The billiard motion inside an ellipsoid Q ⊂ R is completely integrable. Its phase space is a symplectic manifold of dimension 2n, which is mostly foliated with Liouville tori of dimension n. The motion on each Liouville torus becomes just a parallel translation with some frequency ω that varies with the torus. Besides, any billiard trajectory inside Q is tangent to n caustics Qλ1 , . . . , Qλn ...

Caustics form in Lagrangian fluids when fluid elements cross and multi-stream regions form. For low-dimensional Lagrangian fluids, the caustics have been classified by catastrophe theory. In the case of potential flow, for oneand two-dimensional fluids, Arnol’d et al. (1982) related this classification to conditions on the displacement field of the fluid. These conditions are called the caustic...

I investigate the caustics produced by the fall of collisionless dark matter in and out of a galaxy in the limit of negligible velocity dispersion. The outer caustics are spherical shells enveloping the galaxy. The inner caustics are rings. These are located near where the particles with the most angular momentum are at their distance of closest approach to the galactic center. The surface of a...

We experimentally demonstrate first-order (fold) and second-order (cusp) catastrophes in the density of an atomic cloud reflected from an optical barrier in the presence of gravity and show their corresponding universal asymptotic behavior. These catastrophes, arising from classical dynamics, enable robust, field-free refocusing of an expanding atomic cloud with a wide velocity distribution. Sp...

The offset microlensing degeneracy, recently proposed by Zhang et al. (2022), has been shown to generalize the close-wide and inner-outer caustic degeneracies into a unified regime of magnification degeneracy in interpretation 2-body planetary observations. While expects source trajectory pass equidistant caustics degenerate lens configurations, states that same mathematical expression applies ...

introduction: endoscopy is an invasive procedure and finding noninvasive alternative tools in detection of probable upper gastrointestinal (gi) tract injuries following caustic ingestion is an area of interest. the present study aimed to evaluate the screening performance characteristics of thoraco-abdominal computed tomography (ct) scan in this regard. methods: this prospective cross sectional...

The G-function associated to the semisimple Frobenius manifold C/W (where W is a Coxeter group or an extended affine Weyl group) is studied. The general form of the Gfunction is given in terms of a logarithmic singularity over caustics in the manifold. The main result in this paper is a universal formula for the G-function corresponding to the Frobenius manifold C/W̃ (An−1) , where W̃ (An−1) is a...

Volume caustics are beautiful patterns of light which are formed by light that first interacts with a specular surface and that is then scattered inside a participating medium. Although this phenomenon can be simulated, its generation process is usually non-trivial and time-consuming. Motivated by interactive applications, we propose a novel volume caustics rendering method for single-scatterin...

The general validity of the area law for black holes is still an open problem. We first show in detail how to complete the usually incompletely stated text-book proofs under the assumption of piecewise C-smoothness for the surface of the black hole. Then we prove that a black hole surface necessarily contains points where it is not C (called “cusps”) at any time before caustics of the horizon g...

Galactic Exoplanet Survey Telescope (GEST) was proposed for a discovery mission to search for microlensing terrestrial planets toward the Galactic bulge and also Kuiper Belt Objects (KBOs) that are believed to hold vital information of the early history of the solar system. Microlensing planet search method is hinged on photometric singular behavior of lensing (refraction) that is due to discon...