Related papers: Rotating Accelerator-Mode Islands
An ever-growing observational aggregate of extrasolar planets has revealed that systems of planets that reside in or near mean-motion resonances are relatively common. While the origin of such systems is attributed to protoplanetary…
A resonant chain may be formed in a multi-planetary system when ratios of the orbital periods can be expressed as ratios of small integers $T_1:T_2: \cdots :T_N=k_1: k_2: \cdots: k_N$. We investigate the dynamics and possible formation of…
An approximate analytical approach to describe the stochastic motion of sound rays in deep ocean is developed. This is done for a realistic propagation model with an internal wave induced perturbation imposed on the smooth background sound…
We derive a formula predicting dynamical tunneling rates from regular states to the chaotic sea in systems with a mixed phase space. Our approach is based on the introduction of a fictitious integrable system that resembles the regular…
The electromigration-induced shape evolution of two-dimensional vacancy islands on a crystal surface is studied using a continuum approach. We consider the regime where mass transport is restricted to terrace diffusion in the interior of…
We show that the pattern of tunnelling rates can display a vivid and regular pattern when the classical dynamics is of mixed chaotic/regular type. We consider the situation in which the dominant tunnelling route connects to a stable…
Despite more and more observational data, stellar acoustic oscillation modes are not well understood as soon as rotation cannot be treated perturbatively. In a way similar to semiclassical theory in quantum physics, we use acoustic ray…
It is well known that typical Hamiltonian systems have divided phase space consisting of regions with regular dynamics on KAM tori and region(s) with chaotic dynamics called chaotic sea(s). This complex structure makes rigorous analysis of…
We study random walks on a $d$-dimensional torus by affine expanding maps whose linear parts commute. Assuming an irrationality condition on their translation parts, we prove that the Haar measure is the unique stationary measure. We deduce…
Beam instabilities and resonances affect the transverse dynamics in particle accelerators and, when encountered, can trigger emittance growth and beam loss. Resonance lines originate from non linear elements and effects in the lattice,…
The existence of quasinormal modes (QNMs) for waves propagating on pure de Sitter space has been called into question in several works. We definitively prove the existence of quasinormal modes for massless and massive scalar fields in all…
The planetary dynamics of $4/3$, $3/2$, $5/2$, $3/1$ and $4/1$ mean motion resonances is studied by using the model of the general three body problem in a rotating frame and by determining families of periodic orbits for each resonance.…
We present evidence that tunneling processes in near-integrable systems are enhanced due to the manifestation of nonlinear resonances and their respective island chains in phase space. A semiclassical description of this…
The asteroseismology of rapidly rotating pulsating stars is hindered by our poor knowledge of the effect of the rotation on the oscillation properties. Here we present an asymptotic analysis of high-frequency acoustic modes in rapidly…
In two previous papers the author described ``Islands of Instability" that may appear in wavefunction models with nonlinear evolution (of a type proposed originally in the context of the Measurement Problem). Such ``IsoI" represent a new…
Large transporting regular islands are found in the classical phase space of a modified kicked rotor system in which the kicking potential is reversed after every two kicks. The corresponding quantum system, for a variety of system…
We theoretically investigate how one can achieve a preferred rotational direction for the case of a simple electrostatic motor. The motor is composed by a rotor and two electronic reservoirs. Electronic islands on the rotor can exchange…
The Global Magnetorotational Instability (MRI) is investigated for a configuration in which the rotation frequency changes only in a narrow transition region. If the vertical wavelength of the unstable mode is of the same order or smaller…
This article concerns a class of beam equations with damping on rectangular tori. When the generators satisfy certain relationship, by excluding some value of two model parameters, we prove that such models admit small amplitude…
Microwave transport experiments have been performed in a quasi-two-dimensional resonator with randomly distributed scatterers, each mimicking an $r^{-2}$ repulsive potential. Analysis of both stationary wave fields and transient transport…