Related papers: Narrow rings: a scattering billiard model
Dynamics of regular clusters of many non-touching particles falling under gravity in a viscous fluid at low Reynolds number are analysed within the point-particle model. Evolution of two families of particle configurations is determined: 2…
We propose a model of Sinai billiards with moving scatterers, in which the locations and shapes of the scatterers may change by small amounts between collisions. Our main result is the exponential loss of memory of initial data at uniform…
Observational constraints on planet spin-axis has recently become possible, and revealed a system that favors a large spin-axis misalignment, a low stellar spin-orbit misalignment and a high eccentricity. To explain the origin of such…
We investigate the orbital dynamics of a \textit{barred-spiral} model when the system is rotating slowly and corotation is located beyond the end of the spiral arms. In the characteristic of the central family of periodic orbits we find a…
In an ordinary billiard system trajectories of a Hamiltonian system are elastically reflected after a collision with a hypersurface (scatterer). If the scatterer is a submanifold of codimension more than one, we say that the billiard is…
We present an efficient method to solve scattering problems in two-dimensional open billiards with two leads and a complicated scattering region. The basic idea is to transform the scattering region to a rectangle, which will lead to…
This chapter of the book Planetary Ring Systems addresses the origin of planetary rings, one of the least understood processes related to planet formation and evolution. Whereas rings seem ubiquitous around giant planets, their great…
A viable solution to the origin of close binary systems, unaccounted for in recent theories, is presented. Fragmentation, occurring at the end of the secondary collapse phase (during which molecular hydrogen is dissociating), can form…
We suggest that clumpy-dense outflowing equatorial rings around evolved giant stars, such as in supernova 1987A and the Necklace planetary nebula, are formed by bipolar jets that compress gas toward the equatorial plane. The jets are…
A ring system consisting of two dense narrow rings has been discovered around Centaur Chariklo. The existence of these rings around a small object poses various questions, such as their origin, stability, and lifetime. In order to…
We describe conditions under which higher-dimensional billiard models in bounded, convex regions are fully chaotic, generalizing the Bunimovich stadium to dimensions above two. An example is a three-dimensional stadium bounded by a cylinder…
We investigate the classical scattering dynamics of the driven elliptical billiard. Two fundamental scattering mechanisms are identified and employed to understand the rich behavior of the escape rate. A long-time algebraic decay which can…
Hidden attractors are present in many nonlinear dynamical systems and are not associated with equilibria, making them difficult to locate. Recent studies have demonstrated methods of locating hidden attractors, but the route to these…
We introduce the spherical wedge billiard, a dynamical system consisting of a particle moving along a geodesic on a closed non-Euclidean surface of a spherical wedge. We derive the analytic form of the corresponding Poincar\'e map and find…
We study the classical and quantum mechanics of a three-dimensional stadium billiard. It consists of two quarter cylinders that are rotated with respect to each other by 90 degrees, and it is classically chaotic. The billiard exhibits only…
N-body simulations of galactic collisions are employed to investigate the formation of elliptical rings in disk galaxies. The relative inclination between disk and dwarf galaxies is studied with a fine step of five degrees. It is confirmed…
Semiclassical approximations often involve the use of stationary phase approximations. This method can be applied when $\hbar$ is small in comparison to relevant actions or action differences in the corresponding classical system. In many…
We propose a new theory to explain the formation of spiral arms and of all types of outer rings in barred galaxies. We have extended and applied the technique used in celestial mechanics to compute transfer orbits. Thus, our theory is based…
We develop a dynamical theory for the origin of nuclear rings in barred galaxies. In analogy with the standard theory of accretion discs, our theory is based on shear viscous forces among nested annuli of gas. However, the fact that gas…
Recent observations have confirmed the existence of rings around minor bodies in the outer Solar System. These objects may possess satellites as well. Here we analytically investigate the interaction between such rings and satellites. We…