantify the risk of children with congenital malformations developing cancer. Three sources of data were used: the Victorian Cancer Register, the Victorian Perinatal Data Register (VPDR) and the Victorian Congenital Malformations/Birth Defects Register. Cases included all Victorian children born between 1984 and 1993 who developed cancer. Four controls per case, matched on birth date, were randomly selected from the VPDR. Record linkage between registers provided malformation data. A matched case-control analysis was undertaken. Of the 632 cancer cases, 570 (90.2%) were linked to the VPDR. The congenital malformation prevalence in children with cancer was 9.6% compared with 2.5% in the controls [odds ratio (OR) 4.5, 95% CI 3.1-6.7]. A strong association was found with chromosomal defects (OR=16.7, 95% CI 6.1-45.3), in particular Down's syndrome (OR=27.1, 95% CI 6.0-122). Most other birth defect groups were also associated with increased cancer risk. The increased risk of leukaemia in children with Down's syndrome was confirmed, and children with central nervous system (CNS) defects were found to be at increased risk of CNS tumours. The report confirms that children with congenital malformations have increased risks of various malignancies. These findings may provide clues to the underlying aetiology of childhood cancer, as congenital malformations are felt to be a marker of exposures or processes which may increase cancer risk. The usefulness of record linkage between accurate population-based registers in the epidemiological study of disease has also been reinforced
Stickiness in Hamiltonian systems: from sharply divided to hierarchical phase space
We investigate the dynamics of chaotic trajectories in simple yet physically
important Hamiltonian systems with non-hierarchical borders between regular and
chaotic regions with positive measures. We show that the stickiness to the
border of the regular regions in systems with such a sharply divided phase
space occurs through one-parameter families of marginally unstable periodic
orbits and is characterized by an exponent \gamma= 2 for the asymptotic
power-law decay of the distribution of recurrence times. Generic perturbations
lead to systems with hierarchical phase space, where the stickiness is
apparently enhanced due to the presence of infinitely many regular islands and
Cantori. In this case, we show that the distribution of recurrence times can be
composed of a sum of exponentials or a sum of power-laws, depending on the
relative contribution of the primary and secondary structures of the hierarchy.
Numerical verification of our main results are provided for area-preserving
maps, mushroom billiards, and the newly defined magnetic mushroom billiards.Comment: To appear in Phys. Rev. E. A PDF version with higher resolution
figures is available at http://www.pks.mpg.de/~edugal
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