Related papers: Billiards and toy gravitons
Recently were introduced physical billiards where a moving particle is a hard sphere rather than a point as in standard mathematical billiards. It has been shown that in the same billiard tables the physical billiards may have totally…
Systems of pinned billiard balls serve as simplified models of collisions, where all particles remain fixed in their positions while their (pseudo-)velocities evolve in accordance with the laws of conservation of energy and momentum. For…
Mathematical billiards is much like the real game: a point mass, representing the ball, rolls in a straight line on a (perfectly friction-less) table, striking the sides according to the law of reflection. A billiard trajectory is then…
This paper explores two instances where dissipation plays a crucial role in curbing the unbounded energy growth of particles in time-dependent billiards. The first example involves an elliptical-like billiard with inelastic collisions…
We consider the motion of a particle subjected to the constant gravitational field and scattered inelasticaly by hard boundaries which possess the shape of parabola, wedge, and hyperbola. The billiard itself performs oscillations. The…
Dynamical focusing of ensembles of neutral particles in energy and configuration space has been demonstrated recently [C. Petri et al. 2010, Phys. Rev. E (R) {\bf 82}, 035204] using time-dependent elliptical billiards. The interplay of…
This paper deals with the so-called Boltzmann billiard, that is, a billiard subjected to a central force of the type $V(r)=-\alpha/r-\beta/r^2$, $\alpha$ and $\beta$ being positive constants, and with a straight reflection table. In the…
The billiard problem concerns a point particle moving freely in a region of the horizontal plane bounded by a closed curve $\Gamma$, and reflected at each impact with $\Gamma$. The region is called a `billiard', and the reflections are…
A right triangular billiard system is equivalent to the system of two colliding particles confined in a one-dimensional box. In spite of their seeming simplicity, no definite conclusion has been drawn so far concerning their ergodic…
We investigate the dynamics of no-slip billiards, a model in which small rotating disks may exchange linear and angular momentum at collisions with the boundary. We give new results on periodicity and boundedness of orbits which suggest…
One-dimensional billiard, i.e. a chain of colliding particles with equal masses, is well-known example of completely integrable system. Billiards with different particles are generically not integrable, but still exhibit divergence of a…
A system of two masses connected with a weightless rod (called dumbbell in this paper) interacting with a flat boundary is considered. The sharp bound on the number of collisions with the boundary is found using billiard techniques. In…
We propose geometric tools that are suitable for studying the behavior of a billiard trajectory in a homogeneous force field. Two examples are considered: a vertical plane with an open top and with a parabolic or right angle boundary at the…
We consider systems of "pinned balls," i.e., balls that have fixed positions and pseudo-velocities. Pseudo-velocities change according to the same rules as those for velocities of totally elastic collisions between moving balls. The times…
We consider the free motion of a point particle inside a circular billiard with periodically moving boundary, with the assumption that the collisions of the particle with the boundary are elastic so that the energy of the particle is not…
We investigate a circular cavity billiard within which a pair of identical hard disks of smaller but finite size is confined. Each disk shows a free motion except when bouncing elastically with its partner and with the boundary wall.…
We obtain an upper bound of the number of collisions of any billiard trajectory in a polyhedral angle in terms of the minimal eigenvalue of a positive definite matrix which characterizes the angle. Elements of the matrix are scalar products…
We study finite two dimensional spin lattices with definite geometry (spin billiards) demonstrating the display of collective integrable or chaotic dynamics depending on their shape. We show that such systems can be quantum simulated by…
Billiards tables - a minimal model for particles moving in a confined region - are known to present classical (and quantum) different features according to their shape, ranging from strongly chaotic to integrable dynamics. Here we consider…
We present a computational scheme based on classical molecular dynamics to study chaotic billiards in static external magnetic fields. The method allows to treat arbitrary geometries and several interacting particles. We test the scheme for…