Computational Study of the Dynamics of an Asymmetric Wedge Billiard

We introduce the asymmetric wedge billiard as a generalization of the wedge billiard first studied by Lehtihet and Miller in 1986. This is a billiard system in which the billiard ball moves under the influence of a constant gravitational field, colliding elastically with two wedge walls with the collisions obeying the reflection law. Collision maps are given from which derivatives and area-preservation (or lack thereof) were determined. Expressions for the fixed points of the collision maps were also calculated and discussed. Long-term dynamics were determined computationally from which we observed integrable, quasi-periodic and chaotic behavior which were all dependent on the wedge angles.

Counting Collisions in an N-Billiard System Using Angles Between Collision Subspaces

The principal angles between binary collision subspaces in an N-billiard system in d-dimensional Euclidean space are computed. These angles are computed for equal masses and arbitrary masses. We then provide a bound on the number of collisions in the planar 3-billiard system problem. Comparison of this result with known billiard collision bounds in lower dimensions is discussed.

Angular and spatial color mixing using mixing rods with the geometry of a chaotic-dispersive billiard system

For mixing light from different colored LEDs, an optical color mixing system is required to avoid colored shadows and color fringes. Concerning the different color mixing systems, mixing rods are widespread as they provide very good spatial color mixing with high efficiency. The essential disadvantage of mixing rods, so far, is the lack of angular color mixing. The solution presented in this publication is the application of a chaotic-dispersive billiard’s geometry on the cross section of the mixing rod. To show both the spatial and the angular mixing properties of a square and a chaotic-dispersive mixing rod, simulations generated by the raytracing software ASAP are provided. All results are validated with prototype measurements.