Related papers: Rotating Accelerator-Mode Islands
The traditional approach to analyzing mean motion resonances is through canonical perturbation theory. While this is a powerful method, its generality leads to complicated combinations of variables that are challenging to interpret and…
Given the multi-frequency nature of relativistic orbits, transient orbital resonances are expected to be ubiquitous during an extreme-mass-ratio inspiral (EMRI). At a resonance, the orbital dynamics is modified in a nontrivial way,…
Eccentric disks arise in such astrophysical contexts as tidal disruption events, but it is unknown whether the magnetorotational instability (MRI), which powers accretion in circular disks, operates in eccentric disks as well. We examine…
The destruction of regular regions in two-dimensional, area-preserving maps is traditionally described in terms of the breakup of invariant curves and the persistence of transport barriers. Here, we investigate how this scenario changes…
All of the known circumbinary planets are large (> 3 Earth radii). Whilst observational biases may account for this dearth of small planets, in this paper we propose a theoretical explanation. Most of the known planets are near the…
Extreme mass-ratio inspirals (EMRI) are one of the most sensitive probes of black hole spacetimes with gravitational wave measurements. In this work, we systematically analyze the dynamics of an EMRI system near orbital resonances, assuming…
Extreme mass ratio inspirals (EMRIs), where a compact object orbits a massive black hole, are a key source of gravitational waves for the future Laser Interferometer Space Antenna (LISA). Due to their small mass ratio, ($\epsilon \sim…
The restricted three-body problem describes the motion of a massless particle under the influence of two primaries of masses $1-\mu$ and $\mu$ that circle each other with period equal to $2\pi$. For small $\mu$, a resonant periodic motion…
The spectacular variability of microquasars has led to a long string of efforts in order to classify their observed behaviors in a few states. The progress made in the understanding of the Quasi-Periodic Oscillations observed in these…
We experimentally demonstrate a method for selecting small regions of phase space for kicked rotor quantum chaos experiments with cold atoms. Our technique uses quantum accelerator modes to selectively accelerate atomic wavepackets with…
This paper describes a reduced-order quasi-geostrophic coupled ocean-atmosphere model that allows for an arbitrary number of atmospheric and oceanic modes to be retained in the spectral decomposition. The modularity of this new model allows…
Rotation averaging (RA) is a fundamental problem in robotics and computer vision. In RA, the goal is to estimate a set of $N$ unknown orientations $R_{1}, ..., R_{N} \in SO(3)$, given noisy measurements $R_{ij} \sim R^{-1}_{i} R_{j}$ of a…
Resonant States (RS), also known as Quasi-Normal Modes (QNMs), are eigenstates that arise in spectral expansions of linear response functions of open systems. Manipulation of these spatially `divergent' oscillating functions requires a…
According to general relativity, an isolated black hole in vacuum shall be described by the Kerr metric, whose geodesic equations are integrable. The violation of integrability leads to chaos for particles moving around the black hole. This…
We consider sound wave propagation in a range-periodic acoustic waveguide in the deep ocean. It is demonstrated that vertical oscillations of a sound-speed perturbation, induced by ocean internal waves, influence near-axial rays in a…
In this study, we investigate the dynamics of the quantum kicked rotor in the near-resonant regime and observe distinct caustic structures, such as recurring cusps, cusp oscillations, and reticular cusp patterns in high-order resonant…
Special quantum states exist which are quasiclassical quantizations of regions of phase space that are weakly chaotic. In a weakly chaotic region, the orbits are quite regular and remain in the region for some time before escaping and…
Differentially rotating disks under the effect of axial magnetic field are prone to a nonlinear explosive magnetorotational instability (EMRI). The dynamic equations that govern the temporal evolution of the amplitudes of three…
The multiple-planet systems discovered by the Kepler mission exhibit the following feature: planet pairs near first-order mean-motion resonances prefer orbits just outside the nominal resonance, while avoiding those just inside the…
Recent observations of Kepler multi-planet systems have revealed a number of systems with planets very close to second-order mean motion resonances (MMRs, with period ratio $1:3$, $3:5$, etc.) We present an analytic study of resonance…