Multiple Components in Narrow Planetary Rings

Benet, Luis; Merlo, Olivier

doi:10.1103/physrevlett.100.014102

Cited by 4 publications

(5 citation statements)

References 27 publications

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“…This power law arises from combined effects of an infinite hierarchy of islands with a corresponding hierarchy of time scales. Recent investigations of resonance splittings and homoclinic tangles in the vicinity of islands may provide insight into these mechanisms [25][26][27][28].…”

Section: Introductionmentioning

confidence: 99%

Escape of particles in a time-dependent potential well

2011

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We investigate the escape of an ensemble of noninteracting particles inside an infinite potential box that contains a time-dependent potential well. The dynamics of each particle is described by a two-dimensional nonlinear area-preserving mapping for the variables energy and time, leading to a mixed phase space. The chaotic sea in the phase space surrounds periodic islands and is limited by a set of invariant spanning curves. When a hole is introduced in the energy axis, the histogram of frequency for the escape of particles, which we observe to be scaling invariant, grows rapidly until it reaches a maximum and then decreases toward zero at sufficiently long times. A plot of the survival probability of a particle in the dynamics as function of time is observed to be exponential for short times, reaching a crossover time and turning to a slower-decay regime, due to sticky regions observed in the phase space.

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Section: Introductionmentioning

confidence: 99%

Escape of particles in a time-dependent potential well

2011

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“…The stability resonances are defined by the occurrence of a resonant condition (a rational ratio of 2π) of the linear stability exponents of the central linearly stable periodic orbit. Therefore, they are related to the local stability properties of the central stable periodic orbit (Benet and Merlo 2008). Note that the stability resonances must not correspond to mean-motion resonances, which are defined as a rational ratio between the period of the central stable periodic orbit and the period of the disk.…”

Section: Two Degrees Of Freedom and Stability Resonancesmentioning

confidence: 99%

“…We observe that each ring component is related to a different region of the histogram. This is a consequence of the large gap opened by the 1:3 stability resonance, which effectively separates the phase space regions of trapped motion in two disjoint regions (Benet and Merlo 2008). Yet, while the 1:6 stability resonance widens up its corresponding gap, it does not separate enough the phase-space regions around it.…”

Section: Beyond Two Degrees Of Freedom: Strands and Arcsmentioning

confidence: 99%

“…This question was first formulated and answered for bounded Hamiltonian systems of two degrees of freedom in terms of the regions in phase space that exhibit ordered motion (Contopoulos et al 2005;Dvorak and Freistetter 2005). For two degrees of freedom Hamiltonian systems, the volume in phase space of the regions of trapped or ordered motion displays universal behavior in terms of a parameter that controls the dynamics (Contopoulos et al 2005;Dvorak and Freistetter 2005), revealing abrupt changes at specific locations which can be well approximated (Benet and Merlo 2008) and exhibiting self-similar behavior (Simó and Vieiro in preparation). Universality means that the same behavior and predictions are obtained for a wide class of systems.…”

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confidence: 99%

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Phase-space volume of regions of trapped motion: multiple ring components and arcs

Benet

Merlo

2009

Celest Mech Dyn Astr

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The phase-space volume of regions of regular or trapped motion, for bounded or scattering systems with two degrees of freedom respectively, displays universal properties. In particular, sudden reductions in the phase-space volume or gaps are observed at specific values of the parameter which tunes the dynamics; these locations are approximated by the stability resonances. The latter are defined by a resonant condition on the stability exponents of a central linearly stable periodic orbit. We show that, for more than two degrees of freedom, these resonances can be excited opening up gaps, which effectively separate and reduce the regions of trapped motion in phase space. Using the scattering approach to narrow rings and a billiard system as example, we demonstrate that this mechanism yields rings with two or more components. Arcs are also obtained, specifically when an additional (mean-motion) resonance condition is met. We obtain a complete representation of the phase-space volume occupied by the regions of trapped motion.

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“…Most of the work done within the framework of chaotic scattering (or scattering in higher dimensions) deals with a static scattering potential. Recently, it has been found that complex behavior with different characteristics can be observed in scattering systems involving a time-dependent scattering potential [23,24,25,26,27,28,29]. As a representative example of such a system the scattering of freely moving, non-interacting particles off two hard, infinitely heavy, oscillating discs on the plane has been studied.…”

Section: Introductionmentioning

confidence: 99%

Scattering off an oscillating target: Basic mechanisms and their impact on cross sections

et al. 2008

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We investigate classical scattering off a harmonically oscillating target in two spatial dimensions. The shape of the scatterer is assumed to have a boundary which is locally convex at any point and does not support the presence of any periodic orbits in the corresponding dynamics. As a simple example we consider the scattering of a beam of non-interacting particles off a circular hard scatterer. The performed analysis is focused on experimentally accessible quantities, characterizing the system, like the differential cross sections in the outgoing angle and velocity. Despite the absence of periodic orbits and their manifolds in the dynamics, we show that the cross sections acquire rich and multiple structure when the velocity of the particles in the beam becomes of the same order of magnitude as the maximum velocity of the oscillating target. The underlying dynamical pattern is uniquely determined by the phase of the first collision between the beam particles and the scatterer and possesses a universal profile, dictated by the manifolds of the parabolic orbits, which can be understood both qualitatively as well as quantitatively in terms of scattering off a hard wall. We discuss also the inverse problem concerning the possibility to extract properties of the oscillating target from the differential cross sections.

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Multiple Components in Narrow Planetary Rings

Cited by 4 publications

References 27 publications

Escape of particles in a time-dependent potential well

Escape of particles in a time-dependent potential well

Phase-space volume of regions of trapped motion: multiple ring components and arcs

Scattering off an oscillating target: Basic mechanisms and their impact on cross sections

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